bshanks@0: Specific aims bshanks@53: Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in situ transgenic bshanks@53: reporter, microarray voxelation, and others, allow the expression levels of many genes at many locations to be compared. bshanks@53: Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker bshanks@53: genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have bshanks@53: three specific aims: bshanks@30: (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target bshanks@30: anatomical regions bshanks@84: (2) develop an algorithm to suggest new ways of carving up a structure into anatomically distinct regions, based on bshanks@84: spatial patterns in gene expression bshanks@33: (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse bshanks@35: Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of bshanks@35: Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2). bshanks@84: Although our particular application involves the 3D spatial distribution of gene expression, we anticipate that the methods bshanks@84: developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located in a low-dimensional bshanks@84: space. bshanks@84: In terms of the application of the methods to cerebral cortex, aim (1) is to go from cortical areas to marker genes, bshanks@84: and aim (2) is to let the gene profile define the cortical areas. In addition to validating the usefulness of the algorithms, bshanks@84: the application of these methods to cortex will produce immediate benefits, because there are currently no known genetic bshanks@84: markers for most cortical areas. The results of the project will support the development of new ways to selectively target bshanks@84: cortical areas, and it will support the development of a method for identifying the cortical areal boundaries present in small bshanks@84: tissue samples. bshanks@53: All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well as the bshanks@30: machine-readable datasets developed in aim (3), will be published and freely available for others to use. bshanks@30: Background and significance bshanks@84: Aim 1: Given a map of regions, find genes that mark the regions bshanks@84: After defining terms, we will describe a set of principles which determine our strategy to completing this aim. bshanks@84: Machine learning terminology: supervised learning The task of looking for marker genes for known anatomical bshanks@84: regions means that one is looking for a set of genes such that, if the expression level of those genes is known, then the bshanks@84: locations of the regions can be inferred. bshanks@42: If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we bshanks@42: are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to bshanks@42: which region each voxel within the structure belongs. We call this a classification task, because each voxel is being assigned bshanks@42: to a class (namely, its region). bshanks@30: Therefore, an understanding of the relationship between the combination of their expression levels and the locations of bshanks@42: the regions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels bshanks@42: within that voxel; the output is the regional identity of the target voxel, that is, the region to which the target voxel belongs. bshanks@42: We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called a label bshanks@42: (or a class label). bshanks@30: The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a bshanks@30: classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be bshanks@30: analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning bshanks@33: procedure. The construction of the classifier is called training (also learning), and the initial gene expression dataset used bshanks@33: in the construction of the classifier is called training data. bshanks@30: In the machine learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a bshanks@30: task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances bshanks@42: (voxels) for which the labels (regions) are known. bshanks@30: Each gene expression level is called a feature, and the selection of which genes1 to include is called feature selection. bshanks@33: Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with bshanks@33: a separate feature selection phase, whereas other methods combine feature selection with other aspects of training. bshanks@30: One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then bshanks@30: chosen. Some scoring measures can assign a score to a set of selected genes, not just to a single gene; in this case, a dynamic bshanks@30: procedure may be used in which features are added and subtracted from the selected set depending on how much they raise bshanks@30: the score. Such procedures are called “stepwise” or “greedy”. bshanks@30: Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the bshanks@30: learning algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature bshanks@30: selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to bshanks@53: each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares or bshanks@53: average). If only information from nearby voxels is used to calculate a voxel’s sub-score, then we say it is a local scoring bshanks@53: method. If only information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring bshanks@53: method. bshanks@30: Key questions when choosing a learning method are: What are the instances? What are the features? How are the bshanks@30: features chosen? Here are four principles that outline our answers to these questions. bshanks@84: Principle 1: Combinatorial gene expression bshanks@84: It is too much to hope that every anatomical region of interest will be identified by a single gene. For example, in the bshanks@84: cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset. bshanks@84: However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for bshanks@84: which multiple genes are necessary and sufficient is provided in Preliminary Studies, Figure 4). Therefore, each instance bshanks@84: should contain multiple features (genes). bshanks@84: Principle 2: Only look at combinations of small numbers of genes bshanks@84: When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have been selected bshanks@84: as features. The more data that are available to a classifier, the better that it can do. For example, perhaps there are weak bshanks@84: correlations over many genes that add up to a strong signal. So, why not include every gene as a feature? The reason is that bshanks@84: we wish to employ the classifier in situations in which it is not feasible to gather data about every gene. For example, if we bshanks@84: want to use the expression of marker genes as a trigger for some regionally-targeted intervention, then our intervention must bshanks@84: contain a molecular mechanism to check the expression level of each marker gene before it triggers. It is currently infeasible bshanks@84: to design a molecular trigger that checks the level of more than a handful of genes. Similarly, if the goal is to develop a bshanks@84: _________________________________________ bshanks@63: 1Strictly speaking, the features are gene expression levels, but we’ll call them genes. bshanks@84: procedure to do ISH on tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes. bshanks@84: Therefore, we must select only a few genes as features. bshanks@63: The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many bshanks@63: of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task bshanks@63: combines feature selection with supervised learning. bshanks@30: Principle 3: Use geometry in feature selection bshanks@30: When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of bshanks@30: each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information bshanks@30: about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See bshanks@84: Preliminary Studies, figure 3 for evidence of the complementary nature of pointwise and local scoring methods. bshanks@30: Principle 4: Work in 2-D whenever possible bshanks@30: There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When bshanks@30: it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis bshanks@33: algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D bshanks@33: data. bshanks@30: Therefore, when possible, the instances should represent pixels, not voxels. bshanks@43: Related work bshanks@44: There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data bshanks@84: which are not fundamentally spatial2. bshanks@43: As noted above, there has been much work on both supervised learning and there are many available algorithms for bshanks@43: each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the bshanks@43: way that this framework is set up has a large impact on performance. Creating a good framework can require creatively bshanks@43: reconceptualizing the problem domain, and is not merely a mechanical “fine-tuning” of numerical parameters. For example, bshanks@84: we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Studies) may bshanks@43: be necessary in order to achieve the best results in this application. bshanks@53: We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods. bshanks@53: [8 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of bshanks@53: interest, computing what proportion of this structure is covered by the gene’s spatial region. bshanks@53: GeneAtlas[3] and EMAGE [18] allow the user to construct a search query by demarcating regions and then specifing bshanks@53: either the strength of expression or the name of another gene or dataset whose expression pattern is to be matched. For the bshanks@53: similiarity score (match score) between two images (in this case, the query and the gene expression images), GeneAtlas uses bshanks@53: the sum of a weighted L1-norm distance between vectors whose components represent the number of cells within a pixel3 bshanks@53: whose expression is within four discretization levels. EMAGE uses Jaccard similarity, which is equal to the number of true bshanks@53: pixels in the intersection of the two images, divided by the number of pixels in their union. Neither GeneAtlas nor EMAGE bshanks@53: allow one to search for combinations of genes that define a region in concert but not separately. bshanks@53: [10 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components: bshanks@61: ∙Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) bshanks@61: yields a list of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists bshanks@61: of overexpressed genes for selected structures) bshanks@84: ∙Correlation: The user selects a seed voxel and the system then shows the user how much correlation there is between bshanks@84: the gene expression profile of the seed voxel and every other voxel. bshanks@61: ∙Clusters: will be described later bshanks@43: Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we bshanks@43: will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also bshanks@53: search for underexpression. Third, Gene Finder uses a simple pointwise score4, whereas we will also use geometric scores bshanks@84: such as gradient similarity (described in Preliminary Studies). Figures 4, 2, and 3 in the Preliminary Studies section contains bshanks@84: evidence that each of our three choices is the right one. bshanks@53: [4 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni bshanks@51: correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA, bshanks@84: _________________________________________ bshanks@84: 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not bshanks@84: just data which have only a few different locations or which is indexed by anatomical label. bshanks@84: 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity. bshanks@84: 4“Expression energy ratio”, which captures overexpression. bshanks@51: this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for bshanks@51: underexpression, and does not look for combinations of genes. bshanks@53: [7 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary bshanks@46: algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their bshanks@51: match score is Jaccard similarity. bshanks@84: In summary, there has been fruitful work on finding marker genes, but only one of the previous projects explores bshanks@51: combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or bshanks@51: scoring methods. bshanks@84: Aim 2: From gene expression data, discover a map of regions bshanks@30: Machine learning terminology: clustering bshanks@30: If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as bshanks@30: unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances bshanks@46: together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called bshanks@46: clustering or cluster analysis. bshanks@84: The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances bshanks@84: are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels bshanks@84: from the same anatomical region have similar gene expression profiles, at least compared to the other regions. This means bshanks@84: that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into bshanks@84: clusters of voxels with similar gene expression. bshanks@42: It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps bshanks@44: some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they bshanks@42: could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests bshanks@42: the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. bshanks@42: This is called hierarchial clustering. bshanks@30: Similarity scores bshanks@30: A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or bshanks@33: clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and bshanks@30: scoring methods for similarity. bshanks@30: Spatially contiguous clusters; image segmentation bshanks@33: 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 bshanks@33: an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary bshanks@84: Studies, we show that one can get reasonable results without enforcing this constraint; however, we plan to compare these bshanks@33: results against other methods which guarantee contiguous clusters. bshanks@30: Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a bshanks@33: variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into bshanks@30: clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in bshanks@84: our task, there are thousands of color channels (one for each gene), rather than just three. However, there are imaging bshanks@84: tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are often used bshanks@33: to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting bshanks@33: sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene bshanks@33: expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of bshanks@33: spatially arranged data, some of these algorithms are specialized for visual images. bshanks@51: Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression feature bshanks@51: vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying data. bshanks@33: Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the bshanks@30: instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which bshanks@30: “summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature bshanks@30: extraction or dimensionality reduction. The small set of features that such a technique yields is called the reduced feature bshanks@30: set. After the reduced feature set is created, the instances may be replaced by reduced instances, which have as their features bshanks@30: the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced bshanks@30: feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene bshanks@30: expression levels. bshanks@51: Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the bshanks@84: reduced dataset is less than in the original dataset, the running time of clustering algorithms may be much less. Second, it bshanks@84: is thought that some clustering algorithms may give better results on reduced data. bshanks@51: Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example, bshanks@84: one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that bshanks@84: regions with similar gene expression profiles should be nearby on the plot (that is, the property that distance between bshanks@84: pairs of points in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no bshanks@84: arrangement of the points on a 2-D plan will exactly satisfy this property; however, dimensionality reduction techniques allow bshanks@84: one to find arrangements of points that approximately satisfy that property. Note that in this application, dimensionality bshanks@84: reduction is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality bshanks@84: reduction before clustering. bshanks@30: Clustering genes rather than voxels bshanks@30: Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster bshanks@30: the features (genes). There are two ways that clusters of genes could be used. bshanks@30: Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could bshanks@30: have one reduced feature for each gene cluster. bshanks@30: Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression bshanks@53: pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically bshanks@53: interesting region will have multiple genes which each individually pick it out5. This suggests the following procedure: bshanks@42: cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters. bshanks@84: In Preliminary Studies, Figure 7, we show that a number of anatomically recognized cortical regions, as well as some bshanks@84: “superregions” formed by lumping together a few regions, are associated with gene clusters in this fashion. bshanks@51: The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering bshanks@51: algorithms. bshanks@43: Related work bshanks@51: We are aware of five existing efforts to cluster spatial gene expression data. bshanks@53: [15 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis, bshanks@43: two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive bshanks@44: bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving bshanks@53: the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset6 and while the results are bshanks@84: promising, they also demonstrate that NNMF is not necessarily the best dimensionality reduction method for this application bshanks@84: (see Preliminary Studies, Figure 6). bshanks@53: AGEA[10] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation bshanks@53: as the similarity metric. EMAGE[18] allows the user to select a dataset from among a large number of alternatives, or by bshanks@53: running a search query, and then to cluster the genes within that dataset. EMAGE clusters via hierarchial complete linkage bshanks@53: clustering with un-centred correlation as the similarity score. bshanks@53: [4 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and which were bshanks@53: highly correlated with many other genes. They computed the matrix of (rank) correlations between pairs of these genes, and bshanks@53: ordered the rows of this matrix as follows: “the first row of the matrix was chosen to show the strongest contrast between bshanks@53: the highest and lowest correlation coefficient for that row. The remaining rows were then arranged in order of decreasing bshanks@53: similarity using a least squares metric”. The resulting matrix showed four clusters. For each cluster, prototypical spatial bshanks@53: expression patterns were created by averaging the genes in the cluster. The prototypes were analyzed manually, without bshanks@53: clustering voxels bshanks@53: In an interesting twist, [7] applies their technique for finding combinations of marker genes for the purpose of clustering bshanks@46: genes around a “seed gene”. The way they do this is by using the pattern of expression of the seed gene as the target image, bshanks@46: and then searching for other genes which can be combined to reproduce this pattern. Those other genes which are found bshanks@53: are considered to be related to the seed. The same team also describes a method[17] for finding “association rules” such as, bshanks@46: “if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the same gene”. This could be bshanks@46: useful as part of a procedure for clustering voxels. bshanks@46: In summary, although these projects obtained clusterings, there has not been much comparison between different algo- bshanks@51: rithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found. Also, bshanks@53: none of these projects did a separate dimensionality reduction step before clustering pixels, none tried to cluster genes first bshanks@53: in order to guide automated clustering of pixels into spatial regions, and none used co-clustering algorithms. bshanks@63: _________________________________________ bshanks@63: 5This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is bshanks@63: possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression; bshanks@63: perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another possibility is that, although bshanks@63: the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype. bshanks@63: 6We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft bshanks@63: spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was bshanks@63: needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried. bshanks@30: Aim 3 bshanks@30: Background bshanks@84: The cortex is divided into areas and layers. Because of the cortical columnar organization, the parcellation of the cortex bshanks@84: into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the bshanks@84: areas continue downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the bshanks@84: surface. One can picture an area of the cortex as a slice of a six-layered cake7. bshanks@30: Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes, bshanks@84: there are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample into cortical areas, bshanks@30: this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of bshanks@30: their approximate location upon the cortical surface. bshanks@33: Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not bshanks@53: completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a single bshanks@53: agreed-upon map can be seen by contrasting the recent maps given by Swanson[14] on the one hand, and Paxinos and bshanks@53: Franklin[11] on the other. While the maps are certainly very similar in their general arrangement, significant differences bshanks@30: remain in the details. bshanks@36: The Allen Mouse Brain Atlas dataset bshanks@84: The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male, 56-day-old bshanks@36: C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed bshanks@36: in order to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial bshanks@36: resolution is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different bshanks@36: mouse brains were needed in order to measure the expression of many genes. bshanks@36: Next, an automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate bshanks@36: system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 = 159,326 bshanks@53: voxels in the 3D coordinate system, of which 51,533 are in the brain[10]. bshanks@53: Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[20]. The ABA contains bshanks@36: data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our bshanks@84: dataset is derived from only the coronal subset of the ABA, because the sagittal data do not cover the entire cortex, and bshanks@53: also has greater registration error[10]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes bshanks@53: of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[10]. bshanks@53: The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[6], bshanks@84: GenePaint[19], its sister project GeneAtlas[3], BGEM[9], EMAGE[18], EurExpress8, EADHB9, MAMEP10, Xenbase11, bshanks@84: ZFIN[13], Aniseed12, VisiGene13, GEISHA[2], Fruitfly.org[16], COMPARE14 GXD[12], GEO[1]15. With the exception of bshanks@53: the ABA, GenePaint, and EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH bshanks@53: images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of bshanks@84: data available for public download from the website16. Many of these resources focus on developmental gene expression. bshanks@46: Significance bshanks@43: The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the bshanks@42: combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for bshanks@30: drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively bshanks@30: target individual cortical areas. bshanks@30: The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatom- bshanks@33: ical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can bshanks@33: find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that bshanks@30: will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex. bshanks@53: The method developed in aim (2) will provide a genoarchitectonic viewpoint that will contribute to the creation of bshanks@33: a better map. The development of present-day cortical maps was driven by the application of histological stains. It is bshanks@33: conceivable that if a different set of stains had been available which identified a different set of features, then the today’s bshanks@33: cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of bshanks@84: _________________________________________ bshanks@84: 7Outside of isocortex, the number of layers varies. bshanks@84: 8http://www.eurexpress.org/ee/; EurExpress data are also entered into EMAGE bshanks@84: 9http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html bshanks@84: 10http://mamep.molgen.mpg.de/index.php bshanks@84: 11http://xenbase.org/ bshanks@84: 12http://aniseed-ibdm.univ-mrs.fr/ bshanks@84: 13http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources bshanks@84: 14http://compare.ibdml.univ-mrs.fr/ bshanks@84: 15GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE. bshanks@84: 16without prior offline registration bshanks@33: genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been bshanks@63: captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking bshanks@63: at the patterns of gene expression. bshanks@63: While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to bshanks@63: develop could be used to suggest modifications to the human cortical map as well. bshanks@63: Related work bshanks@63: [10 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations bshanks@63: between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either bshanks@46: of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of bshanks@46: the other components of AGEA can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes bshanks@84: for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas17. bshanks@46: In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, (b) there has bshanks@43: been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally bshanks@43: finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo bshanks@43: from gene expression data. bshanks@53: Our project is guided by a concrete application with a well-specified criterion of success (how well we can find marker bshanks@53: genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods. bshanks@53: _________________________________________ bshanks@84: 17In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are bshanks@44: often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel bshanks@46: correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not bshanks@84: 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 bshanks@84: layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot the find marker genes for bshanks@84: 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 bshanks@84: creates that ROI by (pairwise voxel correlation) clustering around the seed. bshanks@84: Preliminary Studies bshanks@75: bshanks@75: bshanks@75: Figure 1: Top row: Genes Nfic and bshanks@69: A930001M12Rik are the most correlated with bshanks@69: area SS (somatosensory cortex). Bottom row: bshanks@78: Genes C130038G02Rik and Cacna1i are those bshanks@69: with the best fit using logistic regression. Within bshanks@78: each picture, the vertical axis roughly corresponds bshanks@78: to anterior at the top and posterior at the bot- bshanks@78: tom, and the horizontal axis roughly corresponds bshanks@78: to medial at the left and lateral at the right. The bshanks@78: red outline is the boundary of region SS. Pixels are bshanks@78: colored according to correlation, with red meaning bshanks@78: high correlation and blue meaning low. Format conversion between SEV, MATLAB, NIFTI bshanks@84: We have created software to (politely) download all of the SEV files18 bshanks@84: from the Allen Institute website. We have also created software to con- bshanks@84: vert between the SEV, MATLAB, and NIFTI file formats, as well as bshanks@84: some of Caret’s file formats. bshanks@75: Flatmap of cortex bshanks@75: We downloaded the ABA data and applied a mask to select only those bshanks@75: voxels which belong to cerebral cortex. We divided the cortex into hemi- bshanks@75: spheres. bshanks@75: Using Caret[5], we created a mesh representation of the surface of the bshanks@75: selected voxels. For each gene, for each node of the mesh, we calculated bshanks@75: an average of the gene expression of the voxels “underneath” that mesh bshanks@75: node. We then flattened the cortex, creating a two-dimensional mesh. bshanks@75: We sampled the nodes of the irregular, flat mesh in order to create bshanks@75: a regular grid of pixel values. We converted this grid into a MATLAB bshanks@75: matrix. bshanks@75: We manually traced the boundaries of each of 49 cortical areas from bshanks@75: the ABA coronal reference atlas slides. We then converted these manual bshanks@75: traces into Caret-format regional boundary data on the mesh surface. bshanks@75: We projected the regions onto the 2-d mesh, and then onto the grid, and bshanks@75: then we converted the region data into MATLAB format. bshanks@84: At this point, the data are in the form of a number of 2-D matrices, bshanks@75: all in registration, with the matrix entries representing a grid of points bshanks@75: (pixels) over the cortical surface: bshanks@75: ∙ A 2-D matrix whose entries represent the regional label associated with bshanks@75: each surface pixel bshanks@75: ∙ For each gene, a 2-D matrix whose entries represent the average expres- bshanks@75: sion level underneath each surface pixel bshanks@75: bshanks@78: Figure 2: Gene Pitx2 bshanks@75: is selectively underex- bshanks@77: pressed in area SS. We created a normalized version of the gene expression data by subtracting each gene’s mean bshanks@84: expression level (over all surface pixels) and dividing the expression level of each gene by its bshanks@84: standard deviation. bshanks@75: The features and the target area are both functions on the surface pixels. They can be referred bshanks@75: to as scalar fields over the space of surface pixels; alternately, they can be thought of as images bshanks@75: which can be displayed on the flatmapped surface. bshanks@75: To move beyond a single average expression level for each surface pixel, we plan to create a bshanks@75: separate matrix for each cortical layer to represent the average expression level within that layer. bshanks@75: Cortical layers are found at different depths in different parts of the cortex. In preparation for bshanks@75: extracting the layer-specific datasets, we have extended Caret with routines that allow the depth bshanks@75: of the ROI for volume-to-surface projection to vary. bshanks@75: In the Research Plan, we describe how we will automatically locate the layer depths. For bshanks@75: validation, we have manually demarcated the depth of the outer boundary of cortical layer 5 bshanks@84: throughout the cortex. bshanks@77: Feature selection and scoring methods bshanks@75: Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a marker. See, bshanks@75: for example, Figure 2. bshanks@75: Correlation Recall that the instances are surface pixels, and consider the problem of attempting to classify each instance bshanks@75: as either a member of a particular anatomical area, or not. The target area can be represented as a boolean mask over the bshanks@75: surface pixels. bshanks@84: _____________________________ bshanks@84: 18SEV is a sparse format for spatial data. It is the format in which the ABA data is made available. bshanks@84: One class of feature selection scoring methods contains methods which calculate some sort of “match” between each gene bshanks@84: image and the target image. Those genes which match the best are good candidates for features. bshanks@75: One of the simplest methods in this class is to use correlation as the match score. We calculated the correlation between bshanks@75: each gene and each cortical area. The top row of Figure 1 shows the three genes most correlated with area SS. bshanks@69: bshanks@69: bshanks@69: Figure 3: The top row shows the two genes which bshanks@69: (individually) best predict area AUD, according bshanks@69: to logistic regression. The bottom row shows the bshanks@69: two genes which (individually) best match area bshanks@69: AUD, according to gradient similarity. From left bshanks@69: to right and top to bottom, the genes are Ssr1, bshanks@69: Efcbp1, Ptk7, and Aph1a. Conditional entropy An information-theoretic scoring method is bshanks@69: to find features such that, if the features (gene expression levels) are bshanks@69: known, uncertainty about the target (the regional identity) is reduced. bshanks@69: Entropy measures uncertainty, so what we want is to find features such bshanks@69: that the conditional distribution of the target has minimal entropy. The bshanks@69: distribution to which we are referring is the probability distribution over bshanks@69: the population of surface pixels. bshanks@69: The simplest way to use information theory is on discrete data, so bshanks@69: we discretized our gene expression data by creating, for each gene, five bshanks@69: thresholded boolean masks of the gene data. For each gene, we created a bshanks@69: boolean mask of its expression levels using each of these thresholds: the bshanks@69: mean of that gene, the mean minus one standard deviation, the mean bshanks@69: minus two standard deviations, the mean plus one standard deviation, bshanks@69: the mean plus two standard deviations. bshanks@69: Now, for each region, we created and ran a forward stepwise pro- bshanks@69: cedure which attempted to find pairs of gene expression boolean masks bshanks@69: such that the conditional entropy of the target area’s boolean mask, con- bshanks@69: ditioned upon the pair of gene expression boolean masks, is minimized. bshanks@69: This finds pairs of genes which are most informative (at least at these bshanks@69: discretization thresholds) relative to the question, “Is this surface pixel bshanks@69: a member of the target area?”. Its advantage over linear methods such bshanks@69: as logistic regression is that it takes account of arbitrarily nonlinear re- bshanks@69: lationships; for example, if the XOR of two variables predicts the target, bshanks@69: conditional entropy would notice, whereas linear methods would not. bshanks@69: bshanks@69: bshanks@69: Figure 4: Upper left: wwc1. Upper right: mtif2. bshanks@69: Lower left: wwc1 + mtif2 (each pixel’s value on bshanks@69: the lower left is the sum of the corresponding pix- bshanks@69: els in the upper row). Gradient similarity We noticed that the previous two scoring bshanks@69: methods, which are pointwise, often found genes whose pattern of ex- bshanks@69: pression did not look similar in shape to the target region. For this bshanks@69: reason we designed a non-pointwise local scoring method to detect when bshanks@69: a gene had a pattern of expression which looked like it had a boundary bshanks@69: whose shape is similar to the shape of the target region. We call this bshanks@69: scoring method “gradient similarity”. bshanks@69: One might say that gradient similarity attempts to measure how bshanks@69: much the border of the area of gene expression and the border of the bshanks@69: target region overlap. However, since gene expression falls off continu- bshanks@69: ously rather than jumping from its maximum value to zero, the spatial bshanks@69: pattern of a gene’s expression often does not have a discrete border. bshanks@69: Therefore, instead of looking for a discrete border, we look for large bshanks@69: gradients. Gradient similarity is a symmetric function over two images bshanks@69: (i.e. two scalar fields). It is is high to the extent that matching pixels bshanks@69: which have large values and large gradients also have gradients which bshanks@69: are oriented in a similar direction. The formula is: bshanks@69: ∑ bshanks@69: pixel∈pixels cos(abs(∠∇1 -∠∇2)) ⋅|∇1| + |∇2| bshanks@41: 2 ⋅ pixel_value1 + pixel_value2 bshanks@41: 2 bshanks@69: where ∇1 and ∇2 are the gradient vectors of the two images at the bshanks@69: current pixel; ∠∇i is the angle of the gradient of image i at the current pixel; |∇i| is the magnitude of the gradient of image bshanks@69: i at the current pixel; and pixel_valuei is the value of the current pixel in image i. bshanks@40: The intuition is that we want to see if the borders of the pattern in the two images are similar; if the borders are similar, bshanks@40: then both images will have corresponding pixels with large gradients (because this is a border) which are oriented in a bshanks@40: similar direction (because the borders are similar). bshanks@69: Most of the genes in Figure 5 were identified via gradient similarity. bshanks@43: Gradient similarity provides information complementary to correlation bshanks@41: To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider bshanks@84: Fig. 3. The top row of Fig. 3 displays the 3 genes which most match area AUD, according to a pointwise method19. The bshanks@84: bottomrow displays the 3 genes which most match AUD according to a method which considers local geometry20 The bshanks@46: pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is bshanks@46: that this includes many areas which don’t have a salient border matching the areal border. The geometric method identifies bshanks@46: genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes bshanks@46: genes which don’t express over the entire area. Genes which have high rankings using both pointwise and border criteria, bshanks@46: such as Aph1a in the example, may be particularly good markers. None of these genes are, individually, a perfect marker bshanks@46: for AUD; we deliberately chose a “difficult” area in order to better contrast pointwise with geometric methods. bshanks@84: Areas which can be identified by single genes Using gradient similarity, we have already found single genes which bshanks@84: roughly identify some areas and groupings of areas. For each of these areas, an example of a gene which roughly identifies bshanks@84: it is shown in Figure 5. We have not yet cross-verified these genes in other atlases. bshanks@84: In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior part of bshanks@84: cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate), VIS bshanks@84: (visual), AUD (auditory). bshanks@84: These results validate our expectation that the ABA dataset can be exploited to find marker genes for many cortical bshanks@84: areas, while also validating the relevancy of our new scoring method, gradient similarity. bshanks@84: Combinations of multiple genes are useful and necessary for some areas bshanks@84: In Figure 4, we give an example of a cortical area which is not marked by any single gene, but which can be identified bshanks@84: combinatorially. Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a bshanks@84: pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure 4 shows wwc1’s spatial bshanks@84: expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, but the bshanks@84: gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding bshanks@84: to the overshoot is the medial surface of the cortex. MO is only found on the dorsal surface. Gene mtif2 is shown in the bshanks@84: upper-right. Mtif2 captures MO’s upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much bshanks@84: on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left image. This bshanks@84: combination captures area MO much better than any single gene. bshanks@84: This shows that our proposal to develop a method to find combinations of marker genes is both possible and necessary. bshanks@84: Feature selection integrated with prediction As noted earlier, in general, any predictive method can be used for bshanks@84: feature selection by running it inside a stepwise wrapper. Also, some predictive methods integrate soft constraints on number bshanks@84: of features used. Examples of both of these will be seen in the section “Multivariate Predictive methods”. bshanks@84: Multivariate Predictive methods bshanks@84: Forward stepwise logistic regression Logistic regression is a popular method for predictive modeling of categorial data. bshanks@84: As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise logistic regression to bshanks@84: find single genes, pairs of genes, and triplets of genes which predict areal identify. This is an example of feature selection bshanks@84: integrated with prediction using a stepwise wrapper. Some of the single genes found were shown in various figures throughout bshanks@84: this document, and Figure 4 shows a combination of genes which was found. bshanks@84: We felt that, for single genes, gradient similarity did a better job than logistic regression at capturing our subjective bshanks@84: impression of a “good gene”. bshanks@84: _________________ bshanks@84: 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 bshanks@84: 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 bshanks@84: they predict area AUD. bshanks@84: 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, bshanks@84: was calculated, and this was used to rank the genes. bshanks@84: bshanks@69: bshanks@69: bshanks@69: bshanks@69: bshanks@69: Figure 5: From left to right and top to bot- bshanks@69: tom, single genes which roughly identify ar- bshanks@77: eas SS (somatosensory primary + supplemen- bshanks@77: tal), SSs (supplemental somatosensory), PIR (pir- bshanks@77: iform), FRP (frontal pole), RSP (retrosplenial), bshanks@69: COApm (Cortical amygdalar, posterior part, me- bshanks@69: dial zone). Grouping some areas together, we bshanks@69: have also found genes to identify the groups bshanks@69: ACA+PL+ILA+DP+ORB+MO (anterior cingu- bshanks@69: late, prelimbic, infralimbic, dorsal peduncular, or- bshanks@69: bital, motor), posterior and lateral visual (VISpm, bshanks@69: VISpl, VISI, VISp; posteromedial, posterolateral, bshanks@69: lateral, and primary visual; the posterior and lat- bshanks@69: eral visual area is distinguished from its neigh- bshanks@69: bors, but not from the entire rest of the cortex). bshanks@69: The genes are Pitx2, Aldh1a2, Ppfibp1, Slco1a5, bshanks@84: Tshz2, Trhr, Col12a1, Ets1. bshanks@84: SVM on all genes at once bshanks@84: 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 bshanks@84: surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%21. This shows that bshanks@84: the genes included in the ABA dataset are sufficient to define much of cortical anatomy. However, as noted above, a classifier bshanks@84: that looks at all the genes at once isn’t as practically useful as a classifier that uses only a few genes. bshanks@84: Data-driven redrawing of the cortical map bshanks@84: We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene expression bshanks@84: profile associated with each voxel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional Scaling bshanks@84: (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment (LTSA), Hessian locally linear bshanks@84: embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic Proximity Embedding (SPE), Fast Maximum bshanks@84: Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing bshanks@63: _________________________________________ bshanks@84: 215-fold cross-validation. bshanks@84: many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the first, second, and third rows of bshanks@84: Figure 6. bshanks@60: bshanks@69: bshanks@69: bshanks@69: bshanks@69: Figure 6: First row: the first 6 reduced dimensions, using PCA. Second bshanks@69: row: the first 6 reduced dimensions, using NNMF. Third row: the first bshanks@69: six reduced dimensions, using landmark Isomap. Bottom row: examples bshanks@69: of kmeans clustering applied to reduced datasets to find 7 clusters. Left: bshanks@69: 19 of the major subdivisions of the cortex. Second from left: PCA. Third bshanks@69: from left: NNMF. Right: Landmark Isomap. Additional details: In the bshanks@69: third and fourth rows, 7 dimensions were found, but only 6 displayed. In bshanks@69: the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions bshanks@84: were used; for landmark Isomap, 7 dimensions were used. bshanks@71: bshanks@71: Figure 7: Prototypes corresponding to sample gene clusters, clustered by bshanks@71: gradient similarity. Region boundaries for the region that most matches bshanks@71: each prototype are overlayed. After applying the dimensionality reduc- bshanks@71: tion, we ran clustering algorithms on the re- bshanks@71: duced data. To date we have tried k-means and bshanks@71: spectral clustering. The results of k-means after bshanks@71: PCA, NNMF, and landmark Isomap are shown bshanks@71: in the last row of Figure 6. To compare, the bshanks@71: leftmost picture on the bottom row of Figure bshanks@71: 6 shows some of the major subdivisions of cor- bshanks@71: tex. These results clearly show that different di- bshanks@71: mensionality reduction techniques capture dif- bshanks@71: ferent aspects of the data and lead to differ- bshanks@71: ent clusterings, indicating the utility of our pro- bshanks@71: posal to produce a detailed comparion of these bshanks@71: techniques as applied to the domain of genomic bshanks@71: anatomy. bshanks@71: Many areas are captured by clusters of genes We also clustered the genes using gradient similarity to see if the bshanks@72: spatial regions defined by any clusters matched known anatomical regions. Figure 7 shows, for ten sample gene clusters, each bshanks@72: cluster’s average expression pattern, compared to a known anatomical boundary. This suggests that it is worth attempting bshanks@72: to cluster genes, and then to use the results to cluster voxels. bshanks@84: Research Design and Methods bshanks@42: Further work on flatmapping bshanks@42: In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo), bshanks@42: 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 bshanks@42: in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane. bshanks@42: In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal bshanks@53: for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret[5]) with bshanks@42: mappings which preserve angle (conformal maps). bshanks@42: Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional. bshanks@42: If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D bshanks@42: structure seems to be wrong. bshanks@30: todo amongst other things: bshanks@63: layerfinding bshanks@30: Develop algorithms that find genetic markers for anatomical regions bshanks@30: 1.Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise, bshanks@30: geometric, and information-theoretic measures. bshanks@30: 2.Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining bshanks@30: the scoring measures developed, we will rank the genes by their ability to delineate each area. bshanks@30: 3.Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any bshanks@30: single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily bshanks@30: combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised bshanks@33: learning techniques which use soft constraints to minimize the number of features, such as sparse support vector bshanks@30: machines. bshanks@33: 4.Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult bshanks@33: to identify because the boundaries are misdrawn, or because it does not “really” exist as a single area, at least on the bshanks@30: genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its bshanks@30: boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create bshanks@30: a larger area which can be fit. bshanks@51: # Linear discriminant analysis bshanks@64: Decision trees todo bshanks@64: For each cortical area, we used the C4.5 algorithm to find a pruned decision tree and ruleset for that area. We achieved bshanks@64: estimated classification accuracy of more than 99.6% on each cortical area (as evaluated on the training data without bshanks@64: cross-validation; so actual accuracy is expected to be lower). However, the resulting decision trees each made use of many bshanks@64: genes. bshanks@30: Apply these algorithms to the cortex bshanks@30: 1.Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert bshanks@30: between SEV, NIFTI and MATLAB formats. bshanks@30: 2.Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it. bshanks@30: 3.Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries. bshanks@30: 4.Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify bshanks@30: that area; and we will also present lists of “panels” of genes that can be used to delineate many areas at once. bshanks@30: Develop algorithms to suggest a division of a structure into anatomical parts bshanks@60: # mixture models, etc bshanks@30: 1.Explore dimensionality reduction algorithms applied to pixels: including TODO bshanks@30: 2.Explore dimensionality reduction algorithms applied to genes: including TODO bshanks@30: 3.Explore clustering algorithms applied to pixels: including TODO bshanks@30: 4.Explore clustering algorithms applied to genes: including gene shaving, TODO bshanks@30: 5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps bshanks@30: 6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex bshanks@51: # Linear discriminant analysis bshanks@51: # jbt, coclustering bshanks@51: # self-organizing map bshanks@53: # confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting bshanks@53: # compare using clustering scores bshanks@64: # multivariate gradient similarity bshanks@66: # deep belief nets bshanks@66: # note: slice artifact bshanks@33: Bibliography & References Cited bshanks@53: [1]Tanya Barrett, Dennis B. 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