cg
changeset 84:d89a99c9ea9a
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author | bshanks@bshanks.dyndns.org |
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date | Tue Apr 21 00:54:22 2009 -0700 (16 years ago) |
parents | 8808b945e2f7 |
children | da8f81785211 |
files | grant.html grant.odt grant.pdf grant.txt |
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1.3 @@ -6,22 +6,28 @@
1.4 three specific aims:
1.5 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target
1.6 anatomical regions
1.7 -(2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns
1.8 -in gene expression
1.9 +(2) develop an algorithm to suggest new ways of carving up a structure into anatomically distinct regions, based on
1.10 +spatial patterns in gene expression
1.11 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse
1.12 Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of
1.13 Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).
1.14 -In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce
1.15 -immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project
1.16 -will support the development of new ways to selectively target cortical areas, and it will support the development of a
1.17 -method for identifying the cortical areal boundaries present in small tissue samples.
1.18 +Although our particular application involves the 3D spatial distribution of gene expression, we anticipate that the methods
1.19 +developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located in a low-dimensional
1.20 +space.
1.21 +In terms of the application of the methods to cerebral cortex, aim (1) is to go from cortical areas to marker genes,
1.22 +and aim (2) is to let the gene profile define the cortical areas. In addition to validating the usefulness of the algorithms,
1.23 +the application of these methods to cortex will produce immediate benefits, because there are currently no known genetic
1.24 +markers for most cortical areas. The results of the project will support the development of new ways to selectively target
1.25 +cortical areas, and it will support the development of a method for identifying the cortical areal boundaries present in small
1.26 +tissue samples.
1.27 All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well as the
1.28 machine-readable datasets developed in aim (3), will be published and freely available for others to use.
1.29 Background and significance
1.30 -Aim 1
1.31 -Machine learning terminology: supervised learning
1.32 -The task of looking for marker genes for anatomical regions means that one is looking for a set of genes such that, if the
1.33 -expression level of those genes is known, then the locations of the regions can be inferred.
1.34 +Aim 1: Given a map of regions, find genes that mark the regions
1.35 +After defining terms, we will describe a set of principles which determine our strategy to completing this aim.
1.36 +Machine learning terminology: supervised learning The task of looking for marker genes for known anatomical
1.37 +regions means that one is looking for a set of genes such that, if the expression level of those genes is known, then the
1.38 +locations of the regions can be inferred.
1.39 If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we
1.40 are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to
1.41 which region each voxel within the structure belongs. We call this a classification task, because each voxel is being assigned
1.42 @@ -55,23 +61,24 @@
1.43 method.
1.44 Key questions when choosing a learning method are: What are the instances? What are the features? How are the
1.45 features chosen? Here are four principles that outline our answers to these questions.
1.46 -Principle 1: Combinatorial gene expression It is too much to hope that every anatomical region of interest will be
1.47 -identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene
1.48 -included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at
1.49 -combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary
1.50 -Results). Therefore, each instance should contain multiple features (genes).
1.51 -Principle 2: Only look at combinations of small numbers of genes When the classifier classifies a voxel, it is
1.52 -only allowed to look at the expression of the genes which have been selected as features. The more data that is available to
1.53 -a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a
1.54 -strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations
1.55 -in which it is not feasible to gather data about every gene. For example, if we want to use the expression of marker genes as
1.56 -a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the
1.57 -expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the
1.58 -level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on tissue samples in order
1.59 -to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as
1.60 -features.
1.61 -__________________________________
1.62 +Principle 1: Combinatorial gene expression
1.63 +It is too much to hope that every anatomical region of interest will be identified by a single gene. For example, in the
1.64 +cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset.
1.65 +However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for
1.66 +which multiple genes are necessary and sufficient is provided in Preliminary Studies, Figure 4). Therefore, each instance
1.67 +should contain multiple features (genes).
1.68 +Principle 2: Only look at combinations of small numbers of genes
1.69 +When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have been selected
1.70 +as features. The more data that are available to a classifier, the better that it can do. For example, perhaps there are weak
1.71 +correlations over many genes that add up to a strong signal. So, why not include every gene as a feature? The reason is that
1.72 +we wish to employ the classifier in situations in which it is not feasible to gather data about every gene. For example, if we
1.73 +want to use the expression of marker genes as a trigger for some regionally-targeted intervention, then our intervention must
1.74 +contain a molecular mechanism to check the expression level of each marker gene before it triggers. It is currently infeasible
1.75 +to design a molecular trigger that checks the level of more than a handful of genes. Similarly, if the goal is to develop a
1.76 +_________________________________________
1.77 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.
1.78 +procedure to do ISH on tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes.
1.79 +Therefore, we must select only a few genes as features.
1.80 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many
1.81 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task
1.82 combines feature selection with supervised learning.
1.83 @@ -79,7 +86,7 @@
1.84 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of
1.85 each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information
1.86 about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See
1.87 -Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods.
1.88 +Preliminary Studies, figure 3 for evidence of the complementary nature of pointwise and local scoring methods.
1.89 Principle 4: Work in 2-D whenever possible
1.90 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When
1.91 it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis
1.92 @@ -88,12 +95,12 @@
1.93 Therefore, when possible, the instances should represent pixels, not voxels.
1.94 Related work
1.95 There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data
1.96 -which is not fundamentally spatial2.
1.97 +which are not fundamentally spatial2.
1.98 As noted above, there has been much work on both supervised learning and there are many available algorithms for
1.99 each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the
1.100 way that this framework is set up has a large impact on performance. Creating a good framework can require creatively
1.101 reconceptualizing the problem domain, and is not merely a mechanical “fine-tuning” of numerical parameters. For example,
1.102 -we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Work) may
1.103 +we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Studies) may
1.104 be necessary in order to achieve the best results in this application.
1.105 We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods.
1.106 [8 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of
1.107 @@ -109,39 +116,40 @@
1.108 ∙Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2)
1.109 yields a list of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists
1.110 of overexpressed genes for selected structures)
1.111 -∙Correlation: The user selects a seed voxel and the shows the user how much correlation there is between the gene
1.112 -expression profile of the seed voxel and every other voxel.
1.113 +∙Correlation: The user selects a seed voxel and the system then shows the user how much correlation there is between
1.114 +the gene expression profile of the seed voxel and every other voxel.
1.115 ∙Clusters: will be described later
1.116 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we
1.117 will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also
1.118 search for underexpression. Third, Gene Finder uses a simple pointwise score4, whereas we will also use geometric scores
1.119 -such as gradient similarity. The Preliminary Data section contains evidence that each of our three choices is the right one.
1.120 +such as gradient similarity (described in Preliminary Studies). Figures 4, 2, and 3 in the Preliminary Studies section contains
1.121 +evidence that each of our three choices is the right one.
1.122 [4 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni
1.123 correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA,
1.124 +_________________________________________
1.125 + 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not
1.126 +just data which have only a few different locations or which is indexed by anatomical label.
1.127 + 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.
1.128 + 4“Expression energy ratio”, which captures overexpression.
1.129 this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for
1.130 underexpression, and does not look for combinations of genes.
1.131 -_________________________________________
1.132 - 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not
1.133 -just data which has only a few different locations or which is indexed by anatomical label.
1.134 - 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.
1.135 - 4“Expression energy ratio”, which captures overexpression.
1.136 [7 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary
1.137 algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their
1.138 match score is Jaccard similarity.
1.139 -In summary, there has been fruitful work on finding marker genes, however, only one of the previous projects explores
1.140 +In summary, there has been fruitful work on finding marker genes, but only one of the previous projects explores
1.141 combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or
1.142 scoring methods.
1.143 -Aim 2
1.144 +Aim 2: From gene expression data, discover a map of regions
1.145 Machine learning terminology: clustering
1.146 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as
1.147 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances
1.148 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called
1.149 clustering or cluster analysis.
1.150 -The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are
1.151 -once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from
1.152 -the same region have similar gene expression profiles, at least compared to the other regions. This means that clustering
1.153 -voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into clusters of voxels
1.154 -with similar gene expression.
1.155 +The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances
1.156 +are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels
1.157 +from the same anatomical region have similar gene expression profiles, at least compared to the other regions. This means
1.158 +that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into
1.159 +clusters of voxels with similar gene expression.
1.160 It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps
1.161 some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they
1.162 could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests
1.163 @@ -154,13 +162,13 @@
1.164 Spatially contiguous clusters; image segmentation
1.165 We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have
1.166 an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary
1.167 -Results, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these
1.168 +Studies, we show that one can get reasonable results without enforcing this constraint; however, we plan to compare these
1.169 results against other methods which guarantee contiguous clusters.
1.170 Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a
1.171 variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into
1.172 clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in
1.173 -our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which
1.174 -use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used
1.175 +our task, there are thousands of color channels (one for each gene), rather than just three. However, there are imaging
1.176 +tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are often used
1.177 to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting
1.178 sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene
1.179 expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of
1.180 @@ -176,16 +184,16 @@
1.181 feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene
1.182 expression levels.
1.183 Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the
1.184 -reduced data set is less than in the original data set, the running time of clustering algorithms may be much less. Second,
1.185 -it is thought that some clustering algorithms may give better results on reduced data.
1.186 +reduced dataset is less than in the original dataset, the running time of clustering algorithms may be much less. Second, it
1.187 +is thought that some clustering algorithms may give better results on reduced data.
1.188 Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example,
1.189 -one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that regions
1.190 -with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points
1.191 -in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of
1.192 -the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find
1.193 -arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction
1.194 -is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction
1.195 -before clustering.
1.196 +one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that
1.197 +regions with similar gene expression profiles should be nearby on the plot (that is, the property that distance between
1.198 +pairs of points in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no
1.199 +arrangement of the points on a 2-D plan will exactly satisfy this property; however, dimensionality reduction techniques allow
1.200 +one to find arrangements of points that approximately satisfy that property. Note that in this application, dimensionality
1.201 +reduction is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality
1.202 +reduction before clustering.
1.203 Clustering genes rather than voxels
1.204 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster
1.205 the features (genes). There are two ways that clusters of genes could be used.
1.206 @@ -195,8 +203,8 @@
1.207 pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically
1.208 interesting region will have multiple genes which each individually pick it out5. This suggests the following procedure:
1.209 cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters.
1.210 -In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some “superregions”
1.211 -formed by lumping together a few regions, are associated with gene clusters in this fashion.
1.212 +In Preliminary Studies, Figure 7, we show that a number of anatomically recognized cortical regions, as well as some
1.213 +“superregions” formed by lumping together a few regions, are associated with gene clusters in this fashion.
1.214 The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering
1.215 algorithms.
1.216 Related work
1.217 @@ -205,7 +213,8 @@
1.218 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive
1.219 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving
1.220 the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset6 and while the results are
1.221 -promising (see Preliminary Data), we think that it will be possible to find an even better method.
1.222 +promising, they also demonstrate that NNMF is not necessarily the best dimensionality reduction method for this application
1.223 +(see Preliminary Studies, Figure 6).
1.224 AGEA[10] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation
1.225 as the similarity metric. EMAGE[18] allows the user to select a dataset from among a large number of alternatives, or by
1.226 running a search query, and then to cluster the genes within that dataset. EMAGE clusters via hierarchial complete linkage
1.227 @@ -237,12 +246,12 @@
1.228 needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.
1.229 Aim 3
1.230 Background
1.231 -The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can
1.232 -be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the areas continue
1.233 -downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can
1.234 -picture an area of the cortex as a slice of many-layered cake.
1.235 +The cortex is divided into areas and layers. Because of the cortical columnar organization, the parcellation of the cortex
1.236 +into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the
1.237 +areas continue downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the
1.238 +surface. One can picture an area of the cortex as a slice of a six-layered cake7.
1.239 Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes,
1.240 -there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas,
1.241 +there are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample into cortical areas,
1.242 this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of
1.243 their approximate location upon the cortical surface.
1.244 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not
1.245 @@ -251,7 +260,7 @@
1.246 Franklin[11] on the other. While the maps are certainly very similar in their general arrangement, significant differences
1.247 remain in the details.
1.248 The Allen Mouse Brain Atlas dataset
1.249 -The Allen Mouse Brain Atlas (ABA) data was produced by doing in-situ hybridization on slices of male, 56-day-old
1.250 +The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male, 56-day-old
1.251 C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed
1.252 in order to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial
1.253 resolution is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different
1.254 @@ -261,15 +270,15 @@
1.255 voxels in the 3D coordinate system, of which 51,533 are in the brain[10].
1.256 Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[20]. The ABA contains
1.257 data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our
1.258 -dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, and
1.259 +dataset is derived from only the coronal subset of the ABA, because the sagittal data do not cover the entire cortex, and
1.260 also has greater registration error[10]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes
1.261 of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[10].
1.262 The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[6],
1.263 -GenePaint[19], its sister project GeneAtlas[3], BGEM[9], EMAGE[18], EurExpress7, EADHB8, MAMEP9, Xenbase10,
1.264 -ZFIN[13], Aniseed11, VisiGene12, GEISHA[2], Fruitfly.org[16], COMPARE13 GXD[12], GEO[1]14. With the exception of
1.265 +GenePaint[19], its sister project GeneAtlas[3], BGEM[9], EMAGE[18], EurExpress8, EADHB9, MAMEP10, Xenbase11,
1.266 +ZFIN[13], Aniseed12, VisiGene13, GEISHA[2], Fruitfly.org[16], COMPARE14 GXD[12], GEO[1]15. With the exception of
1.267 the ABA, GenePaint, and EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH
1.268 images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of
1.269 -data available for public download from the website15. Many of these resources focus on developmental gene expression.
1.270 +data available for public download from the website16. Many of these resources focus on developmental gene expression.
1.271 Significance
1.272 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the
1.273 combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for
1.274 @@ -283,17 +292,18 @@
1.275 a better map. The development of present-day cortical maps was driven by the application of histological stains. It is
1.276 conceivable that if a different set of stains had been available which identified a different set of features, then the today’s
1.277 cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of
1.278 +_________________________________________
1.279 + 7Outside of isocortex, the number of layers varies.
1.280 + 8http://www.eurexpress.org/ee/; EurExpress data are also entered into EMAGE
1.281 + 9http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html
1.282 + 10http://mamep.molgen.mpg.de/index.php
1.283 + 11http://xenbase.org/
1.284 + 12http://aniseed-ibdm.univ-mrs.fr/
1.285 + 13http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources
1.286 + 14http://compare.ibdml.univ-mrs.fr/
1.287 + 15GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.
1.288 + 16without prior offline registration
1.289 genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been
1.290 -_________________________________________
1.291 - 7http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE
1.292 - 8http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html
1.293 - 9http://mamep.molgen.mpg.de/index.php
1.294 - 10http://xenbase.org/
1.295 - 11http://aniseed-ibdm.univ-mrs.fr/
1.296 - 12http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources
1.297 - 13http://compare.ibdml.univ-mrs.fr/
1.298 - 14GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.
1.299 - 15without prior offline registration
1.300 captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking
1.301 at the patterns of gene expression.
1.302 While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to
1.303 @@ -303,7 +313,7 @@
1.304 between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either
1.305 of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of
1.306 the other components of AGEA can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes
1.307 -for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas16.
1.308 +for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas17.
1.309 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, (b) there has
1.310 been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally
1.311 finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo
1.312 @@ -311,14 +321,14 @@
1.313 Our project is guided by a concrete application with a well-specified criterion of success (how well we can find marker
1.314 genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods.
1.315 _________________________________________
1.316 - 16In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are
1.317 + 17In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are
1.318 often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel
1.319 correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not
1.320 -find most cortical areas (there are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have
1.321 -many layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot find marker genes for
1.322 -most cortical areas is that in Gene Finder, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found,
1.323 -and it creates that ROI by (pairwise voxel correlation) clustering around the seed.
1.324 -Preliminary work
1.325 +find cortical areas (there are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have many
1.326 +layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot the find marker genes for
1.327 +cortical areas is that in Gene Finder, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found, and it
1.328 +creates that ROI by (pairwise voxel correlation) clustering around the seed.
1.329 +Preliminary Studies
1.330
1.331
1.332 Figure 1: Top row: Genes Nfic and
1.333 @@ -333,10 +343,10 @@
1.334 red outline is the boundary of region SS. Pixels are
1.335 colored according to correlation, with red meaning
1.336 high correlation and blue meaning low. Format conversion between SEV, MATLAB, NIFTI
1.337 - We have created software to (politely) download all of the SEV files from
1.338 - the Allen Institute website. We have also created software to convert
1.339 - between the SEV, MATLAB, and NIFTI file formats, as well as some of
1.340 - Caret’s file formats.
1.341 + We have created software to (politely) download all of the SEV files18
1.342 + from the Allen Institute website. We have also created software to con-
1.343 + vert between the SEV, MATLAB, and NIFTI file formats, as well as
1.344 + some of Caret’s file formats.
1.345 Flatmap of cortex
1.346 We downloaded the ABA data and applied a mask to select only those
1.347 voxels which belong to cerebral cortex. We divided the cortex into hemi-
1.348 @@ -353,7 +363,7 @@
1.349 traces into Caret-format regional boundary data on the mesh surface.
1.350 We projected the regions onto the 2-d mesh, and then onto the grid, and
1.351 then we converted the region data into MATLAB format.
1.352 - At this point, the data is in the form of a number of 2-D matrices,
1.353 + At this point, the data are in the form of a number of 2-D matrices,
1.354 all in registration, with the matrix entries representing a grid of points
1.355 (pixels) over the cortical surface:
1.356 ∙ A 2-D matrix whose entries represent the regional label associated with
1.357 @@ -364,7 +374,8 @@
1.358 Figure 2: Gene Pitx2
1.359 is selectively underex-
1.360 pressed in area SS. We created a normalized version of the gene expression data by subtracting each gene’s mean
1.361 - expression level (over all surface pixels) and dividing each gene by its standard deviation.
1.362 + expression level (over all surface pixels) and dividing the expression level of each gene by its
1.363 + standard deviation.
1.364 The features and the target area are both functions on the surface pixels. They can be referred
1.365 to as scalar fields over the space of surface pixels; alternately, they can be thought of as images
1.366 which can be displayed on the flatmapped surface.
1.367 @@ -375,15 +386,17 @@
1.368 of the ROI for volume-to-surface projection to vary.
1.369 In the Research Plan, we describe how we will automatically locate the layer depths. For
1.370 validation, we have manually demarcated the depth of the outer boundary of cortical layer 5
1.371 - throughout the cortex.
1.372 +throughout the cortex.
1.373 Feature selection and scoring methods
1.374 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a marker. See,
1.375 for example, Figure 2.
1.376 Correlation Recall that the instances are surface pixels, and consider the problem of attempting to classify each instance
1.377 as either a member of a particular anatomical area, or not. The target area can be represented as a boolean mask over the
1.378 surface pixels.
1.379 -One class of feature selection scoring method are those which calculate some sort of “match” between each gene image
1.380 -and the target image. Those genes which match the best are good candidates for features.
1.381 +_____________________________
1.382 + 18SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.
1.383 +One class of feature selection scoring methods contains methods which calculate some sort of “match” between each gene
1.384 +image and the target image. Those genes which match the best are good candidates for features.
1.385 One of the simplest methods in this class is to use correlation as the match score. We calculated the correlation between
1.386 each gene and each cortical area. The top row of Figure 1 shows the three genes most correlated with area SS.
1.387
1.388 @@ -453,16 +466,51 @@
1.389 Most of the genes in Figure 5 were identified via gradient similarity.
1.390 Gradient similarity provides information complementary to correlation
1.391 To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider
1.392 -Fig. 3. The top row of Fig. 3 displays the 3 genes which most match area AUD, according to a pointwise method17. The
1.393 -_________________________________________
1.394 - 17For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor
1.395 -bottom row displays the 3 genes which most match AUD according to a method which considers local geometry18 The
1.396 +Fig. 3. The top row of Fig. 3 displays the 3 genes which most match area AUD, according to a pointwise method19. The
1.397 +bottomrow displays the 3 genes which most match AUD according to a method which considers local geometry20 The
1.398 pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is
1.399 that this includes many areas which don’t have a salient border matching the areal border. The geometric method identifies
1.400 genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes
1.401 genes which don’t express over the entire area. Genes which have high rankings using both pointwise and border criteria,
1.402 such as Aph1a in the example, may be particularly good markers. None of these genes are, individually, a perfect marker
1.403 for AUD; we deliberately chose a “difficult” area in order to better contrast pointwise with geometric methods.
1.404 +Areas which can be identified by single genes Using gradient similarity, we have already found single genes which
1.405 +roughly identify some areas and groupings of areas. For each of these areas, an example of a gene which roughly identifies
1.406 +it is shown in Figure 5. We have not yet cross-verified these genes in other atlases.
1.407 +In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior part of
1.408 +cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate), VIS
1.409 +(visual), AUD (auditory).
1.410 +These results validate our expectation that the ABA dataset can be exploited to find marker genes for many cortical
1.411 +areas, while also validating the relevancy of our new scoring method, gradient similarity.
1.412 +Combinations of multiple genes are useful and necessary for some areas
1.413 +In Figure 4, we give an example of a cortical area which is not marked by any single gene, but which can be identified
1.414 +combinatorially. Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a
1.415 +pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure 4 shows wwc1’s spatial
1.416 +expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, but the
1.417 +gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding
1.418 +to the overshoot is the medial surface of the cortex. MO is only found on the dorsal surface. Gene mtif2 is shown in the
1.419 +upper-right. Mtif2 captures MO’s upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much
1.420 +on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left image. This
1.421 +combination captures area MO much better than any single gene.
1.422 +This shows that our proposal to develop a method to find combinations of marker genes is both possible and necessary.
1.423 +Feature selection integrated with prediction As noted earlier, in general, any predictive method can be used for
1.424 +feature selection by running it inside a stepwise wrapper. Also, some predictive methods integrate soft constraints on number
1.425 +of features used. Examples of both of these will be seen in the section “Multivariate Predictive methods”.
1.426 +Multivariate Predictive methods
1.427 +Forward stepwise logistic regression Logistic regression is a popular method for predictive modeling of categorial data.
1.428 +As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise logistic regression to
1.429 +find single genes, pairs of genes, and triplets of genes which predict areal identify. This is an example of feature selection
1.430 +integrated with prediction using a stepwise wrapper. Some of the single genes found were shown in various figures throughout
1.431 +this document, and Figure 4 shows a combination of genes which was found.
1.432 +We felt that, for single genes, gradient similarity did a better job than logistic regression at capturing our subjective
1.433 +impression of a “good gene”.
1.434 +_________________
1.435 + 19For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor
1.436 +variable was the value of the expression of the gene underneath that pixel. The resulting scores were used to rank the genes in terms of how well
1.437 +they predict area AUD.
1.438 + 20For each gene the gradient similarity between (a) a map of the expression of each gene on the cortical surface and (b) the shape of area AUD,
1.439 +was calculated, and this was used to rank the genes.
1.440 +
1.441
1.442
1.443
1.444 @@ -483,59 +531,22 @@
1.445 eral visual area is distinguished from its neigh-
1.446 bors, but not from the entire rest of the cortex).
1.447 The genes are Pitx2, Aldh1a2, Ppfibp1, Slco1a5,
1.448 -Tshz2, Trhr, Col12a1, Ets1. Areas which can be identified by single genes Using gradient
1.449 - similarity, we have already found single genes which roughly identify
1.450 - some areas and groupings of areas. For each of these areas, an example
1.451 - of a gene which roughly identifies it is shown in Figure 5. We have not
1.452 - yet cross-verified these genes in other atlases.
1.453 - In addition, there are a number of areas which are almost identified
1.454 - by single genes: COAa+NLOT (anterior part of cortical amygdalar area,
1.455 - nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral
1.456 - anterior cingulate), VIS (visual), AUD (auditory).
1.457 - These results validate our expectation that the ABA dataset can
1.458 - be exploited to find marker genes for many cortical areas, while also
1.459 - validating the relevancy of our new scoring method, gradient similarity.
1.460 - Combinations of multiple genes are useful and necessary for
1.461 - some areas
1.462 - In Figure 4, we give an example of a cortical area which is not marked
1.463 - by any single gene, but which can be identified combinatorially. Acc-
1.464 - cording to logistic regression, gene wwc1 is the best fit single gene for
1.465 - predicting whether or not a pixel on the cortical surface belongs to the
1.466 - motor area (area MO). The upper-left picture in Figure 4 shows wwc1’s
1.467 - spatial expression pattern over the cortex. The lower-right boundary of
1.468 - MO is represented reasonably well by this gene, however the gene over-
1.469 - shoots the upper-left boundary. This flattened 2-D representation does
1.470 - not show it, but the area corresponding to the overshoot is the medial
1.471 - surface of the cortex. MO is only found on the lateral surface. Gene mtif2
1.472 - is shown in the upper-right. Mtif2 captures MO’s upper-left boundary,
1.473 - but not its lower-right boundary. Mtif2 does not express very much on
1.474 - the medial surface. By adding together the values at each pixel in these
1.475 - two figures, we get the lower-left image. This combination captures area
1.476 - MO much better than any single gene.
1.477 - This shows that our proposal to develop a method to find combina-
1.478 - tions of marker genes is both possible and necessary.
1.479 - Feature selection integrated with prediction As noted earlier,
1.480 - in general, any predictive method can be used for feature selection by
1.481 - running it inside a stepwise wrapper. Also, some predictive methods
1.482 - integrate soft constraints on number of features used. Examples of both
1.483 - of these will be seen in the section “Multivariate Predictive methods”.
1.484 - Multivariate Predictive methods
1.485 - Forward stepwise logistic regression Logistic regression is a popu-
1.486 - lar method for predictive modeling of categorial data. As a pilot run,
1.487 - for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed
1.488 - forward stepwise logistic regression to find single genes, pairs of genes,
1.489 - and triplets of genes which predict areal identify. This is an example
1.490 - of feature selection integrated with prediction using a stepwise wrapper.
1.491 - Some of the single genes found were shown in various figures throughout
1.492 +Tshz2, Trhr, Col12a1, Ets1.
1.493 +SVM on all genes at once
1.494 +In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical
1.495 +surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%21. This shows that
1.496 +the genes included in the ABA dataset are sufficient to define much of cortical anatomy. However, as noted above, a classifier
1.497 +that looks at all the genes at once isn’t as practically useful as a classifier that uses only a few genes.
1.498 +Data-driven redrawing of the cortical map
1.499 +We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene expression
1.500 +profile associated with each voxel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional Scaling
1.501 +(MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment (LTSA), Hessian locally linear
1.502 +embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic Proximity Embedding (SPE), Fast Maximum
1.503 +Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing
1.504 _________________________________________
1.505 -variable was the value of the expression of the gene underneath that pixel. The resulting scores were used to rank the genes in terms of how well
1.506 -they predict area AUD.
1.507 - 18For each gene the gradient similarity between (a) a map of the expression of each gene on the cortical surface and (b) the shape of area AUD,
1.508 -was calculated, and this was used to rank the genes.
1.509 - this document, and Figure 4 shows a combination of genes which was
1.510 - found.
1.511 - We felt that, for single genes, gradient similarity did a better job
1.512 -than logistic regression at capturing our subjective impression of a “good gene”.
1.513 + 215-fold cross-validation.
1.514 +many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the first, second, and third rows of
1.515 +Figure 6.
1.516
1.517
1.518
1.519 @@ -548,37 +559,7 @@
1.520 from left: NNMF. Right: Landmark Isomap. Additional details: In the
1.521 third and fourth rows, 7 dimensions were found, but only 6 displayed. In
1.522 the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions
1.523 -were used; for landmark Isomap, 7 dimensions were used. SVM on all genes at once
1.524 - In order to see how well one can do when
1.525 - looking at all genes at once, we ran a support
1.526 - vector machine to classify cortical surface pix-
1.527 - els based on their gene expression profiles. We
1.528 - achieved classification accuracy of about 81%19.
1.529 - This shows that the genes included in the ABA
1.530 - dataset are sufficient to define much of cortical
1.531 - anatomy. As noted above, however, a classifier
1.532 - that looks at all the genes at once isn’t as prac-
1.533 - tically useful as a classifier that uses only a few
1.534 - genes.
1.535 - Data-driven redrawing of the cor-
1.536 - tical map
1.537 - We have applied the following dimensional-
1.538 - ity reduction algorithms to reduce the dimen-
1.539 - sionality of the gene expression profile associ-
1.540 - ated with each voxel: Principal Components
1.541 - Analysis (PCA), Simple PCA (SPCA), Multi-
1.542 - Dimensional Scaling (MDS), Isomap, Land-
1.543 - mark Isomap, Laplacian eigenmaps, Local Tan-
1.544 - gent Space Alignment (LTSA), Hessian locally
1.545 - linear embedding, Diffusion maps, Stochastic
1.546 - Neighbor Embedding (SNE), Stochastic Prox-
1.547 - imity Embedding (SPE), Fast Maximum Vari-
1.548 - ance Unfolding (FastMVU), Non-negative Ma-
1.549 - trix Factorization (NNMF). Space constraints
1.550 - prevent us from showing many of the results,
1.551 - but as a sample, PCA, NNMF, and landmark
1.552 - Isomap are shown in the first, second, and third
1.553 - rows of Figure 6.
1.554 +were used; for landmark Isomap, 7 dimensions were used.
1.555
1.556 Figure 7: Prototypes corresponding to sample gene clusters, clustered by
1.557 gradient similarity. Region boundaries for the region that most matches
1.558 @@ -601,9 +582,7 @@
1.559 spatial regions defined by any clusters matched known anatomical regions. Figure 7 shows, for ten sample gene clusters, each
1.560 cluster’s average expression pattern, compared to a known anatomical boundary. This suggests that it is worth attempting
1.561 to cluster genes, and then to use the results to cluster voxels.
1.562 -_________________________________________
1.563 - 195-fold cross-validation.
1.564 -Research plan
1.565 +Research Design and Methods
1.566 Further work on flatmapping
1.567 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo),
1.568 or by the surface of the structure (as is the case with the cortex). In the former case, the manifold of interest is a plane, but
2.1 Binary file grant.odt has changed
3.1 Binary file grant.pdf has changed
4.1 --- a/grant.txt Mon Apr 20 17:33:37 2009 -0700
4.2 +++ b/grant.txt Tue Apr 21 00:54:22 2009 -0700
4.3 @@ -10,11 +10,13 @@
4.4
4.5 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target anatomical regions\\
4.6
4.7 -(2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns in gene expression\\
4.8 +(2) develop an algorithm to suggest new ways of carving up a structure into anatomically distinct regions, based on spatial patterns in gene expression\\
4.9
4.10 (3) create a 2-D "flat map" dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).\\
4.11
4.12 -In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project will support the development of new ways to selectively target cortical areas, and it will support the development of a method for identifying the cortical areal boundaries present in small tissue samples.
4.13 +Although our particular application involves the 3D spatial distribution of gene expression, we anticipate that the methods developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located in a low-dimensional space.
4.14 +
4.15 +In terms of the application of the methods to cerebral cortex, aim (1) is to go from cortical areas to marker genes, and aim (2) is to let the gene profile define the cortical areas. In addition to validating the usefulness of the algorithms, the application of these methods to cortex will produce immediate benefits, because there are currently no known genetic markers for most cortical areas. The results of the project will support the development of new ways to selectively target cortical areas, and it will support the development of a method for identifying the cortical areal boundaries present in small tissue samples.
4.16
4.17 All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well as the machine-readable datasets developed in aim (3), will be published and freely available for others to use.
4.18
4.19 @@ -23,11 +25,11 @@
4.20
4.21 == Background and significance ==
4.22
4.23 -=== Aim 1 ===
4.24 -
4.25 -\vspace{0.3cm}**Machine learning terminology: supervised learning**
4.26 -
4.27 -The task of looking for marker genes for anatomical regions means that one is looking for a set of genes such that, if the expression level of those genes is known, then the locations of the regions can be inferred.
4.28 +=== Aim 1: Given a map of regions, find genes that mark the regions ===
4.29 +
4.30 +After defining terms, we will describe a set of principles which determine our strategy to completing this aim.
4.31 +
4.32 +\vspace{0.3cm}**Machine learning terminology: supervised learning** The task of looking for marker genes for known anatomical regions means that one is looking for a set of genes such that, if the expression level of those genes is known, then the locations of the regions can be inferred.
4.33
4.34 If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to which region each voxel within the structure belongs. We call this a __classification task__, because each voxel is being assigned to a class (namely, its region).
4.35
4.36 @@ -47,11 +49,13 @@
4.37
4.38
4.39 \vspace{0.3cm}**Principle 1: Combinatorial gene expression**
4.40 +
4.41 It is too much to hope that every anatomical region of interest will be identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary Studies, Figure \ref{MOcombo}). Therefore, each instance should contain multiple features (genes).
4.42
4.43
4.44 \vspace{0.3cm}**Principle 2: Only look at combinations of small numbers of genes**
4.45 -When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have been selected as features. The more data that is available to a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations in which it is not feasible to gather data about every gene. For example, if we want to use the expression of marker genes as a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as features.
4.46 +
4.47 +When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have been selected as features. The more data that are available to a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations in which it is not feasible to gather data about every gene. For example, if we want to use the expression of marker genes as a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as features.
4.48
4.49 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task combines feature selection with supervised learning.
4.50
4.51 @@ -71,7 +75,7 @@
4.52
4.53
4.54 === Related work ===
4.55 -There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data which is not fundamentally spatial\footnote{By "__fundamentally__ spatial" we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not just data which has only a few different locations or which is indexed by anatomical label.}.
4.56 +There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data which are not fundamentally spatial\footnote{By "__fundamentally__ spatial" we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not just data which have only a few different locations or which is indexed by anatomical label.}.
4.57
4.58 As noted above, there has been much work on both supervised learning and there are many available algorithms for each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the way that this framework is set up has a large impact on performance. Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical "fine-tuning" of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Studies) may be necessary in order to achieve the best results in this application.
4.59
4.60 @@ -92,31 +96,31 @@
4.61 cluster which includes the seed voxel, (2) yields a list of genes
4.62 which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of overexpressed genes for selected structures)
4.63
4.64 -\item Correlation: The user selects a seed voxel and
4.65 -the shows the user how much correlation there is between the gene
4.66 +\item Correlation: The user selects a seed voxel and the system
4.67 +then shows the user how much correlation there is between the gene
4.68 expression profile of the seed voxel and every other voxel.
4.69
4.70 \item Clusters: will be described later
4.71 \end{itemize}
4.72
4.73 -Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also search for underexpression. Third, Gene Finder uses a simple pointwise score\footnote{"Expression energy ratio", which captures overexpression.}, whereas we will also use geometric scores such as gradient similarity. Figures \ref{MOcombo}, \ref{hole}, and \ref{AUDgeometry} in the Preliminary Studies section contains evidence that each of our three choices is the right one.
4.74 +Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also search for underexpression. Third, Gene Finder uses a simple pointwise score\footnote{"Expression energy ratio", which captures overexpression.}, whereas we will also use geometric scores such as gradient similarity (described in Preliminary Studies). Figures \ref{MOcombo}, \ref{hole}, and \ref{AUDgeometry} in the Preliminary Studies section contains evidence that each of our three choices is the right one.
4.75
4.76 \cite{chin_genome-scale_2007} looks at the mean expression level of genes within anatomical regions, and applies a Student's t-test with Bonferroni correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA, this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for underexpression, and does not look for combinations of genes.
4.77
4.78 \cite{hemert_matching_2008} describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their match score is Jaccard similarity.
4.79
4.80 -In summary, there has been fruitful work on finding marker genes, however, only one of the previous projects explores combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or scoring methods.
4.81 -
4.82 -
4.83 -
4.84 -
4.85 -=== Aim 2 ===
4.86 +In summary, there has been fruitful work on finding marker genes, but only one of the previous projects explores combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or scoring methods.
4.87 +
4.88 +
4.89 +
4.90 +
4.91 +=== Aim 2: From gene expression data, discover a map of regions ===
4.92
4.93 \vspace{0.3cm}**Machine learning terminology: clustering**
4.94
4.95 -If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as __unsupervised learning__ in the jargon of machine learning. One thing that you can do with such a dataset is to group instances together. A set of similar instances is called a __cluster__, and the activity of finding grouping the data into clusters is called clustering or cluster analysis.
4.96 -
4.97 -The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from the same region have similar gene expression profiles, at least compared to the other regions. This means that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into clusters of voxels with similar gene expression.
4.98 +If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as __unsupervised learning__ in the jargon of machine learning. One thing that you can do with such a dataset is to group instances together. A set of similar instances is called a __cluster__, and the activity of finding grouping the data into clusters is called __clustering__ or __cluster analysis__.
4.99 +
4.100 +The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from the same anatomical region have similar gene expression profiles, at least compared to the other regions. This means that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into clusters of voxels with similar gene expression.
4.101
4.102 It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. This is called hierarchial clustering.
4.103
4.104 @@ -129,9 +133,9 @@
4.105 \vspace{0.3cm}**Spatially contiguous clusters; image segmentation**
4.106
4.107
4.108 -We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary Studies, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these results against other methods which guarantee contiguous clusters.
4.109 -
4.110 -Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these algorithms are specialized for visual images.
4.111 +We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary Studies, we show that one can get reasonable results without enforcing this constraint; however, we plan to compare these results against other methods which guarantee contiguous clusters.
4.112 +
4.113 +Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are thousands of color channels (one for each gene), rather than just three. However, there are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are often used to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these algorithms are specialized for visual images.
4.114
4.115
4.116 \vspace{0.3cm}**Dimensionality reduction**
4.117 @@ -139,9 +143,9 @@
4.118
4.119 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which "summarize" a larger number of features using a smaller number of features; these techniques go by the name of feature extraction or dimensionality reduction. The small set of features that such a technique yields is called the __reduced feature set__. After the reduced feature set is created, the instances may be replaced by __reduced instances__, which have as their features the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene expression levels.
4.120
4.121 -Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the reduced data set is less than in the original data set, the running time of clustering algorithms may be much less. Second, it is thought that some clustering algorithms may give better results on reduced data.
4.122 -
4.123 -Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example, one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that regions with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on a 2-D plan will exactly satisfy this property -- however, dimensionality reduction techniques allow one to find arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering.
4.124 +Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering algorithms may be much less. Second, it is thought that some clustering algorithms may give better results on reduced data.
4.125 +
4.126 +Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example, one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that regions with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on a 2-D plan will exactly satisfy this property; however, dimensionality reduction techniques allow one to find arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering.
4.127
4.128
4.129 \vspace{0.3cm}**Clustering genes rather than voxels**
4.130 @@ -182,21 +186,21 @@
4.131
4.132 \vspace{0.3cm}**Background**
4.133
4.134 -The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the areas continue downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can picture an area of the cortex as a slice of many-layered cake.
4.135 -
4.136 -Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes, there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas, this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of their approximate location upon the cortical surface.
4.137 +The cortex is divided into areas and layers. Because of the cortical columnar organization, the parcellation of the cortex into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the areas continue downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can picture an area of the cortex as a slice of a six-layered cake\footnote{Outside of isocortex, the number of layers varies.}.
4.138 +
4.139 +Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes, there are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample into cortical areas, this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of their approximate location upon the cortical surface.
4.140
4.141 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a single agreed-upon map can be seen by contrasting the recent maps given by Swanson\cite{swanson_brain_2003} on the one hand, and Paxinos and Franklin\cite{paxinos_mouse_2001} on the other. While the maps are certainly very similar in their general arrangement, significant differences remain in the details.
4.142
4.143 \vspace{0.3cm}**The Allen Mouse Brain Atlas dataset**
4.144
4.145 -The Allen Mouse Brain Atlas (ABA) data was produced by doing in-situ hybridization on slices of male, 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed in order to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial resolution is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different mouse brains were needed in order to measure the expression of many genes.
4.146 +The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male, 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed in order to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial resolution is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different mouse brains were needed in order to measure the expression of many genes.
4.147
4.148 Next, an automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 \= 159,326 voxels in the 3D coordinate system, of which 51,533 are in the brain\cite{ng_anatomic_2009}.
4.149
4.150 -Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes\cite{waterston_initial_2002}. The ABA contains data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, and also has greater registration error\cite{ng_anatomic_2009}. Genes were selected by the Allen Institute for coronal sectioning based on, "classes of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern"\cite{ng_anatomic_2009}.
4.151 -
4.152 -The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT\cite{gong_gene_2003}, GenePaint\cite{visel_genepaint.org:atlas_2004}, its sister project GeneAtlas\cite{carson_digital_2005}, BGEM\cite{magdaleno_bgem:in_2006}, EMAGE\cite{venkataraman_emage_2008}, EurExpress\footnote{http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE}, EADHB\footnote{http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html}, MAMEP\footnote{http://mamep.molgen.mpg.de/index.php}, Xenbase\footnote{http://xenbase.org/}, ZFIN\cite{sprague_zebrafish_2006}, Aniseed\footnote{http://aniseed-ibdm.univ-mrs.fr/}, VisiGene\footnote{http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources}, GEISHA\cite{bell_geishawhole-mount_2004}, Fruitfly.org\cite{tomancak_systematic_2002}, COMPARE\footnote{http://compare.ibdml.univ-mrs.fr/} GXD\cite{smith_mouse_2007}, GEO\cite{barrett_ncbi_2007}\footnote{GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.}. With the exception of the ABA, GenePaint, and EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of data available for public download from the website\footnote{without prior offline registration}. Many of these resources focus on developmental gene expression.
4.153 +Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes\cite{waterston_initial_2002}. The ABA contains data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our dataset is derived from only the coronal subset of the ABA, because the sagittal data do not cover the entire cortex, and also has greater registration error\cite{ng_anatomic_2009}. Genes were selected by the Allen Institute for coronal sectioning based on, "classes of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern"\cite{ng_anatomic_2009}.
4.154 +
4.155 +The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT\cite{gong_gene_2003}, GenePaint\cite{visel_genepaint.org:atlas_2004}, its sister project GeneAtlas\cite{carson_digital_2005}, BGEM\cite{magdaleno_bgem:in_2006}, EMAGE\cite{venkataraman_emage_2008}, EurExpress\footnote{http://www.eurexpress.org/ee/; EurExpress data are also entered into EMAGE}, EADHB\footnote{http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html}, MAMEP\footnote{http://mamep.molgen.mpg.de/index.php}, Xenbase\footnote{http://xenbase.org/}, ZFIN\cite{sprague_zebrafish_2006}, Aniseed\footnote{http://aniseed-ibdm.univ-mrs.fr/}, VisiGene\footnote{http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources}, GEISHA\cite{bell_geishawhole-mount_2004}, Fruitfly.org\cite{tomancak_systematic_2002}, COMPARE\footnote{http://compare.ibdml.univ-mrs.fr/} GXD\cite{smith_mouse_2007}, GEO\cite{barrett_ncbi_2007}\footnote{GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.}. With the exception of the ABA, GenePaint, and EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of data available for public download from the website\footnote{without prior offline registration}. Many of these resources focus on developmental gene expression.
4.156
4.157
4.158
4.159 @@ -214,7 +218,7 @@
4.160
4.161 === Related work ===
4.162
4.163 -\cite{ng_anatomic_2009} describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of the other components of AGEA can be applied to cortical areas; AGEA's Gene Finder cannot be used to find marker genes for the cortical areas; and AGEA's hierarchial clustering does not produce clusters corresponding to the cortical areas\footnote{In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not find most cortical areas (there are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot find marker genes for most cortical areas is that in Gene Finder, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found, and it creates that ROI by (pairwise voxel correlation) clustering around the seed.}.
4.164 +\cite{ng_anatomic_2009} describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of the other components of AGEA can be applied to cortical areas; AGEA's Gene Finder cannot be used to find marker genes for the cortical areas; and AGEA's hierarchial clustering does not produce clusters corresponding to the cortical areas\footnote{In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not find cortical areas (there are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot the find marker genes for cortical areas is that in Gene Finder, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found, and it creates that ROI by (pairwise voxel correlation) clustering around the seed.}.
4.165
4.166
4.167 %% Most of the projects which have been discussed have been done by the same groups that develop the public datasets. Although these projects make their algorithms available for use on their own website, none of them have released an open-source software toolkit; instead, users are restricted to using the provided algorithms only on their own dataset.
4.168 @@ -245,7 +249,7 @@
4.169
4.170
4.171 === Format conversion between SEV, MATLAB, NIFTI ===
4.172 -We have created software to (politely) download all of the SEV files from the Allen Institute website. We have also created software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret's file formats.
4.173 +We have created software to (politely) download all of the SEV files\footnote{SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.} from the Allen Institute website. We have also created software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret's file formats.
4.174
4.175
4.176 === Flatmap of cortex ===
4.177 @@ -259,7 +263,7 @@
4.178
4.179 We manually traced the boundaries of each of 49 cortical areas from the ABA coronal reference atlas slides. We then converted these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format.
4.180
4.181 -At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing a grid of points (pixels) over the cortical surface:
4.182 +At this point, the data are in the form of a number of 2-D matrices, all in registration, with the matrix entries representing a grid of points (pixels) over the cortical surface:
4.183
4.184 * A 2-D matrix whose entries represent the regional label associated with each surface pixel
4.185 * For each gene, a 2-D matrix whose entries represent the average expression level underneath each surface pixel
4.186 @@ -271,7 +275,7 @@
4.187
4.188
4.189
4.190 -We created a normalized version of the gene expression data by subtracting each gene's mean expression level (over all surface pixels) and dividing each gene by its standard deviation.
4.191 +We created a normalized version of the gene expression data by subtracting each gene's mean expression level (over all surface pixels) and dividing the expression level of each gene by its standard deviation.
4.192
4.193 The features and the target area are both functions on the surface pixels. They can be referred to as scalar fields over the space of surface pixels; alternately, they can be thought of as images which can be displayed on the flatmapped surface.
4.194
4.195 @@ -297,7 +301,7 @@
4.196 \vspace{0.3cm}**Correlation**
4.197 Recall that the instances are surface pixels, and consider the problem of attempting to classify each instance as either a member of a particular anatomical area, or not. The target area can be represented as a boolean mask over the surface pixels.
4.198
4.199 -One class of feature selection scoring method are those which calculate some sort of "match" between each gene image and the target image. Those genes which match the best are good candidates for features.
4.200 +One class of feature selection scoring methods contains methods which calculate some sort of "match" between each gene image and the target image. Those genes which match the best are good candidates for features.
4.201
4.202 One of the simplest methods in this class is to use correlation as the match score. We calculated the correlation between each gene and each cortical area. The top row of Figure \ref{SScorrLr} shows the three genes most correlated with area SS.
4.203
4.204 @@ -372,14 +376,14 @@
4.205
4.206 \vspace{0.3cm}**Combinations of multiple genes are useful and necessary for some areas**
4.207
4.208 -In Figure \ref{MOcombo}, we give an example of a cortical area which is not marked by any single gene, but which can be identified combinatorially. Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure \ref{MOcombo} shows wwc1's spatial expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the lateral surface. Gene mtif2 is shown in the upper-right. Mtif2 captures MO's upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left image. This combination captures area MO much better than any single gene.
4.209 +In Figure \ref{MOcombo}, we give an example of a cortical area which is not marked by any single gene, but which can be identified combinatorially. Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure \ref{MOcombo} shows wwc1's spatial expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, but the gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the dorsal surface. Gene mtif2 is shown in the upper-right. Mtif2 captures MO's upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left image. This combination captures area MO much better than any single gene.
4.210
4.211 This shows that our proposal to develop a method to find combinations of marker genes is both possible and necessary.
4.212
4.213 %% wwc1\footnote{"WW, C2 and coiled-coil domain containing 1"; EntrezGene ID 211652}
4.214 %% mtif2\footnote{"mitochondrial translational initiation factor 2"; EntrezGene ID 76784}
4.215
4.216 -%%Acccording to logistic regression, gene wwc1\footnote{"WW, C2 and coiled-coil domain containing 1"; EntrezGene ID 211652} is the best fit single gene for predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure \ref{MOcombo} shows wwc1's spatial expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the lateral surface.
4.217 +%%Acccording to logistic regression, gene wwc1\footnote{"WW, C2 and coiled-coil domain containing 1"; EntrezGene ID 211652} is the best fit single gene for predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure \ref{MOcombo} shows wwc1's spatial expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, but the gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the lateral surface.
4.218
4.219 %%Gene mtif2\footnote{"mitochondrial translational initiation factor 2"; EntrezGene ID 76784} is shown in figure the upper-right of Fig. \ref{MOcombo}. Mtif2 captures MO's upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left of Figure \ref{MOcombo}. This combination captures area MO much better than any single gene.
4.220
4.221 @@ -409,7 +413,7 @@
4.222
4.223 \vspace{0.3cm}**SVM on all genes at once**
4.224
4.225 -In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%\footnote{5-fold cross-validation.}. This shows that the genes included in the ABA dataset are sufficient to define much of cortical anatomy. As noted above, however, a classifier that looks at all the genes at once isn't as practically useful as a classifier that uses only a few genes.
4.226 +In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%\footnote{5-fold cross-validation.}. This shows that the genes included in the ABA dataset are sufficient to define much of cortical anatomy. However, as noted above, a classifier that looks at all the genes at once isn't as practically useful as a classifier that uses only a few genes.
4.227
4.228
4.229
4.230 @@ -537,11 +541,3 @@
4.231 two hemis
4.232
4.233
4.234 -%%"genomic anatomy" is a name found in the titles of one of the cited papers which seems good; maybe "computational genomic anatomy"
4.235 -
4.236 -%% todo: actually i'm pretty sure AGEA doesn't find ANY areas, but i said "most" and "often" to be cautious.
4.237 -
4.238 -%% todo: MO is only found on the lateral surface (todo).
4.239 -%% todo: predicted genes like Riken
4.240 -
4.241 -%% todo: should we disclose genes?