bshanks@0: Specific aims bshanks@15: Massive new datasets obtained with techniques such as in situ hybridization bshanks@0: (ISH) and BAC-transgenics allow the expression levels of many genes at many bshanks@0: locations to be compared. Our goal is to develop automated methods to relate bshanks@0: spatial variation in gene expression to anatomy. We want to find marker genes bshanks@0: for specific anatomical regions, and also to draw new anatomical maps based on bshanks@0: gene expression patterns. We have three specific aims: bshanks@0: (1) develop an algorithm to screen spatial gene expression data for combina- bshanks@0: tions of marker genes which selectively target anatomical regions bshanks@0: (2) develop an algorithm to suggest new ways of carving up a structure into bshanks@0: anatomical subregions, based on spatial patterns in gene expression bshanks@0: (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains bshanks@0: a flattened version of the Allen Mouse Brain Atlas ISH data, as well as bshanks@0: the boundaries of cortical anatomical areas. Use this dataset to validate bshanks@0: the methods developed in (1) and (2). bshanks@0: In addition to validating the usefulness of the algorithms, the application of bshanks@0: these methods to cerebral cortex will produce immediate benefits, because there bshanks@0: are currently no known genetic markers for many cortical areas. The results bshanks@0: of the project will support the development of new ways to selectively target bshanks@0: cortical areas, and it will support the development of a method for identifying bshanks@0: the cortical areal boundaries present in small tissue samples. bshanks@0: All algorithms that we develop will be implemented in an open-source soft- bshanks@0: ware toolkit. The toolkit, as well as the machine-readable datasets developed bshanks@0: in aim (3), will be published and freely available for others to use. bshanks@0: Background and significance bshanks@0: Aim 1 bshanks@16: Machine learning terminology: supervised learning bshanks@16: The task of looking for marker genes for anatomical subregions means that bshanks@16: one is looking for a set of genes such that, if the expression level of those genes bshanks@16: is known, then the locations of the subregions can be inferred. bshanks@0: If we define the subregions so that they cover the entire anatomical structure bshanks@0: to be divided, then instead of saying that we are using gene expression to find bshanks@0: the locations of the subregions, we may say that we are using gene expression to bshanks@0: determine to which subregion each voxel within the structure belongs. We call bshanks@0: this a classification task, because each voxel is being assigned to a class (namely, bshanks@0: its subregion). bshanks@0: Therefore, an understanding of the relationship between the combination of bshanks@0: their expression levels and the locations of the subregions may be expressed as bshanks@16: a function. The input to this function is a voxel, along with the gene expression bshanks@15: 1 bshanks@15: bshanks@0: levels within that voxel; the output is the subregional identity of the target bshanks@0: voxel, that is, the subregion to which the target voxel belongs. We call this bshanks@0: function a classifier. In general, the input to a classifier is called an instance, bshanks@15: and the output is called a label (or a class label). bshanks@0: The object of aim 1 is not to produce a single classifier, but rather to develop bshanks@0: an automated method for determining a classifier for any known anatomical bshanks@0: structure. Therefore, we seek a procedure by which a gene expression dataset bshanks@0: may be analyzed in concert with an anatomical atlas in order to produce a bshanks@0: classifier. Such a procedure is a type of a machine learning procedure. The bshanks@0: construction of the classifier is called training (also learning), and the initial bshanks@0: gene expression dataset used in the construction of the classifier is called training bshanks@0: data. bshanks@0: In the machine learning literature, this sort of procedure may be thought bshanks@0: of as a supervised learning task, defined as a task in whcih the goal is to learn bshanks@0: a mapping from instances to labels, and the training data consists of a set of bshanks@0: instances (voxels) for which the labels (subregions) are known. bshanks@0: Each gene expression level is called a feature, and the selection of which bshanks@0: genes to include is called feature selection. Feature selection is one component bshanks@0: of the task of learning a classifier. Some methods for learning classifiers start bshanks@0: out with a separate feature selection phase, whereas other methods combine bshanks@0: feature selection with other aspects of training. bshanks@0: One class of feature selection methods assigns some sort of score to each bshanks@0: candidate gene. The top-ranked genes are then chosen. Some scoring measures bshanks@0: can assign a score to a set of selected genes, not just to a single gene; in this bshanks@0: case, a dynamic procedure may be used in which features are added and sub- bshanks@0: tracted from the selected set depending on how much they raise the score. Such bshanks@0: procedures are called “stepwise” or “greedy”. bshanks@0: Although the classifier itself may only look at the gene expression data within bshanks@0: each voxel before classifying that voxel, the learning algorithm which constructs bshanks@0: the classifier may look over the entire dataset. We can categorize score-based bshanks@0: feature selection methods depending on how the score of calculated. Often bshanks@0: the score calculation consists of assigning a sub-score to each voxel, and then bshanks@0: aggregating these sub-scores into a final score (the aggregation is often a sum or bshanks@0: a sum of squares). If only information from nearby voxels is used to calculate a bshanks@0: voxel’s sub-score, then we say it is a local scoring method. If only information bshanks@0: from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a bshanks@0: pointwise scoring method. bshanks@0: Key questions when choosing a learning method are: What are the instances? bshanks@0: What are the features? How are the features chosen? Here are four principles bshanks@0: that outline our answers to these questions. bshanks@16: Principle 1: Combinatorial gene expression bshanks@16: Above, we defined an “instance” as the combination of a voxel with the bshanks@16: “associated gene expression data”. In our case this refers to the expression level bshanks@16: of genes within the voxel, but should we include the expression levels of all bshanks@16: genes, or only a few of them? bshanks@16: It is too much to hope that every anatomical region of interest will be iden- bshanks@15: 2 bshanks@15: bshanks@0: tified by a single gene. For example, in the cortex, there are some areas which bshanks@0: are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) bshanks@0: dataset. However, at least some of these areas can be delineated by looking bshanks@0: at combinations of genes (an example of an area for which multiple genes are bshanks@0: necessary and sufficient is provided in Preliminary Results). bshanks@16: Principle 2: Only look at combinations of small numbers of genes bshanks@16: When the classifier classifies a voxel, it is only allowed to look at the expres- bshanks@16: sion of the genes which have been selected as features. The more data that is bshanks@16: available to a classifier, the better that it can do. For example, perhaps there bshanks@16: are weak correlations over many genes that add up to a strong signal. So, why bshanks@16: not include every gene as a feature? The reason is that we wish to employ bshanks@16: the classifier in situations in which it is not feasible to gather data about every bshanks@16: gene. For example, if we want to use the expression of marker genes as a trigger bshanks@16: for some regionally-targeted intervention, then our intervention must contain a bshanks@16: molecular mechanism to check the expression level of each marker gene before bshanks@16: it triggers. It is currently infeasible to design a molecular trigger that checks bshanks@16: the level of more than a handful of genes. Similarly, if the goal is to develop a bshanks@16: procedure to do ISH on tissue samples in order to label their anatomy, then it bshanks@16: is infeasible to label more than a few genes. Therefore, we must select only a bshanks@16: few genes as features. bshanks@16: Principle 3: Use geometry in feature selection bshanks@16: When doing feature selection with score-based methods, the simplest thing bshanks@16: to do would be to score the performance of each voxel by itself and then com- bshanks@16: bine these scores (pointwise scoring). A more powerful approach is to also use bshanks@16: information about the geometric relations between each voxel and its neighbors; bshanks@16: this requires non-pointwise, local scoring methods. See Preliminary Results for bshanks@16: evidence of the complementary nature of pointwise and local scoring methods. bshanks@16: Principle 4: Work in 2-D whenever possible bshanks@16: There are many anatomical structures which are commonly characterized in bshanks@0: terms of a two-dimensional manifold. When it is known that the structure that bshanks@0: one is looking for is two-dimensional, the results may be improved by allowing bshanks@0: the analysis algorithm to take advantage of this prior knowledge. In addition, bshanks@0: it is easier for humans to visualize and work with 2-D data. bshanks@0: Therefore, when possible, the instances should represent pixels, not voxels. bshanks@1: Aim 2 bshanks@16: Machine learning terminology: clustering bshanks@16: If one is given a dataset consisting merely of instances, with no class labels, bshanks@16: then analysis of the dataset is referred to as unsupervised learning in the jargon bshanks@16: of machine learning. One thing that you can do with such a dataset is to group bshanks@15: instances together. A set of similar instances is called a cluster, and the activity bshanks@15: of finding grouping the data into clusters is called clustering or cluster analysis. bshanks@15: The task of deciding how to carve up a structure into anatomical subregions bshanks@15: can be put into these terms. The instances are once again voxels (or pixels) bshanks@15: along with their associated gene expression profiles. We make the assumption bshanks@16: 3 bshanks@16: bshanks@15: that voxels from the same subregion have similar gene expression profiles, at bshanks@15: least compared to the other subregions. This means that clustering voxels is bshanks@15: the same as finding potential subregions; we seek a partitioning of the voxels bshanks@15: into subregions, that is, into clusters of voxels with similar gene expression. bshanks@15: It is desirable to determine not just one set of subregions, but also how bshanks@15: these subregions relate to each other, if at all; perhaps some of the subregions bshanks@15: are more similar to each other than to the rest, suggesting that, although at a bshanks@15: fine spatial scale they could be considered separate, on a coarser spatial scale bshanks@15: they could be grouped together into one large subregion. This suggests the bshanks@15: outcome of clustering may be a hierarchial tree of clusters, rather than a single bshanks@15: set of clusters which partition the voxels. This is called hierarchial clustering. bshanks@16: Similarity scores bshanks@16: todo bshanks@16: Spatially contiguous clusters; image segmentation bshanks@16: We have shown that aim 2 is a type of clustering task. In fact, it is a bshanks@16: special type of clustering task because we have an additional constraint on bshanks@16: clusters; voxels grouped together into a cluster must be spatially contiguous. bshanks@16: In Preliminary Results, we show that one can get reasonable results without bshanks@16: enforcing this constraint, however, we plan to compare these results against bshanks@16: other methods which guarantee contiguous clusters. bshanks@15: Perhaps the biggest source of continguous clustering algorithms is the field bshanks@15: of computer vision, which has produced a variety of image segmentation algo- bshanks@15: rithms. Image segmentation is the task of partitioning the pixels in a digital bshanks@15: image into clusters, usually contiguous clusters. Aim 2 is similar to an image bshanks@15: segmentation task. There are two main differences; in our task, there are thou- bshanks@15: sands of color channels (one for each gene), rather than just three. There are bshanks@15: imaging tasks which use more than three colors, however, for example multispec- bshanks@15: tral imaging and hyperspectral imaging, which are often used to process satellite bshanks@15: imagery. A more crucial difference is that there are various cues which are ap- bshanks@15: propriate for detecting sharp object boundaries in a visual scene but which are bshanks@15: not appropriate for segmenting abstract spatial data such as gene expression. bshanks@15: Although many image segmentation algorithms can be expected to work well bshanks@15: for segmenting other sorts of spatially arranged data, some of these algorithms bshanks@15: are specialized for visual images. bshanks@16: Dimensionality reduction bshanks@16: Unlike aim 1, there is no externally-imposed need to select only a handful bshanks@16: of informative genes for inclusion in the instances. However, some clustering bshanks@16: algorithms perform better on small numbers of features. There are techniques bshanks@15: which “summarize” a larger number of features using a smaller number of fea- bshanks@15: tures; these techniques go by the name of feature extraction or dimensionality bshanks@15: reduction. The small set of features that such a technique yields is called the bshanks@15: reduced feature set. After the reduced feature set is created, the instances may bshanks@15: be replaced by reduced instances, which have as their features the reduced fea- bshanks@15: ture set rather than the original feature set of all gene expression levels. Note bshanks@15: that the features in the reduced feature set do not necessarily correspond to bshanks@15: genes; each feature in the reduced set may be any function of the set of gene bshanks@16: 4 bshanks@16: bshanks@15: expression levels. bshanks@15: Another use for dimensionality reduction is to visualize the relationships bshanks@15: between subregions. For example, one might want to make a 2-D plot upon bshanks@15: which each subregion is represented by a single point, and with the property bshanks@15: that subregions with similar gene expression profiles should be nearby on the bshanks@15: plot (that is, the property that distance between pairs of points in the plot bshanks@15: should be proportional to some measure of dissimilarity in gene expression). It bshanks@15: is likely that no arrangement of the points on a 2-D plan will exactly satisfy bshanks@15: this property – however, dimensionality reduction techniques allow one to find bshanks@15: arrangements of points that approximately satisfy that property. Note that bshanks@15: in this application, dimensionality reduction is being applied after clustering; bshanks@15: whereas in the previous paragraph, we were talking about using dimensionality bshanks@15: reduction before clustering. bshanks@16: Clustering genes rather than voxels bshanks@16: Although the ultimate goal is to cluster the instances (voxels or pixels), one bshanks@15: strategy to achieve this goal is to first cluster the features (genes). There are bshanks@15: two ways that clusters of genes could be used. bshanks@15: Gene clusters could be used as part of dimensionality reduction: rather than bshanks@15: have one feature for each gene, we could have one reduced feature for each gene bshanks@15: cluster. bshanks@15: Gene clusters could also be used to directly yield a clustering on instances. bshanks@15: This is because many genes have an expression pattern which seems to pick bshanks@15: out a single, spatially continguous subregion. Therefore, it seems likely that an bshanks@15: anatomically interesting subregion will have multiple genes which each individ- bshanks@15: ually pick it out1. This suggests the following procedure: cluster together genes bshanks@15: which pick out similar subregions, and then to use the more popular common bshanks@15: subregions as the final clusters. In the Preliminary Data we show that a num- bshanks@15: ber of anatomically recognized cortical regions, as well as some “superregions” bshanks@15: formed by lumping together a few regions, are associated with gene clusters in bshanks@15: this fashion. bshanks@0: Aim 3 bshanks@16: Background bshanks@16: The cortex is divided into areas and layers. To a first approximation, the bshanks@16: parcellation of the cortex into areas can be drawn as a 2-D map on the surface of bshanks@16: the cortex. In the third dimension, the boundaries between the areas continue bshanks@16: downwards into the cortical depth, perpendicular to the surface. The layer bshanks@0: boundaries run parallel to the surface. One can picture an area of the cortex as bshanks@0: a slice of many-layered cake. bshanks@16: ___ bshanks@16: 1This would seem to contradict our finding in aim 1 that some cortical areas are combina- bshanks@16: torially coded by multiple genes. However, it is possible that the currently accepted cortical bshanks@16: maps divide the cortex into subregions which are unnatural from the point of view of gene bshanks@16: expression; perhaps there is some other way to map the cortex for which each subregion can bshanks@16: be identified by single genes. bshanks@16: 5 bshanks@16: bshanks@0: Although it is known that different cortical areas have distinct roles in both bshanks@0: normal functioning and in disease processes, there are no known marker genes bshanks@0: for many cortical areas. When it is necessary to divide a tissue sample into bshanks@0: cortical areas, this is a manual process that requires a skilled human to combine bshanks@0: multiple visual cues and interpret them in the context of their approximate bshanks@0: location upon the cortical surface. bshanks@0: Even the questions of how many areas should be recognized in cortex, and bshanks@0: what their arrangement is, are still not completely settled. A proposed division bshanks@0: of the cortex into areas is called a cortical map. In the rodent, the lack of a bshanks@0: single agreed-upon map can be seen by contrasting the recent maps given by bshanks@0: Swanson?? on the one hand, and Paxinos and Franklin?? on the other. While bshanks@0: the maps are certainly very similar in their general arrangement, significant bshanks@0: differences remain in the details. bshanks@16: Significance bshanks@16: The method developed in aim (1) will be applied to each cortical area to find bshanks@0: a set of marker genes such that the combinatorial expression pattern of those bshanks@0: genes uniquely picks out the target area. Finding marker genes will be useful bshanks@0: for drug discovery as well as for experimentation because marker genes can be bshanks@0: used to design interventions which selectively target individual cortical areas. bshanks@0: The application of the marker gene finding algorithm to the cortex will bshanks@0: also support the development of new neuroanatomical methods. In addition to bshanks@0: finding markers for each individual cortical areas, we will find a small panel bshanks@0: of genes that can find many of the areal boundaries at once. This panel of bshanks@0: marker genes will allow the development of an ISH protocol that will allow bshanks@0: experimenters to more easily identify which anatomical areas are present in bshanks@0: small samples of cortex. bshanks@0: The method developed in aim (3) will provide a genoarchitectonic viewpoint bshanks@0: that will contribute to the creation of a better map. The development of present- bshanks@0: day cortical maps was driven by the application of histological stains. It is bshanks@0: conceivable that if a different set of stains had been available which identified bshanks@0: a different set of features, then the today’s cortical maps would have come out bshanks@0: differently. Since the number of classes of stains is small compared to the number bshanks@0: of genes, it is likely that there are many repeated, salient spatial patterns in bshanks@0: the gene expression which have not yet been captured by any stain. Therefore, bshanks@0: current ideas about cortical anatomy need to incorporate what we can learn bshanks@0: from looking at the patterns of gene expression. bshanks@0: While we do not here propose to analyze human gene expression data, it is bshanks@0: conceivable that the methods we propose to develop could be used to suggest bshanks@0: modifications to the human cortical map as well. bshanks@0: Related work bshanks@1: todo bshanks@15: vs. AGEA – i wrote something on this but i’m going to rewrite it bshanks@16: 6 bshanks@16: bshanks@0: Preliminary work bshanks@15: Format conversion between SEV, MATLAB, NIFTI bshanks@15: todo bshanks@15: Flatmap of cortex bshanks@15: todo bshanks@16: Using combinations of multiple genes is necessary and sufficient to bshanks@15: delineate some cortical areas bshanks@16: Here we give an example of a cortical area which is not marked by any bshanks@16: single gene, but which can be identified combinatorially. according to logistic bshanks@16: regression, gene wwc12 is the best fit single gene for predicting whether or not a bshanks@16: pixel on the cortical surface belongs to the motor area (area MO). The upper-left bshanks@0: picture in Figure shows wwc1’s spatial expression pattern over the cortex. The bshanks@0: lower-right boundary of MO is represented reasonably well by this gene, however bshanks@0: the gene overshoots the upper-left boundary. This flattened 2-D representation bshanks@0: does not show it, but the area corresponding to the overshoot is the medial bshanks@0: surface of the cortex. MO is only found on the lateral surface (todo). bshanks@15: Gnee mtif23 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s bshanks@0: upper-left boundary, but not its lower-right boundary. Mtif2 does not express bshanks@0: very much on the medial surface. By adding together the values at each pixel bshanks@16: in these two figures, we get the lower-left of Figure . This combination captures bshanks@16: area MO much better than any single gene. bshanks@16: Geometric and pointwise scoring methods provide complementary bshanks@16: information bshanks@16: To show that local geometry can provide useful information that cannot be bshanks@16: detected via pointwise analyses, consider Fig. . The top row of Fig. displays the bshanks@16: 3 genes which most match area AUD, according to a pointwise method4. The bshanks@16: bottom row displays the 3 genes which most match AUD according to a method bshanks@16: which considers local geometry5 The pointwise method in the top row identifies bshanks@16: genes which express more strongly in AUD than outside of it; its weakness is that bshanks@16: this includes many areas which don’t have a salient border matching the areal bshanks@16: border. The geometric method identifies genes whose salient expression border bshanks@16: seems to partially line up with the border of AUD; its weakness is that this bshanks@16: includes genes which don’t express over the entire area. Genes which have high bshanks@16: rankings using both pointwise and border criteria, such as Aph1a in the example, bshanks@15: __________________________ bshanks@15: 2“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652 bshanks@15: 3“mitochondrial translational initiation factor 2”; EntrezGene ID 76784 bshanks@16: 4For each gene, a logistic regression in which the response variable was whether or not a bshanks@16: surface pixel was within area AUD, and the predictor variable was the value of the expression bshanks@16: of the gene underneath that pixel. The resulting scores were used to rank the genes in terms bshanks@16: of how well they predict area AUD. bshanks@16: 5For each gene the gradient similarity (see section ??) between (a) a map of the expression bshanks@16: of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this bshanks@16: was used to rank the genes. bshanks@15: 7 bshanks@0: bshanks@0: bshanks@0: bshanks@0: Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 bshanks@0: (each pixel’s value on the lower left is the sum of the corresponding pixels in bshanks@0: the upper row). Within each picture, the vertical axis roughly corresponds to bshanks@0: anterior at the top and posterior at the bottom, and the horizontal axis roughly bshanks@0: corresponds to medial at the left and lateral at the right. The red outline is bshanks@0: the boundary of region MO. Pixels are colored approximately according to the bshanks@0: density of expressing cells underneath each pixel, with red meaning a lot of bshanks@0: expression and blue meaning little. bshanks@15: 8 bshanks@15: bshanks@15: bshanks@15: bshanks@15: Figure 2: The top row shows the three genes which (individually) best predict bshanks@15: area AUD, according to logistic regression. The bottom row shows the three bshanks@15: genes which (individually) best match area AUD, according to gradient similar- bshanks@15: ity. From left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a, bshanks@15: Ptk7, Aph1a again, and Lepr bshanks@0: may be particularly good markers. None of these genes are, individually, a bshanks@0: perfect marker for AUD; we deliberately chose a “difficult” area in order to bshanks@0: better contrast pointwise with geometric methods. bshanks@16: Areas which can be identified by single genes bshanks@16: todo bshanks@15: Aim 1 (and Aim 3) bshanks@16: SVM on all genes at once bshanks@16: In order to see how well one can do when looking at all genes at once, we bshanks@16: ran a support vector machine to classify cortical surface pixels based on their bshanks@16: gene expression profiles. We achieved classification accuracy of about 81%6. bshanks@16: As noted above, however, a classifier that looks at all the genes at once isn’t bshanks@16: practically useful. bshanks@16: The requirement to find combinations of only a small number of genes limits bshanks@16: us from straightforwardly applying many of the most simple techniques from bshanks@16: the field of supervised machine learning. In the parlance of machine learning, bshanks@16: our task combines feature selection with supervised learning. bshanks@16: Decision trees bshanks@16: todo bshanks@16: ____________________ bshanks@15: 6Using the Shogun SVM package (todo:cite), with parameters type=GMNPSVM (multi- bshanks@15: class b-SVM), kernal = gaussian with sigma = 0.1, c = 10, epsilon = 1e-1 – these are the bshanks@15: first parameters we tried, so presumably performance would improve with different choices of bshanks@15: parameters. 5-fold cross-validation. bshanks@6: 9 bshanks@6: bshanks@15: Aim 2 (and Aim 3) bshanks@15: Raw dimensionality reduction results bshanks@15: Dimensionality reduction plus K-means or spectral clus- bshanks@15: tering bshanks@16: Many areas are captured by clusters of genes bshanks@16: todo bshanks@15: todo bshanks@15: Research plan bshanks@15: todo bshanks@15: amongst other thigns: bshanks@16: Develop algorithms that find genetic markers for anatomical re- bshanks@16: gions bshanks@0: 1. Develop scoring measures for evaluating how good individual genes are at bshanks@0: marking areas: we will compare pointwise, geometric, and information- bshanks@0: theoretic measures. bshanks@0: 2. Develop a procedure to find single marker genes for anatomical regions: for bshanks@0: each cortical area, by using or combining the scoring measures developed, bshanks@0: we will rank the genes by their ability to delineate each area. bshanks@0: 3. Extend the procedure to handle difficult areas by using combinatorial cod- bshanks@0: ing: for areas that cannot be identified by any single gene, identify them bshanks@0: with a handful of genes. We will consider both (a) algorithms that incre- bshanks@0: mentally/greedily combine single gene markers into sets, such as forward bshanks@0: stepwise regression and decision trees, and also (b) supervised learning bshanks@0: techniques which use soft constraints to minimize the number of features, bshanks@0: such as sparse support vector machines. bshanks@0: 4. Extend the procedure to handle difficult areas by combining or redrawing bshanks@0: the boundaries: An area may be difficult to identify because the bound- bshanks@0: aries are misdrawn, or because it does not “really” exist as a single area, bshanks@0: at least on the genetic level. We will develop extensions to our procedure bshanks@0: which (a) detect when a difficult area could be fit if its boundary were bshanks@0: redrawn slightly, and (b) detect when a difficult area could be combined bshanks@0: with adjacent areas to create a larger area which can be fit. bshanks@16: Apply these algorithms to the cortex bshanks@0: 1. Create open source format conversion tools: we will create tools to bulk bshanks@0: download the ABA dataset and to convert between SEV, NIFTI and MAT- bshanks@0: LAB formats. bshanks@16: 10 bshanks@16: bshanks@0: 2. Flatmap the ABA cortex data: map the ABA data onto a plane and draw bshanks@0: the cortical area boundaries onto it. bshanks@0: 3. Find layer boundaries: cluster similar voxels together in order to auto- bshanks@0: matically find the cortical layer boundaries. bshanks@0: 4. Run the procedures that we developed on the cortex: we will present, for bshanks@0: each area, a short list of markers to identify that area; and we will also bshanks@0: present lists of “panels” of genes that can be used to delineate many areas bshanks@0: at once. bshanks@16: Develop algorithms to suggest a division of a structure into anatom- bshanks@0: ical parts bshanks@0: 1. Explore dimensionality reduction algorithms applied to pixels: including bshanks@0: TODO bshanks@0: 2. Explore dimensionality reduction algorithms applied to genes: including bshanks@0: TODO bshanks@0: 3. Explore clustering algorithms applied to pixels: including TODO bshanks@0: 4. Explore clustering algorithms applied to genes: including gene shaving, bshanks@0: TODO bshanks@0: 5. Develop an algorithm to use dimensionality reduction and/or hierarchial bshanks@0: clustering to create anatomical maps bshanks@0: 6. Run this algorithm on the cortex: present a hierarchial, genoarchitectonic bshanks@0: map of the cortex bshanks@15: ______________________________________________ bshanks@15: stuff i dunno where to put yet (there is more scattered through grant- bshanks@15: oldtext): bshanks@16: Principle 4: Work in 2-D whenever possible bshanks@16: In anatomy, the manifold of interest is usually either defined by a combina- bshanks@16: tion of two relevant anatomical axes (todo), or by the surface of the structure bshanks@16: (as is the case with the cortex). In the former case, the manifold of interest is bshanks@16: a plane, but in the latter case it is curved. If the manifold is curved, there are bshanks@16: various methods for mapping the manifold into a plane. bshanks@16: The method that we will develop will begin by mapping the data into a bshanks@16: 2-D plane. Although the manifold that characterized cortical areas is known bshanks@16: to be the cortical surface, it remains to be seen which method of mapping the bshanks@16: manifold into a plane is optimal for this application. We will compare mappings bshanks@16: which attempt to preserve size (such as the one used by Caret??) with mappings bshanks@16: which preserve angle (conformal maps). bshanks@16: Although there is much 2-D organization in anatomy, there are also struc- bshanks@16: tures whose shape is fundamentally 3-dimensional. If possible, we would like bshanks@16: the method we develop to include a statistical test that warns the user if the bshanks@16: assumption of 2-D structure seems to be wrong. bshanks@15: 11 bshanks@15: bshanks@16: