1.1 --- a/grant.txt Sun Apr 12 02:49:55 2009 -0700 1.2 +++ b/grant.txt Sun Apr 12 03:39:30 2009 -0700 1.3 @@ -15,7 +15,9 @@ 1.4 == Background and significance == 1.5 1.6 === Aim 1 === 1.7 -==== Machine learning terminology: supervised learning ==== 1.8 + 1.9 +**Machine learning terminology: supervised learning** 1.10 + 1.11 The task of looking for marker genes for anatomical subregions 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 subregions can be inferred. 1.12 1.13 If we define the subregions 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 subregions, we may say that we are using gene expression to determine to which subregion each voxel within the structure belongs. We call this a __classification task__, because each voxel is being assigned to a class (namely, its subregion). 1.14 @@ -34,20 +36,28 @@ 1.15 1.16 Key questions when choosing a learning method are: What are the instances? What are the features? How are the features chosen? Here are four principles that outline our answers to these questions. 1.17 1.18 -==== Principle 1: Combinatorial gene expression ==== 1.19 + 1.20 +**Principle 1: Combinatorial gene expression** 1.21 + 1.22 Above, we defined an "instance" as the combination of a voxel with the "associated gene expression data". In our case this refers to the expression level of genes within the voxel, but should we include the expression levels of all genes, or only a few of them? 1.23 1.24 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 Results). 1.25 1.26 -==== Principle 2: Only look at combinations of small numbers of genes ==== 1.27 + 1.28 +**Principle 2: Only look at combinations of small numbers of genes** 1.29 + 1.30 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. 1.31 1.32 1.33 -==== Principle 3: Use geometry in feature selection ==== 1.34 + 1.35 +**Principle 3: Use geometry in feature selection** 1.36 + 1.37 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods. 1.38 1.39 1.40 -==== Principle 4: Work in 2-D whenever possible ==== 1.41 + 1.42 +**Principle 4: Work in 2-D whenever possible** 1.43 + 1.44 1.45 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D data. 1.46 1.47 @@ -55,30 +65,40 @@ 1.48 1.49 1.50 === Aim 2 === 1.51 -==== Machine learning terminology: clustering ==== 1.52 + 1.53 +**Machine learning terminology: clustering** 1.54 + 1.55 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. 1.56 1.57 The task of deciding how to carve up a structure into anatomical subregions 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 subregion have similar gene expression profiles, at least compared to the other subregions. This means that clustering voxels is the same as finding potential subregions; we seek a partitioning of the voxels into subregions, that is, into clusters of voxels with similar gene expression. 1.58 1.59 It is desirable to determine not just one set of subregions, but also how these subregions relate to each other, if at all; perhaps some of the subregions 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 subregion. 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. 1.60 1.61 -==== Similarity scores ==== 1.62 - 1.63 -todo 1.64 - 1.65 -==== Spatially contiguous clusters; image segmentation ==== 1.66 + 1.67 +**Similarity scores** 1.68 + 1.69 + 1.70 +todo 1.71 + 1.72 + 1.73 +**Spatially contiguous clusters; image segmentation** 1.74 + 1.75 1.76 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 Results, 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. 1.77 1.78 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. 1.79 1.80 -==== Dimensionality reduction ==== 1.81 + 1.82 +**Dimensionality reduction** 1.83 + 1.84 1.85 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. 1.86 1.87 Another use for dimensionality reduction is to visualize the relationships between subregions. For example, one might want to make a 2-D plot upon which each subregion is represented by a single point, and with the property that subregions 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. 1.88 1.89 -==== Clustering genes rather than voxels ==== 1.90 + 1.91 +**Clustering genes rather than voxels** 1.92 + 1.93 1.94 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes could be used. 1.95 1.96 @@ -91,7 +111,9 @@ 1.97 1.98 1.99 === Aim 3 === 1.100 -==== Background ==== 1.101 + 1.102 +**Background** 1.103 + 1.104 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. 1.105 1.106 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. 1.107 @@ -100,7 +122,9 @@ 1.108 1.109 1.110 1.111 -==== Significance ==== 1.112 + 1.113 +**Significance** 1.114 + 1.115 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively target individual cortical areas. 1.116 1.117 The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatomical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex. 1.118 @@ -125,7 +149,9 @@ 1.119 todo 1.120 1.121 1.122 -==== Using combinations of multiple genes is necessary and sufficient to delineate some cortical areas ==== 1.123 + 1.124 +**Using combinations of multiple genes is necessary and sufficient to delineate some cortical areas** 1.125 + 1.126 Here we give an example of a cortical area which is not marked by any single gene, but which can be identified combinatorially. according 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 (todo). 1.127 1.128 Gnee 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. 1.129 @@ -139,7 +165,9 @@ 1.130 \end{figure} 1.131 1.132 1.133 -==== Geometric and pointwise scoring methods provide complementary information ==== 1.134 + 1.135 +**Geometric and pointwise scoring methods provide complementary information** 1.136 + 1.137 1.138 1.139 To show that local geometry can provide useful information that cannot be detected via pointwise analyses, consider Fig. \ref{AUDgeometry}. The top row of Fig. \ref{AUDgeometry} displays the 3 genes which most match area AUD, according to a pointwise method\footnote{For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor 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 they predict area AUD.}. The bottom row displays the 3 genes which most match AUD according to a method which considers local geometry\footnote{For each gene the gradient similarity (see section \ref{gradientSim}) between (a) a map of the expression of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this was used to rank the genes.} The pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is that this includes many areas which don't have a salient border matching the areal border. The geometric method identifies genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes genes which don't express over the entire area. Genes which have high rankings using both pointwise and border criteria, such as $Aph1a$ in the example, may be particularly good markers. None of these genes are, individually, a perfect marker for AUD; we deliberately chose a "difficult" area in order to better contrast pointwise with geometric methods. 1.140 @@ -156,20 +184,26 @@ 1.141 \caption{The top row shows the three genes which (individually) best predict area AUD, according to logistic regression. The bottom row shows the three genes which (individually) best match area AUD, according to gradient similarity. From left to right and top to bottom, the genes are $Ssr1$, $Efcbp1$, $Aph1a$, $Ptk7$, $Aph1a$ again, and $Lepr$} 1.142 \end{figure} 1.143 1.144 -==== Areas which can be identified by single genes ==== 1.145 + 1.146 +**Areas which can be identified by single genes** 1.147 + 1.148 todo 1.149 1.150 1.151 === Aim 1 (and Aim 3) === 1.152 1.153 1.154 -==== SVM on all genes at once ==== 1.155 + 1.156 +**SVM on all genes at once** 1.157 + 1.158 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{Using the Shogun SVM package (todo:cite), with parameters type=GMNPSVM (multiclass b-SVM), kernal = gaussian with sigma = 0.1, c = 10, epsilon = 1e-1 -- these are the first parameters we tried, so presumably performance would improve with different choices of parameters. 5-fold cross-validation.}. As noted above, however, a classifier that looks at all the genes at once isn't practically useful. 1.159 1.160 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. 1.161 1.162 1.163 -==== Decision trees ==== 1.164 + 1.165 +**Decision trees** 1.166 + 1.167 todo 1.168 1.169 1.170 @@ -181,7 +215,9 @@ 1.171 === Dimensionality reduction plus K-means or spectral clustering === 1.172 1.173 1.174 -==== Many areas are captured by clusters of genes ==== 1.175 + 1.176 +**Many areas are captured by clusters of genes** 1.177 + 1.178 todo 1.179 1.180 1.181 @@ -202,20 +238,26 @@ 1.182 1.183 amongst other thigns: 1.184 1.185 -==== Develop algorithms that find genetic markers for anatomical regions ==== 1.186 + 1.187 +**Develop algorithms that find genetic markers for anatomical regions** 1.188 + 1.189 # Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise, geometric, and information-theoretic measures. 1.190 # Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining the scoring measures developed, we will rank the genes by their ability to delineate each area. 1.191 # Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised learning techniques which use soft constraints to minimize the number of features, such as sparse support vector machines. 1.192 # Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult to identify because the boundaries are misdrawn, or because it does not "really" exist as a single area, at least on the genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create a larger area which can be fit. 1.193 1.194 1.195 -==== Apply these algorithms to the cortex ==== 1.196 + 1.197 +**Apply these algorithms to the cortex** 1.198 + 1.199 # Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert between SEV, NIFTI and MATLAB formats. 1.200 # Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it. 1.201 # Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries. 1.202 # Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify that area; and we will also present lists of "panels" of genes that can be used to delineate many areas at once. 1.203 1.204 -==== Develop algorithms to suggest a division of a structure into anatomical parts ==== 1.205 + 1.206 +**Develop algorithms to suggest a division of a structure into anatomical parts** 1.207 + 1.208 # Explore dimensionality reduction algorithms applied to pixels: including TODO 1.209 # Explore dimensionality reduction algorithms applied to genes: including TODO 1.210 # Explore clustering algorithms applied to pixels: including TODO 1.211 @@ -231,7 +273,9 @@ 1.212 1.213 stuff i dunno where to put yet (there is more scattered through grant-oldtext): 1.214 1.215 -==== Principle 4: Work in 2-D whenever possible ==== 1.216 + 1.217 +**Principle 4: Work in 2-D whenever possible** 1.218 + 1.219 1.220 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo), 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 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane. 1.221