bshanks@112: Introduction bshanks@112: Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohisto- bshanks@112: chemistry, in situ transgenic reporter, microarray voxelation, and others, allow the expression levels bshanks@112: of many genes at many locations to be compared. Our goal is to develop automated methods to bshanks@112: relate spatial variation in gene expression to anatomy. We want to find marker genes for specific bshanks@96: anatomical regions, and also to draw new anatomical maps based on gene expression patterns. bshanks@112: We will validate these methods by applying them to 46 anatomical areas within the cerebral cortex, bshanks@112: by using the Allen Mouse Brain Atlas coronal dataset (ABA). bshanks@112: This project has three primary goals: bshanks@112: (1) develop an algorithm to screen spatial gene expression data for combinations of marker bshanks@112: genes which selectively target anatomical regions. bshanks@112: (2) develop an algorithm to suggest new ways of carving up a structure into anatomically dis- bshanks@112: tinct regions, based on spatial patterns in gene expression. bshanks@112: (3) adapt our tools for the analysis of multi/hyperspectral imaging data from the Geographic bshanks@112: Information Systems (GIS) community. bshanks@112: We will create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened bshanks@112: version of the Allen Mouse Brain Atlas ISH data, as well as the boundaries of cortical anatomical bshanks@112: areas. We will use this dataset to validate the methods developed in (1) and (2). In addition to bshanks@112: its use in neuroscience, this dataset will be useful as a sample dataset for the machine learning bshanks@112: community. bshanks@112: Although our particular application involves the 3D spatial distribution of gene expression, the bshanks@112: methods we will develop will generalize to any high-dimensional data over points located in a low- bshanks@112: dimensional space. In particular, our methods could be applied to the analysis of multi/hyperspectral bshanks@112: imaging data, or alternately to genome-wide sequencing data derived from sets of tissues and dis- bshanks@112: ease states. bshanks@112: All algorithms that we develop will be implemented in a GPL open-source software toolkit. The bshanks@112: toolkit and the datasets will be published and freely available for others to use. bshanks@112: __________________ bshanks@112: Background and related work bshanks@112: Cortical anatomy bshanks@112: The cortex is divided into areas and layers. Because of the cortical columnar organization, the bshanks@112: parcellation of the cortex into areas can be drawn as a 2-D map on the surface of the cortex. In the bshanks@112: third dimension, the boundaries between the areas continue downwards into the cortical depth, bshanks@112: perpendicular to the surface. The layer boundaries run parallel to the surface. One can picture an bshanks@112: area of the cortex as a slice of a six-layered cake1. bshanks@112: It is known that different cortical areas have distinct roles in both normal functioning and in bshanks@112: disease processes, yet there are no known marker genes for most cortical areas. When it is nec- bshanks@112: essary to divide a tissue sample into cortical areas, this is a manual process that requires a skilled bshanks@112: 1Outside of isocortex, the number of layers varies. bshanks@112: 1 bshanks@112: bshanks@112: human to combine multiple visual cues and interpret them in the context of their approximate bshanks@112: location upon the cortical surface. bshanks@112: Even the questions of how many areas should be recognized in cortex, and what their arrange- bshanks@112: ment is, are still not completely settled. A proposed division of the cortex into areas is called a bshanks@112: cortical map. In the rodent, the lack of a single agreed-upon map can be seen by contrasting the bshanks@112: recent maps given by Swanson[21] on the one hand, and Paxinos and Franklin[16] on the other. bshanks@112: While the maps are certainly very similar in their general arrangement, significant differences re- bshanks@112: main. bshanks@112: The Allen Mouse Brain Atlas dataset bshanks@112: The Allen Mouse Brain Atlas (ABA) data[13] were produced by doing in-situ hybridization on bshanks@112: slices of male, 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, bshanks@112: and these pictures were semi-automatically analyzed to create a digital measurement of gene bshanks@112: expression levels at each location in each slice. Per slice, cellular spatial resolution is achieved. bshanks@112: Using this method, a single physical slice can only be used to measure one single gene; many bshanks@112: different mouse brains were needed in order to measure the expression of many genes. bshanks@112: Mus musculus is thought to contain about 22,000 protein-coding genes[26]. The ABA contains bshanks@112: data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured bshanks@112: in coronal sections. Our dataset is derived from only the coronal subset of the ABA2. An auto- bshanks@112: mated nonlinear alignment procedure located the 2D data from the various slices in a single 3D bshanks@112: coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a bshanks@112: side. There are 67x41x58 = 159,326 voxels, of which 51,533 are in the brain[15]. For each voxel bshanks@112: and each gene, the expression energy[13] within that voxel is made available. bshanks@112: The ABA is not the only large public spatial gene expression dataset[8][25][5][14][24][4][23][20][3]. bshanks@112: However, with the exception of the ABA, GenePaint[25], and EMAGE[24], most of the other re- bshanks@112: sources have not (yet) extracted the expression intensity from the ISH images and registered the bshanks@112: results into a single 3-D space. bshanks@112: The remainder of the background section will be divided into three parts, one for each major bshanks@112: goal. bshanks@112: Goal 1, From Areas to Genes: Given a map of regions, find genes that mark those regions bshanks@112: Machine learning terminology: classifiers The task of looking for marker genes for known bshanks@112: anatomical regions means that one is looking for a set of genes such that, if the expression level bshanks@112: of those genes is known, then the locations of the regions can be inferred. bshanks@112: If we define the regions so that they cover the entire anatomical structure to be subdivided, bshanks@112: and restrict ourselves to looking at one voxel at a time, we may say that we are using gene bshanks@112: expression in each voxel to assign that voxel to the proper area. We call this a classification bshanks@112: task, because each voxel is being assigned to a class (namely, its region). An understanding bshanks@112: of the relationship between the combination of gene expression levels and the locations of the bshanks@112: regions may be expressed as a function. The input to this function is a voxel, along with the gene bshanks@112: expression levels within that voxel; the output is the regional identity of the target voxel, that is, the bshanks@112: ____________________________________ bshanks@112: 2The sagittal data do not cover the entire cortex, and also have greater registration error[15]. Genes were selected bshanks@112: by the Allen Institute for coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc bshanks@112: identification of a marked non-ubiquitous expression pattern”[15]. bshanks@112: 2 bshanks@112: bshanks@112: region to which the target voxel belongs. We call this function a classifier. In general, the input to bshanks@112: a classifier is called an instance, and the output is called a label (or a class label). bshanks@112: Our goal is not to produce a single classifier, but rather to develop an automated method for bshanks@112: determining a classifier for any known anatomical structure. Therefore, we seek a procedure by bshanks@112: which a gene expression dataset may be analyzed in concert with an anatomical atlas in order to bshanks@112: produce a classifier. The initial gene expression dataset used in the construction of the classifier bshanks@112: is called training data. In the machine learning literature, this sort of procedure may be thought bshanks@112: of as a supervised learning task, defined as a task in which the goal is to learn a mapping from bshanks@112: instances to labels, and the training data consists of a set of instances (voxels) for which the labels bshanks@112: (regions) are known. bshanks@112: Each gene expression level is called a feature, and the selection of which genes3 to look at is bshanks@112: called feature selection. Feature selection is one component of the task of learning a classifier. bshanks@112: One class of feature selection methods assigns some sort of score to each candidate gene. bshanks@112: The top-ranked genes are then chosen. Some scoring measures can assign a score to a set of bshanks@112: selected genes, not just to a single gene; in this case, a dynamic procedure may be used in which bshanks@112: features are added and subtracted from the selected set depending on how much they raise the bshanks@112: score. Such procedures are called “stepwise” or “greedy”. bshanks@112: Although the classifier itself may only look at the gene expression data within each voxel be- bshanks@112: fore classifying that voxel, the algorithm which constructs the classifier may look over the entire bshanks@112: dataset. We can categorize score-based feature selection methods depending on how the score bshanks@112: of calculated. Often the score calculation consists of assigning a sub-score to each voxel, and bshanks@112: then aggregating these sub-scores into a final score. If only information from nearby voxels is bshanks@112: used to calculate a voxel’s sub-score, then we say it is a local scoring method. If only information bshanks@112: from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring bshanks@112: method. bshanks@112: Our Strategy for Goal 1 bshanks@112: Key questions when choosing a learning method are: What are the instances? What are the bshanks@112: features? How are the features chosen? Here are four principles that outline our answers to these bshanks@112: questions. bshanks@112: Principle 1: Combinatorial gene expression bshanks@112: It is too much to hope that every anatomical region of interest will be identified by a single bshanks@112: gene. For example, in the cortex, there are some areas which are not clearly delineated by any bshanks@112: gene included in the ABA coronal dataset. However, at least some of these areas can be delin- bshanks@112: eated by looking at combinations of genes (an example of an area for which multiple genes are bshanks@112: necessary and sufficient is provided in Preliminary Results, Figure 4). Therefore, each instance bshanks@112: should contain multiple features (genes). bshanks@112: Principle 2: Only look at combinations of small numbers of genes bshanks@112: When the classifier classifies a voxel, it is only allowed to look at the expression of the genes bshanks@112: which have been selected as features. The more data that are available to a classifier, the better bshanks@112: that it can do. Why not include every gene as a feature? The reason is that we wish to employ the bshanks@112: classifier in situations in which it is not feasible to gather data about every gene. For example, if we bshanks@112: ____________________________________ bshanks@112: 3Strictly speaking, the features are gene expression levels, but we’ll call them genes. bshanks@112: 3 bshanks@112: bshanks@112: want to use the expression of marker genes as a trigger for some regionally-targeted intervention, bshanks@112: then our intervention must contain a molecular mechanism to check the expression level of each bshanks@112: marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks bshanks@112: the level of more than a handful of genes. Therefore, we must select only a few genes as features. bshanks@112: The requirement to find combinations of only a small number of genes limits us from straightfor- bshanks@112: wardly applying many of the most simple techniques from the field of supervised machine learning. bshanks@112: In the parlance of machine learning, our task combines feature selection with supervised learning. bshanks@112: Principle 3: Use geometry in feature selection bshanks@112: When doing feature selection with score-based methods, the simplest thing to do would be bshanks@112: to score the performance of each voxel by itself and then combine these scores (pointwise scor- bshanks@112: ing). A more powerful approach is to also use information about the geometric relations between bshanks@112: each voxel and its neighbors; this requires non-pointwise, local scoring methods. See Preliminary bshanks@112: Results, figure 3 for evidence of the complementary nature of pointwise and local scoring methods. bshanks@112: Principle 4: Work in 2-D whenever possible bshanks@112: There are many anatomical structures which are commonly characterized in terms of a two- bshanks@112: dimensional manifold. When it is known that the structure that one is looking for is two-dimensional, bshanks@112: the results may be improved by allowing the analysis algorithm to take advantage of this prior bshanks@112: knowledge. In addition, it is easier for humans to visualize and work with 2-D data. bshanks@112: Goal 2, From Genes to Areas: given gene expression data, discover a map of regions bshanks@101: Machine learning terminology: clustering bshanks@112: If one is given a dataset consisting merely of instances, with no class labels, then analysis of bshanks@112: the dataset is referred to as unsupervised learning in the jargon of machine learning. One thing bshanks@112: that you can do with such a dataset is to group instances together. A set of similar instances is bshanks@112: called a cluster, and the activity of grouping the data into clusters is called clustering or cluster bshanks@112: analysis. bshanks@112: The task of deciding how to carve up a structure into anatomical regions can be put into these bshanks@112: terms. The instances are once again voxels (or pixels) along with their associated gene expression bshanks@112: profiles. We make the assumption that voxels from the same anatomical region have similar gene bshanks@112: expression profiles, at least compared to the other regions. This means that clustering voxels is bshanks@112: the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into bshanks@112: clusters of voxels with similar gene expression. bshanks@112: It is desirable to determine not just one set of regions, but also how these regions relate to bshanks@112: each other. The outcome of clustering may be a hierarchical tree of clusters, rather than a single bshanks@112: set of clusters which partition the voxels. This is called hierarchical clustering. bshanks@112: Similarity scores A crucial choice when designing a clustering method is how to measure bshanks@112: similarity, across either pairs of instances, or clusters, or both. There is much overlap between bshanks@112: scoring methods for feature selection (discussed above under Goal 1) and scoring methods for bshanks@112: similarity. bshanks@112: Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene bshanks@112: expression feature vector. By “dimension”, we mean the dimension of this vector, not the spatial bshanks@112: 4 bshanks@112: bshanks@112: dimension of the underlying data. bshanks@112: bshanks@112: bshanks@104: Figure 1: Top row: Genes Nfic bshanks@112: and A930001M12Rik are the most bshanks@104: correlated with area SS (somatosen- bshanks@112: sory cortex). Bottom row: Genes bshanks@104: C130038G02Rik and Cacna1i are bshanks@112: those with the best fit using logistic bshanks@104: regression. Within each picture, the bshanks@104: vertical axis roughly corresponds to bshanks@104: anterior at the top and posterior at the bshanks@104: bottom, and the horizontal axis roughly bshanks@104: corresponds to medial at the left and bshanks@104: lateral at the right. The red outline is bshanks@104: the boundary of region SS. Pixels are bshanks@104: colored according to correlation, with bshanks@104: red meaning high correlation and blue bshanks@112: meaning low. Unlike Goal 1, there is no externally-imposed need to bshanks@112: select only a handful of informative genes for inclusion bshanks@112: in the instances. However, some clustering algorithms bshanks@112: perform better on small numbers of features4. There are bshanks@112: techniques which “summarize” a larger number of fea- bshanks@112: tures using a smaller number of features; these tech- bshanks@112: niques go by the name of feature extraction or dimen- bshanks@112: sionality reduction. The small set of features that such a bshanks@112: technique yields is called the reduced feature set. Note bshanks@112: that the features in the reduced feature set do not neces- bshanks@112: sarily correspond to genes; each feature in the reduced bshanks@112: set may be any function of the set of gene expression bshanks@112: levels. bshanks@112: Clustering genes rather than voxels Although the bshanks@112: ultimate goal is to cluster the instances (voxels or pixels), bshanks@112: one strategy to achieve this goal is to first cluster the bshanks@112: features (genes). There are two ways that clusters of bshanks@112: genes could be used. bshanks@112: Gene clusters could be used as part of dimensionality bshanks@112: reduction: rather than have one feature for each gene, bshanks@112: we could have one reduced feature for each gene cluster. bshanks@112: Gene clusters could also be used to directly yield a bshanks@112: clustering on instances. This is because many genes bshanks@112: have an expression pattern which seems to pick out a bshanks@112: single, spatially contiguous region. This suggests the fol- bshanks@112: lowing procedure: cluster together genes which pick out bshanks@112: similar regions, and then to use the more popular com- bshanks@112: mon regions as the final clusters. In Preliminary Results, bshanks@112: Figure 7, we show that a number of anatomically recog- bshanks@112: nized cortical regions, as well as some “superregions” formed by lumping together a few regions, bshanks@112: are associated with gene clusters in this fashion. bshanks@112: Goal 3: interoperability with multi/hyperspectral imaging analysis software bshanks@112: A typical color image associates each pixel with a vector of three values. Multispectral and hyper- bshanks@112: spectral images, however, are images which associate each pixel with a vector containing many bshanks@112: values. The different positions in the vector correspond to different bands of electromagnetic bshanks@112: wavelengths5. bshanks@112: Some analysis techniques for hyperspectral imaging, especially preprocessing and calibration bshanks@112: techniques, make use of the information that the different values captured at each pixel represent bshanks@112: ____________________________________ bshanks@112: 4First, because the number of features in the reduced dataset is less than in the original dataset, the running time of bshanks@112: clustering algorithms may be much less. Second, it is thought that some clustering algorithms may give better results bshanks@112: on reduced data. bshanks@112: 5In hyperspectral imaging, the bands are adjacent, and the number of different bands is larger. For conciseness, we bshanks@112: discuss only hyperspectral imaging, but our methods are also well suited to multispectral imaging with many bands. bshanks@112: 5 bshanks@112: bshanks@112: adjacent wavelengths of light, which can be combined to make a spectrum. Other analysis tech- bshanks@112: niques ignore the interpretation of the values measured, and their relationship to each other within bshanks@112: the electromagnetic spectrum, instead treating them blindly as completely separate features. bshanks@112: With both hyperspectral imaging and spatial gene expression data, each location in space bshanks@112: is associated with more than three numerical feature values. The analysis of hyperspectral im- bshanks@112: ages can involve supervised classification and unsupervised learning. Often hyperspectral images bshanks@112: come from satellites looking at the Earth, and it is desirable to classify what sort of objects occupy bshanks@112: a given area of land. Sometimes detailed training data is not available, in which case it is desirable bshanks@112: at least to cluster together those regions of land which contain similar objects. bshanks@112: We believe that it may be possible for these two different field to share some common compu- bshanks@112: tational tools. To this end, we intend to make use of existing hyperspectral imaging software when bshanks@112: possible, and to develop new software in such a way so as to make it easy to use for the purpose bshanks@112: of hyperspectral image analysis, as well as for our primary purpose of spatial gene expression bshanks@112: data analysis. bshanks@112: Related work bshanks@112: bshanks@112: Figure 2: Gene Pitx2 bshanks@112: is selectively underex- bshanks@112: pressed in area SS. As noted above, the GIS community has developed tools for supervised bshanks@112: classification and unsupervised clustering in the context of the analysis bshanks@112: of hyperspectral imaging data. One tool is Spectral Python6. Spectral bshanks@112: Python implements various supervised and unsupervised classification bshanks@112: methods, as well as utility functions for loading, viewing, and saving bshanks@112: spatial data. Although Spectral Python has feature extraction methods bshanks@112: (such as principal components analysis) which create a small set of bshanks@112: new features computed based on the original features, it does not have bshanks@112: feature selection methods, that is, methods to select a small subset bshanks@112: out of the original features (although feature selection in hyperspectral bshanks@112: imaging has been investigated by others[19]. bshanks@112: There is a substantial body of work on the analysis of gene expression data. Most of this con- bshanks@112: cerns gene expression data which are not fundamentally spatial7. Here we review only that work bshanks@112: which concerns the automated analysis of spatial gene expression data with respect to anatomy. bshanks@112: Relating to Goal 1, GeneAtlas[5] and EMAGE [24] allow the user to construct a search query by bshanks@112: demarcating regions and then specifying either the strength of expression or the name of another bshanks@112: gene or dataset whose expression pattern is to be matched. Neither GeneAtlas nor EMAGE allow bshanks@112: one to search for combinations of genes that define a region in concert. bshanks@112: Relating to Goal 2, EMAGE[24] allows the user to select a dataset from among a large number bshanks@112: of alternatives, or by running a search query, and then to cluster the genes within that dataset. bshanks@112: EMAGE clusters via hierarchical complete linkage clustering. bshanks@112: [15] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene bshanks@112: Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the bshanks@112: seed voxel, (2) yields a list of genes which are overexpressed in that cluster. Correlation: The user bshanks@112: selects a seed voxel and the system then shows the user how much correlation there is between bshanks@112: the gene expression profile of the seed voxel and every other voxel. Clusters: AGEA includes a bshanks@112: ____________________________________ bshanks@112: 6http://spectralpython.sourceforge.net/ bshanks@112: 7By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by bshanks@112: spatial coordinates; not just data which have only a few different locations or which is indexed by anatomical label. bshanks@112: 6 bshanks@112: bshanks@112: preset hierarchical clustering of voxels based on a recursive bifurcation algorithm with correlation bshanks@112: as the similarity metric. AGEA has been applied to the cortex. The paper describes interesting bshanks@112: results on the structure of correlations between voxel gene expression profiles within a handful of bshanks@112: cortical areas. However, that analysis neither looks for genes marking cortical areas, nor does it bshanks@112: suggest a cortical map based on gene expression data. Neither of the other components of AGEA bshanks@112: can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes for the bshanks@112: cortical areas; and AGEA’s hierarchical clustering does not produce clusters corresponding to the bshanks@112: cortical areas8. bshanks@112: bshanks@112: bshanks@104: Figure 3: The top row shows the two bshanks@104: genes which (individually) best predict bshanks@104: area AUD, according to logistic regres- bshanks@112: sion. The bottom row shows the two bshanks@112: genes which (individually) best match bshanks@112: area AUD, according to gradient sim- bshanks@104: ilarity. From left to right and top to bshanks@104: bottom, the genes are Ssr1, Efcbp1, bshanks@112: Ptk7, and Aph1a. [6] looks at the mean expression level of genes within bshanks@112: anatomical regions, and applies a Student’s t-test to de- bshanks@112: termine whether the mean expression level of a gene is bshanks@112: significantly higher in the target region. This relates to bshanks@112: our Goal 1. [6] also clusters genes, relating to our Goal bshanks@112: 2. For each cluster, prototypical spatial expression pat- bshanks@112: terns were created by averaging the genes in the cluster. bshanks@112: The prototypes were analyzed manually, without cluster- bshanks@112: ing voxels. bshanks@112: These related works differ from our strategy for Goal bshanks@112: 1 in at least three ways. First, they find only single genes, bshanks@112: whereas we will also look for combinations of genes. bshanks@112: Second, they usually can only use overexpression as bshanks@112: a marker, whereas we will also search for underexpres- bshanks@112: sion. Third, they use scores based on pointwise expres- bshanks@112: sion levels, whereas we will also use geometric scores bshanks@112: such as gradient similarity (described in Preliminary Re- bshanks@112: sults). Figures 4, 2, and 3 in the Preliminary Results bshanks@112: section contain evidence that each of our three choices bshanks@112: is the right one. bshanks@112: [10] describes a technique to find combinations of bshanks@112: marker genes to pick out an anatomical region. They bshanks@112: use an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) bshanks@112: images in order to match a target image. They apply their technique for finding combinations of bshanks@112: marker genes for the purpose of clustering genes around a “seed gene”. bshanks@112: Relating to our Goal 2, some researchers have attempted to parcellate cortex on the basis of bshanks@112: non-gene expression data. For example, [17], [2], [18], and [1] associate spots on the cortex with bshanks@112: the radial profile9 of response to some stain ([12] uses MRI), extract features from this profile, and bshanks@112: then use similarity between surface pixels to cluster. bshanks@112: [22] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In bshanks@112: addition to manual analysis, two clustering methods were employed, a modified Non-negative bshanks@112: Matrix Factorization (NNMF), and a hierarchical bifurcation clustering scheme using correlation as bshanks@112: ____________________________________ bshanks@112: 8In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but bshanks@112: the same layer are often stronger than pairwise correlations between the gene expression of voxels in different layers bshanks@112: but the same area. Therefore, a pairwise voxel correlation clustering algorithm will tend to create clusters representing bshanks@112: cortical layers, not areas. bshanks@112: 9A radial profile is a profile along a line perpendicular to the cortical surface. bshanks@112: 7 bshanks@112: bshanks@112: similarity. The paper yielded impressive results, proving the usefulness of computational genomic bshanks@112: anatomy. We have run NNMF on the cortical dataset, and while the results are promising, other bshanks@112: methods may perform as well or better (see Preliminary Results, Figure 6). bshanks@112: Comparing previous work with our Goal 1, there has been fruitful work on finding marker genes, bshanks@112: but only one of the projects explored combinations of marker genes, and none of them compared bshanks@112: the results obtained by using different algorithms or scoring methods. Comparing previous work bshanks@112: with Goal 2, although some projects obtained clusterings, there has not been much comparison bshanks@112: between different algorithms or scoring methods, so it is likely that the best clustering method for bshanks@112: this application has not yet been found. Also, none of these projects did a separate dimensionality bshanks@112: reduction step before clustering pixels, or tried to cluster genes first in order to guide automated bshanks@112: clustering of pixels into spatial regions, or used co-clustering algorithms. bshanks@112: In summary, (a) only one of the previous projects explores combinations of marker genes, (b) bshanks@112: there has been almost no comparison of different algorithms or scoring methods, and (c) there bshanks@112: has been no work on computationally finding marker genes applied to cortical areas, or on finding bshanks@112: a hierarchical clustering that will yield a map of cortical areas de novo from gene expression data. bshanks@112: Our project is guided by a concrete application with a well-specified criterion of success (how bshanks@112: well we can find marker genes for / reproduce the layout of cortical areas), which will provide a bshanks@112: solid basis for comparing different methods. bshanks@112: _________________________________________________ bshanks@112: Data sharing plan bshanks@112: bshanks@112: bshanks@104: Figure 4: Upper left: wwc1. Upper bshanks@104: right: mtif2. Lower left: wwc1 + mtif2 bshanks@104: (each pixel’s value on the lower left is bshanks@104: the sum of the corresponding pixels in bshanks@112: the upper row). We are enthusiastic about the sharing of methods and bshanks@112: data, and at the conclusion of the project, we will make bshanks@112: all of our data and computer source code publically avail- bshanks@112: able, either in supplemental attachments to publications, bshanks@112: or on a website. The source code will be released under bshanks@112: the GNU Public License. We intend to include a soft- bshanks@112: ware program which, when run, will take as input the bshanks@112: Allen Brain Atlas raw data, and produce as output all bshanks@112: numbers and charts found in publications resulting from bshanks@112: the project. Source code to be released will include ex- bshanks@112: tensions to Caret[7], an existing open-source scientific bshanks@112: imaging program, and to Spectral Python. Data to be bshanks@112: released will include the 2-D “flat map” dataset. This bshanks@112: dataset will be submitted to a machine learning dataset bshanks@112: repository. bshanks@112: Broader impacts bshanks@112: In addition to validating the usefulness of the algorithms, bshanks@112: the application of these methods to cortex will produce bshanks@112: immediate benefits, because there are currently no known genetic markers for most cortical areas. bshanks@112: The method developed in Goal 1 will be applied to each cortical area to find a set of marker bshanks@112: genes such that the combinatorial expression pattern of those genes uniquely picks out the target bshanks@112: area. Finding marker genes will be useful for drug discovery as well as for experimentation be- bshanks@112: cause marker genes can be used to design interventions which selectively target individual cortical bshanks@112: areas. bshanks@112: 8 bshanks@112: bshanks@112: The application of the marker gene finding algorithm to the cortex will also support the develop- bshanks@112: ment of new neuroanatomical methods. In addition to finding markers for each individual cortical bshanks@112: areas, we will find a small panel of genes that can find many of the areal boundaries at once. bshanks@112: The method developed in Goal 2 will provide a genoarchitectonic viewpoint that will contribute bshanks@112: to the creation of a better cortical map. bshanks@112: The methods we will develop will be applicable to other datasets beyond the brain, and even to bshanks@112: datasets outside of biology. The software we develop will be useful for the analysis of hyperspectral bshanks@112: images. Our project will draw attention to this area of overlap between neuroscience and GIS, and bshanks@112: may lead to future collaborations between these two fields. The cortical dataset that we produce bshanks@112: will be useful in the machine learning community as a sample dataset that new algorithms can be bshanks@112: tested against. The availability of this sample dataset to the machine learning community may lead bshanks@112: to more interest in the design of machine learning algorithms to analyze spatial gene expression. bshanks@112: _ bshanks@112: Preliminary Results bshanks@112: Format conversion between SEV, MATLAB, NIFTI bshanks@112: We have created software to (politely) download all of the SEV files10 from the Allen Institute bshanks@112: website. We have also created software to convert between the SEV, MATLAB, and NIFTI file bshanks@112: formats, as well as some of Caret’s file formats. bshanks@112: Flatmap of cortex bshanks@112: We downloaded the ABA data and selected only those voxels which belong to cerebral cortex. bshanks@112: We divided the cortex into hemispheres. Using Caret[7], we created a mesh representation of the bshanks@112: surface of the selected voxels. For each gene, and for each node of the mesh, we calculated an bshanks@112: average of the gene expression of the voxels “underneath” that mesh node. We then flattened bshanks@112: the cortex, creating a two-dimensional mesh. We converted this grid into a MATLAB matrix. We bshanks@112: manually traced the boundaries of each of 46 cortical areas from the ABA coronal reference atlas bshanks@112: slides, and converted this region data into MATLAB format. bshanks@112: At this point, the data are in the form of a number of 2-D matrices, all in registration, with the bshanks@112: matrix entries representing a grid of points (pixels) over the cortical surface. There is one 2-D bshanks@112: matrix whose entries represent the regional label associated with each surface pixel. And for each bshanks@112: gene, there is a 2-D matrix whose entries represent the average expression level underneath each bshanks@112: surface pixel. The features and the target area are both functions on the surface pixels. They can bshanks@112: be referred to as scalar fields over the space of surface pixels; alternately, they can be thought of bshanks@112: as images which can be displayed on the flatmapped surface. bshanks@112: Feature selection and scoring methods bshanks@112: Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes bshanks@112: serve as a marker. For example, see Figure 2. bshanks@112: Correlation Recall that the instances are surface pixels, and consider the problem of attempt- bshanks@112: ing to classify each instance as either a member of a particular anatomical area, or not. The target bshanks@112: area can be represented as a boolean mask over the surface pixels. bshanks@112: 10SEV is a sparse format for spatial data. It is the format in which the ABA data is made available. bshanks@112: 9 bshanks@112: bshanks@112: We calculated the correlation between each gene and each cortical area. The top row of Figure bshanks@112: 1 shows the three genes most correlated with area SS. bshanks@112: Conditional entropy bshanks@112: For each region, we created and ran a forward stepwise procedure which attempted to find bshanks@112: pairs of genes such that the conditional entropy of the target area’s boolean mask, conditioned bshanks@112: upon the gene pair’s thresholded expression levels, is minimized. bshanks@112: This finds pairs of genes which are most informative (at least at these threshold levels) relative bshanks@112: to the question, “Is this surface pixel a member of the target area?”. The advantage over linear bshanks@112: methods such as logistic regression is that this takes account of arbitrarily nonlinear relationships; bshanks@112: for example, if the XOR of two variables predicts the target, conditional entropy would notice, bshanks@112: whereas linear methods would not. bshanks@112: Gradient similarity We noticed that the previous two scoring methods, which are pointwise, bshanks@112: often found genes whose pattern of expression did not look similar in shape to the target region. bshanks@112: For this reason we designed a non-pointwise scoring method to detect when a gene had a pattern bshanks@112: of expression which looked like it had a boundary whose shape is similar to the shape of the target bshanks@112: region. We call this scoring method “gradient similarity”. The formula is: bshanks@112: ∑ bshanks@112: pixel∈pixels cos(∠∇1 -∠∇2) ⋅|∇1| + |∇2| bshanks@112: 2 ⋅ pixel_value1 + pixel_value2 bshanks@112: 2 bshanks@112: where ∇1 and ∇2 are the gradient vectors of the two images at the current pixel; ∠∇i is the bshanks@112: angle of the gradient of image i at the current pixel; |∇i| is the magnitude of the gradient of image bshanks@112: i at the current pixel; and pixel_valuei is the value of the current pixel in image i. bshanks@112: The intuition is that we want to see if the borders of the pattern in the two images are similar; if bshanks@112: the borders are similar, then both images will have corresponding pixels with large gradients (be- bshanks@112: cause this is a border) which are oriented in a similar direction (because the borders are similar). bshanks@112: Gradient similarity provides information complementary to correlation bshanks@112: To show that gradient similarity can provide useful information that cannot be detected via bshanks@112: pointwise analyses, consider Fig. 3. The pointwise method in the top row identifies genes which bshanks@112: express more strongly in AUD than outside of it; its weakness is that this includes many areas bshanks@112: which don’t have a salient border matching the areal border. The geometric method identifies bshanks@112: genes whose salient expression border seems to partially line up with the border of AUD; its bshanks@112: weakness is that this includes genes which don’t express over the entire area. bshanks@112: Areas which can be identified by single genes Using gradient similarity, we have already bshanks@112: found single genes which roughly identify some areas and groupings of areas. For each of these bshanks@112: areas, an example of a gene which roughly identifies it is shown in Figure 5. We have not yet bshanks@112: cross-verified these genes in other atlases. bshanks@112: In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT bshanks@112: (anterior part of cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), bshanks@112: ACAv (ventral anterior cingulate), VIS (visual), AUD (auditory). bshanks@112: These results validate our expectation that the ABA dataset can be exploited to find marker bshanks@112: genes for many cortical areas, while also validating the relevancy of our new scoring method, bshanks@112: gradient similarity. bshanks@112: 10 bshanks@112: bshanks@112: bshanks@112: bshanks@112: bshanks@112: bshanks@104: Figure 5: From left to right and top bshanks@104: to bottom, single genes which roughly bshanks@104: identify areas SS (somatosensory pri- bshanks@112: mary + supplemental), SSs (supple- bshanks@104: mental somatosensory), PIR (piriform), bshanks@112: FRP (frontal pole), RSP (retrosplenial), bshanks@112: COApm (Cortical amygdalar, poste- bshanks@112: rior part, medial zone). Grouping bshanks@112: some areas together, we have also bshanks@112: found genes to identify the groups bshanks@104: ACA+PL+ILA+DP+ORB+MO (anterior bshanks@104: cingulate, prelimbic, infralimbic, dor- bshanks@104: sal peduncular, orbital, motor), poste- bshanks@112: rior and lateral visual (VISpm, VISpl, bshanks@104: VISI, VISp; posteromedial, posterolat- bshanks@112: eral, lateral, and primary visual; the bshanks@104: posterior and lateral visual area is dis- bshanks@104: tinguished from its neighbors, but not bshanks@104: from the entire rest of the cortex). The bshanks@112: genes are Pitx2, Aldh1a2, Ppfibp1, bshanks@112: Slco1a5, Tshz2, Trhr, Col12a1, Ets1. Combinations of multiple genes are useful and bshanks@112: necessary for some areas bshanks@112: In Figure 4, we give an example of a cortical area bshanks@112: which is not marked by any single gene, but which can be bshanks@112: identified combinatorially. According to logistic regres- bshanks@112: sion, gene wwc1 is the best fit single gene for predicting bshanks@112: whether or not a pixel on the cortical surface belongs to bshanks@112: the motor area (area MO). The upper-left picture in Fig- bshanks@112: ure 4 shows wwc1’s spatial expression pattern over the bshanks@112: cortex. The lower-right boundary of MO is represented bshanks@112: reasonably well by this gene, but the gene overshoots bshanks@112: the upper-left boundary. This flattened 2-D representa- bshanks@112: tion does not show it, but the area corresponding to the bshanks@112: overshoot is the medial surface of the cortex. MO is only bshanks@112: found on the dorsal surface. Gene mtif2 is shown in the bshanks@112: upper-right. Mtif2 captures MO’s upper-left boundary, but bshanks@112: not its lower-right boundary. Mtif2 does not express very bshanks@112: much on the medial surface. By adding together the val- bshanks@112: ues at each pixel in these two figures, we get the lower- bshanks@112: left image. This combination captures area MO much bshanks@112: better than any single gene. bshanks@112: This shows that our proposal to develop a method to bshanks@112: find combinations of marker genes is both possible and bshanks@112: necessary. bshanks@112: Multivariate supervised learning bshanks@112: Forward stepwise logistic regression Logistic regres- bshanks@112: sion is a popular method for predictive modeling of cat- bshanks@112: egorical data. As a pilot run, for five cortical areas (SS, bshanks@112: AUD, RSP, VIS, and MO), we performed forward step- bshanks@112: wise logistic regression to find single genes, pairs of bshanks@112: genes, and triplets of genes which predict areal identify. bshanks@112: This is an example of feature selection integrated with bshanks@112: prediction using a stepwise wrapper. Some of the sin- bshanks@112: gle genes found were shown in various figures through- bshanks@112: out this document, and Figure 4 shows a combination of bshanks@112: genes which was found. bshanks@112: SVM on all genes at once bshanks@112: In order to see how well one can do when looking at bshanks@112: all genes at once, we ran a support vector machine to bshanks@112: classify cortical surface pixels based on their gene ex- bshanks@112: pression profiles. We achieved classification accuracy of bshanks@112: about 81%11. However, as noted above, a classifier that bshanks@112: ____________________________________ bshanks@112: 115-fold cross-validation. bshanks@112: 11 bshanks@112: bshanks@112: looks at all the genes at once isn’t as practically useful bshanks@112: as a classifier that uses only a few genes. bshanks@112: Data-driven redrawing of the cortical map bshanks@112: We have applied the following dimensionality reduction algorithms to reduce the dimensionality bshanks@112: of the gene expression profile associated with each pixel: Principal Components Analysis (PCA), bshanks@112: Simple PCA, Multi-Dimensional Scaling, Isomap, Landmark Isomap, Laplacian eigenmaps, Local bshanks@112: Tangent Space Alignment, Stochastic Proximity Embedding, Fast Maximum Variance Unfolding, bshanks@112: Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing many of bshanks@112: the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the first, second, bshanks@112: and third rows of Figure 6. bshanks@112: After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. bshanks@112: To date we have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, bshanks@112: and landmark Isomap are shown in the bottom row of Figure 6. To compare, the leftmost picture bshanks@112: on the bottom row of Figure 6 shows some of the major subdivisions of cortex. These results show bshanks@112: that different dimensionality reduction techniques capture different aspects of the data and lead bshanks@112: to different clusterings, indicating the utility of our proposal to produce a detailed comparison of bshanks@112: these techniques as applied to the domain of genomic anatomy. bshanks@112: Many areas are captured by clusters of genes We also clustered the genes using gradient bshanks@112: similarity to see if the spatial regions defined by any clusters matched known anatomical regions. bshanks@112: Figure 7 shows, for ten sample gene clusters, each cluster’s average expression pattern, com- bshanks@112: pared to a known anatomical boundary. This suggests that it is worth attempting to cluster genes, bshanks@112: and then to use the results to cluster pixels. bshanks@112: Our plan: what remains to be done bshanks@112: Flatmap cortex and segment cortical layers bshanks@112: There are multiple ways to flatten 3-D data into 2-D. We will compare mappings from manifolds to bshanks@112: planes which attempt to preserve size (such as the one used by Caret[7]) with mappings which bshanks@112: preserve angle (conformal maps). We will also develop a segmentation algorithm to automatically bshanks@112: identify the layer boundaries. bshanks@112: Develop algorithms that find genetic markers for anatomical regions bshanks@112: Scoring measures and feature selection We will develop scoring methods for evaluating how bshanks@112: good individual genes are at marking areas. We will compare pointwise, geometric, and information- bshanks@112: theoretic measures. We already developed one entirely new scoring method (gradient similarity), bshanks@112: but we may develop more. Scoring measures that we will explore will include the L1 norm, cor- bshanks@112: relation, expression energy ratio, conditional entropy, gradient similarity, Jaccard similarity, Dice bshanks@112: similarity, Hough transform, and statistical tests such as Student’s t-test, and the Mann-Whitney bshanks@112: U test (a non-parametric test). In addition, any classifier induces a scoring measure on genes by bshanks@112: taking the prediction error when using that gene to predict the target. bshanks@112: Using some combination of these measures, we will develop a procedure to find single marker bshanks@112: genes for anatomical regions: for each cortical area, we will rank the genes by their ability to bshanks@112: delineate that area. We will quantitatively compare the list of single genes generated by our bshanks@112: method to the lists generated by methods which are mentioned in Related Work. bshanks@112: 12 bshanks@112: bshanks@112: bshanks@104: Figure 6: First row: the first 6 reduced dimensions, using PCA. Sec- bshanks@112: ond row: the first 6 reduced dimensions, using NNMF. Third row: the bshanks@112: first six reduced dimensions, using landmark Isomap. Bottom row: bshanks@112: examples of kmeans clustering applied to reduced datasets to find bshanks@112: 7 clusters. Left: 19 of the major subdivisions of the cortex. Sec- bshanks@112: ond from left: PCA. Third from left: NNMF. Right: Landmark Isomap. bshanks@112: Additional details: In the third and fourth rows, 7 dimensions were bshanks@112: found, but only 6 displayed. In the last row: for PCA, 50 dimensions bshanks@112: were used; for NNMF, 6 dimensions were used; for landmark Isomap, bshanks@112: 7 dimensions were used. Some cortical areas have bshanks@112: no single marker genes but bshanks@112: can be identified by com- bshanks@112: binatorial coding. This re- bshanks@112: quires multivariate scoring bshanks@112: measures and feature se- bshanks@112: lection procedures. Many bshanks@112: of the measures, such bshanks@112: as expression energy, gra- bshanks@112: dient similarity, Jaccard, bshanks@112: Dice, Hough, Student’s t, bshanks@112: and Mann-Whitney U are bshanks@112: univariate. We will ex- bshanks@112: tend these scoring mea- bshanks@112: sures for use in multivariate bshanks@112: feature selection, that is, bshanks@112: for scoring how well com- bshanks@112: binations of genes, rather bshanks@112: than individual genes, can bshanks@112: distinguish a target area. bshanks@112: There are existing mul- bshanks@112: tivariate forms of some bshanks@112: of the univariate scoring bshanks@112: measures, for example, bshanks@112: Hotelling’s T-square is a bshanks@112: multivariate analog of Stu- bshanks@112: dent’s t. bshanks@112: We will develop a fea- bshanks@112: ture selection procedure for choosing the best small set of marker genes for a given anatomical bshanks@112: area. In addition to using the scoring measures that we develop, we will also explore (a) feature bshanks@112: selection using a stepwise wrapper over “vanilla” classifiers such as logistic regression, (b) super- bshanks@112: vised learning methods such as decision trees which incrementally/greedily combine single gene bshanks@112: markers into sets, and (c) supervised learning methods which use soft constraints to minimize bshanks@112: number of features used, such as sparse support vector machines (SVMs). bshanks@112: Since errors of displacement and of shape may cause genes and target areas to match less bshanks@112: than they should, we will consider the robustness of feature selection methods in the presence of bshanks@112: error. Some of these methods, such as the Hough transform, are designed to be resistant in the bshanks@112: presence of error, but many are not. bshanks@112: An area may be difficult to identify because the boundaries are misdrawn in the atlas, or be- bshanks@112: cause the shape of the natural domain of gene expression corresponding to the area is different bshanks@112: from the shape of the area as recognized by anatomists. We will develop extensions to our pro- bshanks@112: cedure which (a) detect when a difficult area could be fit if its boundary were redrawn slightly12, bshanks@112: ____________________________________ bshanks@112: 12Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene ex- bshanks@112: pression by multiple sources of evidence. Interestingly, the need to detect “natural spatial domains of gene expression” bshanks@112: in a data-driven fashion means that the methods of Goal 2 might be useful in achieving Goal 1, as well – particularly bshanks@112: 13 bshanks@112: bshanks@112: and (b) detect when a difficult area could be combined with adjacent areas to create a larger area bshanks@112: which can be fit. bshanks@112: A future publication on the method that we develop in Goal 1 will review the scoring measures bshanks@112: and quantitatively compare their performance in order to provide a foundation for future research bshanks@112: of methods of marker gene finding. We will measure the robustness of the scoring measures as bshanks@112: well as their absolute performance on our dataset. bshanks@112: Develop algorithms to suggest a division of a structure into anatomical parts bshanks@112: bshanks@112: Figure 7: Prototypes corresponding to sample gene clus- bshanks@112: ters, clustered by gradient similarity. Region boundaries for bshanks@112: the region that most matches each prototype are overlaid. Dimensionality reduction on gene bshanks@112: expression profiles We have al- bshanks@112: ready described the application of bshanks@112: ten dimensionality reduction algo- bshanks@112: rithms for the purpose of replacing bshanks@112: the gene expression profiles, which bshanks@112: are vectors of about 4000 gene ex- bshanks@112: pression levels, with a smaller num- bshanks@112: ber of features. We plan to further ex- bshanks@112: plore and interpret these results, as bshanks@112: well as to apply other unsupervised bshanks@112: learning algorithms, including inde- bshanks@112: pendent components analysis, self- bshanks@112: organizing maps, and generative models such as deep Boltzmann machines. We will explore bshanks@112: ways to quantitatively compare the relevance of the different dimensionality reduction methods for bshanks@112: identifying cortical areal boundaries. bshanks@112: Dimensionality reduction on pixels Instead of applying dimensionality reduction to the gene bshanks@112: expression profiles, the same techniques can be applied instead to the pixels. It is possible that bshanks@112: the features generated in this way by some dimensionality reduction techniques will directly corre- bshanks@112: spond to interesting spatial regions. bshanks@112: Clustering and segmentation on pixels We will explore clustering and image segmentation bshanks@112: algorithms in order to segment the pixels into regions. We will explore k-means, spectral cluster- bshanks@112: ing, gene shaving[9], recursive division clustering, multivariate generalizations of edge detectors, bshanks@112: multivariate generalizations of watershed transformations, region growing, active contours, graph bshanks@112: partitioning methods, and recursive agglomerative clustering with various linkage functions. These bshanks@112: methods can be combined with dimensionality reduction. bshanks@112: Clustering on genes We have already shown that the procedure of clustering genes according bshanks@112: to gradient similarity, and then creating an averaged prototype of each cluster’s expression pattern, bshanks@112: yields some spatial patterns which match cortical areas (Figure 7). We will further explore the bshanks@112: clustering of genes. bshanks@112: In addition to using the cluster expression prototypes directly to identify spatial regions, this bshanks@112: might be useful as a component of dimensionality reduction. For example, one could imagine bshanks@112: clustering similar genes and then replacing their expression levels with a single average expression bshanks@112: ____________________________________ bshanks@112: discriminative dimensionality reduction. bshanks@112: 14 bshanks@112: bshanks@112: level, thereby removing some redundancy from the gene expression profiles. One could then bshanks@112: perform clustering on pixels (possibly after a second dimensionality reduction step) in order to bshanks@112: identify spatial regions. It remains to be seen whether removal of redundancy would help or hurt bshanks@112: the ultimate goal of identifying interesting spatial regions. bshanks@112: Co-clustering We will explore some algorithms which simultaneously incorporate clustering bshanks@112: on instances and on features (in our case, pixels and genes), for example, IRM[11]. These are bshanks@112: called co-clustering or biclustering algorithms. bshanks@112: Compare different methods In order to tell which method is best for genomic anatomy, for bshanks@112: each experimental method we will compare the cortical map found by unsupervised learning to a bshanks@112: cortical map derived from the Allen Reference Atlas. We will explore various quantitative metrics bshanks@112: that purport to measure how similar two clusterings are, such as Jaccard, Rand index, Fowlkes- bshanks@112: Mallows, variation of information, Larsen, Van Dongen, and others. bshanks@112: Discriminative dimensionality reduction In addition to using a purely data-driven approach bshanks@112: to identify spatial regions, it might be useful to see how well the known regions can be recon- bshanks@112: structed from a small number of features, even if those features are chosen by using knowledge of bshanks@112: the regions. For example, linear discriminant analysis could be used as a dimensionality reduction bshanks@112: technique in order to identify a few features which are the best linear summary of gene expression bshanks@112: profiles for the purpose of discriminating between regions. This reduced feature set could then be bshanks@112: used to cluster pixels into regions. Perhaps the resulting clusters will be similar to the reference bshanks@112: atlas, yet more faithful to natural spatial domains of gene expression than the reference atlas is. bshanks@112: Apply the new methods to the cortex bshanks@112: Using the methods developed in Goal 1, we will present, for each cortical area, a short list of bshanks@112: markers to identify that area; and we will also present lists of “panels” of genes that can be used bshanks@112: to delineate many areas at once. bshanks@112: Because in most cases the ABA coronal dataset only contains one ISH per gene, it is possible bshanks@112: for an unrelated combination of genes to seem to identify an area when in fact it is only coinci- bshanks@112: dence. There are three ways we will validate our marker genes to guard against this. First, we bshanks@112: will confirm that putative combinations of marker genes express the same pattern in both hemi- bshanks@112: spheres. Second, we will manually validate our final results on other gene expression datasets bshanks@112: such as EMAGE, GeneAtlas, and GENSAT[8]. Third, we may conduct ISH experiments jointly with bshanks@112: collaborators to get further data on genes of particular interest. bshanks@112: Using the methods developed in Goal 2, we will present one or more hierarchical cortical bshanks@112: maps. We will identify and explain how the statistical structure in the gene expression data led to bshanks@112: any unexpected or interesting features of these maps, and we will provide biological hypotheses bshanks@112: to interpret any new cortical areas, or groupings of areas, which are discovered. bshanks@112: Apply the new methods to hyperspectral datasets bshanks@112: Our software will be able to read and write file formats common in the hyperspectral imaging bshanks@112: community such as Erdas LAN and ENVI, and it will be able to convert between the SEV and NIFTI bshanks@112: formats from neuroscience and the ENVI format from GIS. The methods developed in Goals 1 and bshanks@112: 2 will be implemented either as part of Spectral Python or as a separate tool that interoperates bshanks@112: with Spectral Python. The methods will be run on hyperspectral satellite image datasets, and their bshanks@112: performance will be compared to existing hyperspectral analysis techniques. bshanks@112: 15 bshanks@112: bshanks@112: References Cited bshanks@112: [1] Chris Adamson, Leigh Johnston, Terrie Inder, Sandra Rees, Iven Mareels, and Gary Egan. bshanks@112: A Tracking Approach to Parcellation of the Cerebral Cortex, volume 3749/2005 of Lecture bshanks@112: Notes in Computer Science, pages 294–301. Springer Berlin / Heidelberg, 2005. bshanks@112: [2] J. Annese, A. Pitiot, I. D. Dinov, and A. W. Toga. A myelo-architectonic method for the struc- bshanks@112: tural classification of cortical areas. NeuroImage, 21(1):15–26, 2004. bshanks@112: [3] Tanya Barrett, Dennis B. Troup, Stephen E. Wilhite, Pierre Ledoux, Dmitry Rudnev, Carlos bshanks@112: Evangelista, Irene F. Kim, Alexandra Soboleva, Maxim Tomashevsky, and Ron Edgar. 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