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| bshanks@0 | 1 Specific aims
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| bshanks@53 | 2 Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in situ transgenic
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| bshanks@53 | 3 reporter, microarray voxelation, and others, allow the expression levels of many genes at many locations to be compared.
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| bshanks@53 | 4 Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker
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| bshanks@53 | 5 genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have
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| bshanks@53 | 6 three specific aims:
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| bshanks@30 | 7 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target
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| bshanks@30 | 8 anatomical regions
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| bshanks@42 | 9 (2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns
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| bshanks@42 | 10 in gene expression
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| bshanks@33 | 11 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse
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| bshanks@35 | 12 Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of
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| bshanks@35 | 13 Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).
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| bshanks@30 | 14 In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce
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| bshanks@30 | 15 immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project
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| bshanks@33 | 16 will support the development of new ways to selectively target cortical areas, and it will support the development of a
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| bshanks@33 | 17 method for identifying the cortical areal boundaries present in small tissue samples.
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| bshanks@53 | 18 All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well as the
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| bshanks@30 | 19 machine-readable datasets developed in aim (3), will be published and freely available for others to use.
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| bshanks@30 | 20 Background and significance
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| bshanks@30 | 21 Aim 1
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| bshanks@30 | 22 Machine learning terminology: supervised learning
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| bshanks@42 | 23 The task of looking for marker genes for anatomical regions means that one is looking for a set of genes such that, if the
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| bshanks@42 | 24 expression level of those genes is known, then the locations of the regions can be inferred.
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| bshanks@42 | 25 If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we
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| bshanks@42 | 26 are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to
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| bshanks@42 | 27 which region each voxel within the structure belongs. We call this a classification task, because each voxel is being assigned
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| bshanks@42 | 28 to a class (namely, its region).
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| bshanks@30 | 29 Therefore, an understanding of the relationship between the combination of their expression levels and the locations of
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| bshanks@42 | 30 the regions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels
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| bshanks@42 | 31 within that voxel; the output is the regional identity of the target voxel, that is, the region to which the target voxel belongs.
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| bshanks@42 | 32 We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called a label
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| bshanks@42 | 33 (or a class label).
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| bshanks@30 | 34 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a
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| bshanks@30 | 35 classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be
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| bshanks@30 | 36 analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning
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| bshanks@33 | 37 procedure. The construction of the classifier is called training (also learning), and the initial gene expression dataset used
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| bshanks@33 | 38 in the construction of the classifier is called training data.
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| bshanks@30 | 39 In the machine learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a
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| bshanks@30 | 40 task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances
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| bshanks@42 | 41 (voxels) for which the labels (regions) are known.
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| bshanks@30 | 42 Each gene expression level is called a feature, and the selection of which genes1 to include is called feature selection.
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| bshanks@33 | 43 Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with
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| bshanks@33 | 44 a separate feature selection phase, whereas other methods combine feature selection with other aspects of training.
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| bshanks@30 | 45 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then
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| bshanks@30 | 46 chosen. Some scoring measures can assign a score to a set of selected genes, not just to a single gene; in this case, a dynamic
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| bshanks@30 | 47 procedure may be used in which features are added and subtracted from the selected set depending on how much they raise
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| bshanks@30 | 48 the score. Such procedures are called “stepwise” or “greedy”.
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| bshanks@30 | 49 Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the
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| bshanks@30 | 50 learning algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature
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| bshanks@30 | 51 selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to
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| bshanks@53 | 52 each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares or
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| bshanks@53 | 53 average). If only information from nearby voxels is used to calculate a voxel’s sub-score, then we say it is a local scoring
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| bshanks@53 | 54 method. If only information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring
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| bshanks@53 | 55 method.
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| bshanks@30 | 56 Key questions when choosing a learning method are: What are the instances? What are the features? How are the
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| bshanks@30 | 57 features chosen? Here are four principles that outline our answers to these questions.
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| bshanks@30 | 58 Principle 1: Combinatorial gene expression It is too much to hope that every anatomical region of interest will be
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| bshanks@30 | 59 identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene
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| bshanks@30 | 60 included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at
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| bshanks@30 | 61 combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary
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| bshanks@30 | 62 Results). Therefore, each instance should contain multiple features (genes).
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| bshanks@30 | 63 Principle 2: Only look at combinations of small numbers of genes When the classifier classifies a voxel, it is
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| bshanks@30 | 64 only allowed to look at the expression of the genes which have been selected as features. The more data that is available to
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| bshanks@30 | 65 a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a
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| bshanks@30 | 66 strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations
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| bshanks@30 | 67 in which it is not feasible to gather data about every gene. For example, if we want to use the expression of marker genes as
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| bshanks@30 | 68 a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the
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| bshanks@30 | 69 expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the
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| bshanks@33 | 70 level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on tissue samples in order
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| bshanks@30 | 71 to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as
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| bshanks@30 | 72 features.
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| bshanks@63 | 73 __________________________________
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| bshanks@63 | 74 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.
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| bshanks@63 | 75 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many
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| bshanks@63 | 76 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task
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| bshanks@63 | 77 combines feature selection with supervised learning.
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| bshanks@30 | 78 Principle 3: Use geometry in feature selection
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| bshanks@30 | 79 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of
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| bshanks@30 | 80 each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information
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| bshanks@30 | 81 about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See
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| bshanks@30 | 82 Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods.
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| bshanks@30 | 83 Principle 4: Work in 2-D whenever possible
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| bshanks@30 | 84 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When
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| bshanks@30 | 85 it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis
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| bshanks@33 | 86 algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D
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| bshanks@33 | 87 data.
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| bshanks@30 | 88 Therefore, when possible, the instances should represent pixels, not voxels.
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| bshanks@43 | 89 Related work
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| bshanks@44 | 90 There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data
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| bshanks@44 | 91 which is not fundamentally spatial2.
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| bshanks@43 | 92 As noted above, there has been much work on both supervised learning and there are many available algorithms for
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| bshanks@43 | 93 each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the
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| bshanks@43 | 94 way that this framework is set up has a large impact on performance. Creating a good framework can require creatively
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| bshanks@43 | 95 reconceptualizing the problem domain, and is not merely a mechanical “fine-tuning” of numerical parameters. For example,
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| bshanks@43 | 96 we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Work) may
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| bshanks@43 | 97 be necessary in order to achieve the best results in this application.
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| bshanks@53 | 98 We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods.
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| bshanks@53 | 99 [8 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of
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| bshanks@53 | 100 interest, computing what proportion of this structure is covered by the gene’s spatial region.
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| bshanks@53 | 101 GeneAtlas[3] and EMAGE [18] allow the user to construct a search query by demarcating regions and then specifing
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| bshanks@53 | 102 either the strength of expression or the name of another gene or dataset whose expression pattern is to be matched. For the
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| bshanks@53 | 103 similiarity score (match score) between two images (in this case, the query and the gene expression images), GeneAtlas uses
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| bshanks@53 | 104 the sum of a weighted L1-norm distance between vectors whose components represent the number of cells within a pixel3
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| bshanks@53 | 105 whose expression is within four discretization levels. EMAGE uses Jaccard similarity, which is equal to the number of true
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| bshanks@53 | 106 pixels in the intersection of the two images, divided by the number of pixels in their union. Neither GeneAtlas nor EMAGE
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| bshanks@53 | 107 allow one to search for combinations of genes that define a region in concert but not separately.
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| bshanks@53 | 108 [10 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components:
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| bshanks@61 | 109 ∙Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2)
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| bshanks@61 | 110 yields a list of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists
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| bshanks@61 | 111 of overexpressed genes for selected structures)
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| bshanks@61 | 112 ∙Correlation: The user selects a seed voxel and the shows the user how much correlation there is between the gene
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| bshanks@43 | 113 expression profile of the seed voxel and every other voxel.
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| bshanks@61 | 114 ∙Clusters: will be described later
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| bshanks@43 | 115 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we
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| bshanks@43 | 116 will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also
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| bshanks@53 | 117 search for underexpression. Third, Gene Finder uses a simple pointwise score4, whereas we will also use geometric scores
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| bshanks@43 | 118 such as gradient similarity. The Preliminary Data section contains evidence that each of our three choices is the right one.
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| bshanks@53 | 119 [4 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni
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| bshanks@51 | 120 correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA,
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| bshanks@51 | 121 this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for
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| bshanks@51 | 122 underexpression, and does not look for combinations of genes.
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| bshanks@63 | 123 _________________________________________
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| bshanks@63 | 124 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not
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| bshanks@63 | 125 just data which has only a few different locations or which is indexed by anatomical label.
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| bshanks@63 | 126 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.
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| bshanks@63 | 127 4“Expression energy ratio”, which captures overexpression.
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| bshanks@53 | 128 [7 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary
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| bshanks@46 | 129 algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their
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| bshanks@51 | 130 match score is Jaccard similarity.
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| bshanks@51 | 131 In summary, there has been fruitful work on finding marker genes, however, only one of the previous projects explores
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| bshanks@51 | 132 combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or
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| bshanks@51 | 133 scoring methods.
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| bshanks@30 | 134 Aim 2
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| bshanks@30 | 135 Machine learning terminology: clustering
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| bshanks@30 | 136 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as
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| bshanks@30 | 137 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances
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| bshanks@46 | 138 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called
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| bshanks@46 | 139 clustering or cluster analysis.
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| bshanks@46 | 140 The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are
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| bshanks@46 | 141 once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from
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| bshanks@42 | 142 the same region have similar gene expression profiles, at least compared to the other regions. This means that clustering
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| bshanks@42 | 143 voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into clusters of voxels
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| bshanks@42 | 144 with similar gene expression.
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| bshanks@42 | 145 It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps
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| bshanks@44 | 146 some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they
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| bshanks@42 | 147 could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests
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| bshanks@42 | 148 the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels.
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| bshanks@42 | 149 This is called hierarchial clustering.
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| bshanks@30 | 150 Similarity scores
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| bshanks@30 | 151 A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or
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| bshanks@33 | 152 clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and
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| bshanks@30 | 153 scoring methods for similarity.
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| bshanks@30 | 154 Spatially contiguous clusters; image segmentation
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| bshanks@33 | 155 We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have
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| bshanks@33 | 156 an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary
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| bshanks@33 | 157 Results, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these
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| bshanks@33 | 158 results against other methods which guarantee contiguous clusters.
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| bshanks@30 | 159 Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a
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| bshanks@33 | 160 variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into
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| bshanks@30 | 161 clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in
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| bshanks@30 | 162 our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which
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| bshanks@33 | 163 use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used
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| bshanks@33 | 164 to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting
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| bshanks@33 | 165 sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene
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| bshanks@33 | 166 expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of
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| bshanks@33 | 167 spatially arranged data, some of these algorithms are specialized for visual images.
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| bshanks@51 | 168 Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression feature
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| bshanks@51 | 169 vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying data.
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| bshanks@33 | 170 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the
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| bshanks@30 | 171 instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which
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| bshanks@30 | 172 “summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature
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| bshanks@30 | 173 extraction or dimensionality reduction. The small set of features that such a technique yields is called the reduced feature
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| bshanks@30 | 174 set. After the reduced feature set is created, the instances may be replaced by reduced instances, which have as their features
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| bshanks@30 | 175 the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced
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| bshanks@30 | 176 feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene
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| bshanks@30 | 177 expression levels.
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| bshanks@51 | 178 Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the
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| bshanks@51 | 179 reduced data set is less than in the original data set, the running time of clustering algorithms may be much less. Second,
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| bshanks@51 | 180 it is thought that some clustering algorithms may give better results on reduced data.
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| bshanks@51 | 181 Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example,
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| bshanks@51 | 182 one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that regions
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| bshanks@51 | 183 with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points
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| bshanks@51 | 184 in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of
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| bshanks@51 | 185 the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find
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| bshanks@51 | 186 arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction
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| bshanks@51 | 187 is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction
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| bshanks@51 | 188 before clustering.
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| bshanks@30 | 189 Clustering genes rather than voxels
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| bshanks@30 | 190 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster
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| bshanks@30 | 191 the features (genes). There are two ways that clusters of genes could be used.
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| bshanks@30 | 192 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could
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| bshanks@30 | 193 have one reduced feature for each gene cluster.
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| bshanks@30 | 194 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression
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| bshanks@53 | 195 pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically
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| bshanks@53 | 196 interesting region will have multiple genes which each individually pick it out5. This suggests the following procedure:
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| bshanks@42 | 197 cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters.
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| bshanks@42 | 198 In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some “superregions”
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| bshanks@42 | 199 formed by lumping together a few regions, are associated with gene clusters in this fashion.
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| bshanks@51 | 200 The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering
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| bshanks@51 | 201 algorithms.
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| bshanks@43 | 202 Related work
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| bshanks@51 | 203 We are aware of five existing efforts to cluster spatial gene expression data.
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| bshanks@53 | 204 [15 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,
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| bshanks@43 | 205 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive
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| bshanks@44 | 206 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving
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| bshanks@53 | 207 the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset6 and while the results are
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| bshanks@44 | 208 promising (see Preliminary Data), we think that it will be possible to find an even better method.
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| bshanks@53 | 209 AGEA[10] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation
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| bshanks@53 | 210 as the similarity metric. EMAGE[18] allows the user to select a dataset from among a large number of alternatives, or by
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| bshanks@53 | 211 running a search query, and then to cluster the genes within that dataset. EMAGE clusters via hierarchial complete linkage
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| bshanks@53 | 212 clustering with un-centred correlation as the similarity score.
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| bshanks@53 | 213 [4 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and which were
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| bshanks@53 | 214 highly correlated with many other genes. They computed the matrix of (rank) correlations between pairs of these genes, and
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| bshanks@53 | 215 ordered the rows of this matrix as follows: “the first row of the matrix was chosen to show the strongest contrast between
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| bshanks@53 | 216 the highest and lowest correlation coefficient for that row. The remaining rows were then arranged in order of decreasing
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| bshanks@53 | 217 similarity using a least squares metric”. The resulting matrix showed four clusters. For each cluster, prototypical spatial
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| bshanks@53 | 218 expression patterns were created by averaging the genes in the cluster. The prototypes were analyzed manually, without
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| bshanks@53 | 219 clustering voxels
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| bshanks@53 | 220 In an interesting twist, [7] applies their technique for finding combinations of marker genes for the purpose of clustering
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| bshanks@46 | 221 genes around a “seed gene”. The way they do this is by using the pattern of expression of the seed gene as the target image,
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| bshanks@46 | 222 and then searching for other genes which can be combined to reproduce this pattern. Those other genes which are found
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| bshanks@53 | 223 are considered to be related to the seed. The same team also describes a method[17] for finding “association rules” such as,
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| bshanks@46 | 224 “if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the same gene”. This could be
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| bshanks@46 | 225 useful as part of a procedure for clustering voxels.
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| bshanks@46 | 226 In summary, although these projects obtained clusterings, there has not been much comparison between different algo-
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| bshanks@51 | 227 rithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found. Also,
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| bshanks@53 | 228 none of these projects did a separate dimensionality reduction step before clustering pixels, none tried to cluster genes first
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| bshanks@53 | 229 in order to guide automated clustering of pixels into spatial regions, and none used co-clustering algorithms.
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| bshanks@63 | 230 _________________________________________
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| bshanks@63 | 231 5This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is
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| bshanks@63 | 232 possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression;
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| bshanks@63 | 233 perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another possibility is that, although
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| bshanks@63 | 234 the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.
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| bshanks@63 | 235 6We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft
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| bshanks@63 | 236 spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was
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| bshanks@63 | 237 needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.
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| bshanks@30 | 238 Aim 3
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| bshanks@30 | 239 Background
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| bshanks@33 | 240 The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can
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| bshanks@33 | 241 be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the areas continue
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| bshanks@33 | 242 downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can
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| bshanks@33 | 243 picture an area of the cortex as a slice of many-layered cake.
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| bshanks@30 | 244 Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes,
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| bshanks@30 | 245 there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas,
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| bshanks@30 | 246 this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of
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| bshanks@30 | 247 their approximate location upon the cortical surface.
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| bshanks@33 | 248 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not
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| bshanks@53 | 249 completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a single
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| bshanks@53 | 250 agreed-upon map can be seen by contrasting the recent maps given by Swanson[14] on the one hand, and Paxinos and
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| bshanks@53 | 251 Franklin[11] on the other. While the maps are certainly very similar in their general arrangement, significant differences
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| bshanks@30 | 252 remain in the details.
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| bshanks@36 | 253 The Allen Mouse Brain Atlas dataset
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| bshanks@36 | 254 The Allen Mouse Brain Atlas (ABA) data was produced by doing in-situ hybridization on slices of male, 56-day-old
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| bshanks@36 | 255 C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed
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| bshanks@36 | 256 in order to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial
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| bshanks@36 | 257 resolution is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different
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| bshanks@36 | 258 mouse brains were needed in order to measure the expression of many genes.
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| bshanks@36 | 259 Next, an automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate
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| bshanks@36 | 260 system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 = 159,326
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| bshanks@53 | 261 voxels in the 3D coordinate system, of which 51,533 are in the brain[10].
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| bshanks@53 | 262 Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[20]. The ABA contains
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| bshanks@36 | 263 data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our
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| bshanks@46 | 264 dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, and
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| bshanks@53 | 265 also has greater registration error[10]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes
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| bshanks@53 | 266 of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[10].
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| bshanks@53 | 267 The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[6],
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| bshanks@53 | 268 GenePaint[19], its sister project GeneAtlas[3], BGEM[9], EMAGE[18], EurExpress7, EADHB8, MAMEP9, Xenbase10,
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| bshanks@53 | 269 ZFIN[13], Aniseed11, VisiGene12, GEISHA[2], Fruitfly.org[16], COMPARE13 GXD[12], GEO[1]14. With the exception of
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| bshanks@53 | 270 the ABA, GenePaint, and EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH
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| bshanks@53 | 271 images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of
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| bshanks@53 | 272 data available for public download from the website15. Many of these resources focus on developmental gene expression.
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| bshanks@46 | 273 Significance
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| bshanks@43 | 274 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the
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| bshanks@42 | 275 combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for
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| bshanks@30 | 276 drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively
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| bshanks@30 | 277 target individual cortical areas.
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| bshanks@30 | 278 The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatom-
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| bshanks@33 | 279 ical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can
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| bshanks@33 | 280 find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that
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| bshanks@30 | 281 will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex.
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| bshanks@53 | 282 The method developed in aim (2) will provide a genoarchitectonic viewpoint that will contribute to the creation of
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| bshanks@33 | 283 a better map. The development of present-day cortical maps was driven by the application of histological stains. It is
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| bshanks@33 | 284 conceivable that if a different set of stains had been available which identified a different set of features, then the today’s
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| bshanks@33 | 285 cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of
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| bshanks@33 | 286 genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been
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| bshanks@53 | 287 _________________________________________
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| bshanks@53 | 288 7http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE
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| bshanks@53 | 289 8http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html
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| bshanks@53 | 290 9http://mamep.molgen.mpg.de/index.php
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| bshanks@53 | 291 10http://xenbase.org/
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| bshanks@53 | 292 11http://aniseed-ibdm.univ-mrs.fr/
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| bshanks@53 | 293 12http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources
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| bshanks@53 | 294 13http://compare.ibdml.univ-mrs.fr/
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| bshanks@53 | 295 14GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.
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| bshanks@53 | 296 15without prior offline registration
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| bshanks@63 | 297 captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking
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| bshanks@63 | 298 at the patterns of gene expression.
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| bshanks@63 | 299 While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to
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| bshanks@63 | 300 develop could be used to suggest modifications to the human cortical map as well.
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| bshanks@63 | 301 Related work
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| bshanks@63 | 302 [10 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations
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| bshanks@63 | 303 between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either
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| bshanks@46 | 304 of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of
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| bshanks@46 | 305 the other components of AGEA can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes
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| bshanks@53 | 306 for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas16.
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| bshanks@46 | 307 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, (b) there has
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| bshanks@43 | 308 been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally
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| bshanks@43 | 309 finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo
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| bshanks@43 | 310 from gene expression data.
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| bshanks@53 | 311 Our project is guided by a concrete application with a well-specified criterion of success (how well we can find marker
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| bshanks@53 | 312 genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods.
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| bshanks@53 | 313 _________________________________________
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| bshanks@53 | 314 16In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are
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| bshanks@44 | 315 often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel
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| bshanks@46 | 316 correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not
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| bshanks@44 | 317 find most cortical areas (there are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have
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| bshanks@44 | 318 many layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot find marker genes for
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| bshanks@44 | 319 most cortical areas is that in Gene Finder, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found,
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| bshanks@44 | 320 and it creates that ROI by (pairwise voxel correlation) clustering around the seed.
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| bshanks@64 | 321
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| bshanks@64 | 322
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| bshanks@64 | 323 Figure 1: Gene Pitx2 is selectively underexpressed in area SS (somatosensory).
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| bshanks@30 | 324 Preliminary work
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| bshanks@30 | 325 Format conversion between SEV, MATLAB, NIFTI
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| bshanks@35 | 326 We have created software to (politely) download all of the SEV files from the Allen Institute website. We have also created
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| bshanks@38 | 327 software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret’s file formats.
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| bshanks@30 | 328 Flatmap of cortex
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| bshanks@36 | 329 We downloaded the ABA data and applied a mask to select only those voxels which belong to cerebral cortex. We divided
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| bshanks@36 | 330 the cortex into hemispheres.
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| bshanks@53 | 331 Using Caret[5], we created a mesh representation of the surface of the selected voxels. For each gene, for each node of
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| bshanks@42 | 332 the mesh, we calculated an average of the gene expression of the voxels “underneath” that mesh node. We then flattened
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| bshanks@42 | 333 the cortex, creating a two-dimensional mesh.
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| bshanks@36 | 334 We sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this grid
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| bshanks@36 | 335 into a MATLAB matrix.
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| bshanks@36 | 336 We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted
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| bshanks@42 | 337 these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d
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| bshanks@42 | 338 mesh, and then onto the grid, and then we converted the region data into MATLAB format.
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| bshanks@37 | 339 At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing
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| bshanks@37 | 340 a grid of points (pixels) over the cortical surface:
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| bshanks@36 | 341 ∙A 2-D matrix whose entries represent the regional label associated with each surface pixel
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| bshanks@36 | 342 ∙For each gene, a 2-D matrix whose entries represent the average expression level underneath each surface pixel
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| bshanks@38 | 343 We created a normalized version of the gene expression data by subtracting each gene’s mean expression level (over all
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| bshanks@38 | 344 surface pixels) and dividing each gene by its standard deviation.
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| bshanks@40 | 345 The features and the target area are both functions on the surface pixels. They can be referred to as scalar fields over
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| bshanks@40 | 346 the space of surface pixels; alternately, they can be thought of as images which can be displayed on the flatmapped surface.
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| bshanks@37 | 347 To move beyond a single average expression level for each surface pixel, we plan to create a separate matrix for each
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| bshanks@37 | 348 cortical layer to represent the average expression level within that layer. Cortical layers are found at different depths in
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| bshanks@37 | 349 different parts of the cortex. In preparation for extracting the layer-specific datasets, we have extended Caret with routines
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| bshanks@37 | 350 that allow the depth of the ROI for volume-to-surface projection to vary.
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| bshanks@36 | 351 In the Research Plan, we describe how we will automatically locate the layer depths. For validation, we have manually
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| bshanks@36 | 352 demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex.
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| bshanks@38 | 353 Feature selection and scoring methods
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| bshanks@64 | 354 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a marker. See,
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| bshanks@64 | 355 for example, Figure 1.
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| bshanks@38 | 356 Correlation Recall that the instances are surface pixels, and consider the problem of attempting to classify each instance
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| bshanks@46 | 357 as either a member of a particular anatomical area, or not. The target area can be represented as a boolean mask over the
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| bshanks@38 | 358 surface pixels.
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| bshanks@40 | 359 One class of feature selection scoring method are those which calculate some sort of “match” between each gene image
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| bshanks@40 | 360 and the target image. Those genes which match the best are good candidates for features.
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| bshanks@38 | 361 One of the simplest methods in this class is to use correlation as the match score. We calculated the correlation between
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| bshanks@64 | 362 each gene and each cortical area. The top row of Figure 2 shows the three genes most correlated with area SS.
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| bshanks@64 | 363
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| bshanks@64 | 364
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| bshanks@64 | 365
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| bshanks@64 | 366 Figure 2: Top row: Genes Nfic, A930001M12Rik, C130038G02Rik are the most correlated with area SS (somatosensory
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| bshanks@64 | 367 cortex). Bottom row: Genes C130038G02Rik, Cacna1i, Car10 are those with the best fit using logistic regression. Within
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| bshanks@64 | 368 each picture, the vertical axis roughly corresponds to anterior at the top and posterior at the bottom, and the horizontal
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| bshanks@64 | 369 axis roughly corresponds to medial at the left and lateral at the right. The red outline is the boundary of region MO. Pixels
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| bshanks@64 | 370 are colored according to correlation, with red meaning high correlation and blue meaning low.
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| bshanks@38 | 371 Conditional entropy An information-theoretic scoring method is to find features such that, if the features (gene
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| bshanks@38 | 372 expression levels) are known, uncertainty about the target (the regional identity) is reduced. Entropy measures uncertainty,
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| bshanks@38 | 373 so what we want is to find features such that the conditional distribution of the target has minimal entropy. The distribution
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| bshanks@38 | 374 to which we are referring is the probability distribution over the population of surface pixels.
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| bshanks@38 | 375 The simplest way to use information theory is on discrete data, so we discretized our gene expression data by creating,
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| bshanks@46 | 376 for each gene, five thresholded boolean masks of the gene data. For each gene, we created a boolean mask of its expression
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| bshanks@40 | 377 levels using each of these thresholds: the mean of that gene, the mean minus one standard deviation, the mean minus two
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| bshanks@40 | 378 standard deviations, the mean plus one standard deviation, the mean plus two standard deviations.
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| bshanks@39 | 379 Now, for each region, we created and ran a forward stepwise procedure which attempted to find pairs of gene expression
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| bshanks@46 | 380 boolean masks such that the conditional entropy of the target area’s boolean mask, conditioned upon the pair of gene
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| bshanks@46 | 381 expression boolean masks, is minimized.
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| bshanks@39 | 382 This finds pairs of genes which are most informative (at least at these discretization thresholds) relative to the question,
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| bshanks@63 | 383 “Is this surface pixel a member of the target area?”. Its advantage over linear methods such as logistic regression is that it
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| bshanks@63 | 384 takes account of arbitrarily nonlinear relationships; for example, if the XOR of two variables predicts the target, conditional
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| bshanks@63 | 385 entropy would notice, whereas linear methods would not.
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| bshanks@39 | 386 Gradient similarity We noticed that the previous two scoring methods, which are pointwise, often found genes whose
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| bshanks@64 | 387 pattern of expression did not look similar in shape to the target region. For this reason we designed a non-pointwise local
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| bshanks@39 | 388 scoring method to detect when a gene had a pattern of expression which looked like it had a boundary whose shape is similar
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| bshanks@40 | 389 to the shape of the target region. We call this scoring method “gradient similarity”.
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| bshanks@40 | 390 One might say that gradient similarity attempts to measure how much the border of the area of gene expression and
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| bshanks@40 | 391 the border of the target region overlap. However, since gene expression falls off continuously rather than jumping from its
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| bshanks@40 | 392 maximum value to zero, the spatial pattern of a gene’s expression often does not have a discrete border. Therefore, instead
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| bshanks@40 | 393 of looking for a discrete border, we look for large gradients. Gradient similarity is a symmetric function over two images
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| bshanks@40 | 394 (i.e. two scalar fields). It is is high to the extent that matching pixels which have large values and large gradients also have
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| bshanks@40 | 395 gradients which are oriented in a similar direction. The formula is:
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| bshanks@41 | 396 ∑
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| bshanks@41 | 397 pixel<img src="cmsy7-32.png" alt="∈" />pixels cos(abs(∠∇1 -∠∇2)) ⋅|∇1| + |∇2|
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| bshanks@41 | 398 2 ⋅ pixel_value1 + pixel_value2
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| bshanks@41 | 399 2
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| bshanks@40 | 400 where ∇1 and ∇2 are the gradient vectors of the two images at the current pixel; ∠∇i is the angle of the gradient of
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| bshanks@41 | 401 image i at the current pixel; |∇i| is the magnitude of the gradient of image i at the current pixel; and pixel_valuei is the
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| bshanks@40 | 402 value of the current pixel in image i.
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| bshanks@40 | 403 The intuition is that we want to see if the borders of the pattern in the two images are similar; if the borders are similar,
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| bshanks@40 | 404 then both images will have corresponding pixels with large gradients (because this is a border) which are oriented in a
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| bshanks@40 | 405 similar direction (because the borders are similar).
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| bshanks@64 | 406 Most of the genes in Figure 4 were identified via gradient similarity.
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| bshanks@43 | 407 Gradient similarity provides information complementary to correlation
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| bshanks@64 | 408
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| bshanks@64 | 409
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| bshanks@64 | 410
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| bshanks@64 | 411 Figure 3: The top row shows the three genes which (individually) best predict area AUD, according to logistic regression.
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| bshanks@64 | 412 The bottom row shows the three genes which (individually) best match area AUD, according to gradient similarity. From
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| bshanks@64 | 413 left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a, Ptk7, Aph1a again, and Lepr
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| bshanks@41 | 414 To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider
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| bshanks@64 | 415 Fig. 3. The top row of Fig. 3 displays the 3 genes which most match area AUD, according to a pointwise method17. The
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| bshanks@53 | 416 bottom row displays the 3 genes which most match AUD according to a method which considers local geometry18 The
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| bshanks@46 | 417 pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is
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| bshanks@46 | 418 that this includes many areas which don’t have a salient border matching the areal border. The geometric method identifies
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| bshanks@46 | 419 genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes
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| bshanks@46 | 420 genes which don’t express over the entire area. Genes which have high rankings using both pointwise and border criteria,
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| bshanks@46 | 421 such as Aph1a in the example, may be particularly good markers. None of these genes are, individually, a perfect marker
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| bshanks@46 | 422 for AUD; we deliberately chose a “difficult” area in order to better contrast pointwise with geometric methods.
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| bshanks@64 | 423 Areas which can be identified by single genes Using gradient similarity, we have already found single genes which
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| bshanks@64 | 424 roughly identify some areas and groupings of areas. For each of these areas, an example of a gene which roughly identifies
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| bshanks@64 | 425 it is shown in Figure 4. We have not yet cross-verified these genes in other atlases.
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| bshanks@64 | 426 In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior part of
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| bshanks@64 | 427 cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate), VIS
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| bshanks@64 | 428 (visual), AUD (auditory).
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| bshanks@61 | 429 Combinations of multiple genes are useful and necessary for some areas
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| bshanks@64 | 430 In Figure 5, we give an example of a cortical area which is not marked by any single gene, but which can be identified
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| bshanks@64 | 431 combinatorially.
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| bshanks@64 | 432 Feature selection integrated with prediction As noted earlier, in general, any predictive method can be used for
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| bshanks@64 | 433 feature selection by running it inside a stepwise wrapper. Also, some predictive methods integrate soft constraints on number
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| bshanks@65 | 434 of features used. Examples of both of these will be seen in the section “Multivariate Predictive methods”.
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| bshanks@65 | 435 Multivariate Predictive methods
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| bshanks@64 | 436 Forward stepwise logistic regression As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed
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| bshanks@64 | 437 forward stepwise logistic regression to find single genes, pairs of genes, and triplets of genes which predict areal identify.
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| bshanks@64 | 438 This is an example of feature selection integrated with prediction using a stepwise wrapper. Some of the single genes found
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| bshanks@64 | 439 were shown in various figures throughout this document, and Figure 5 shows a combination of genes which was found.
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| bshanks@64 | 440 We felt that, for single genes, gradient similarity did a better job than logistic regression at capturing our subjective
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| bshanks@64 | 441 impression of a “good gene”.
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| bshanks@64 | 442 SVM on all genes at once
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| bshanks@64 | 443 In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical
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| bshanks@63 | 444 _________________________________________
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| bshanks@53 | 445 17For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor
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| bshanks@41 | 446 variable was the value of the expression of the gene underneath that pixel. The resulting scores were used to rank the genes in terms of how well
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| bshanks@62 | 447 they predict area AUD.
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| bshanks@62 | 448 18For each gene the gradient similarity between (a) a map of the expression of each gene on the cortical surface and (b) the shape of area AUD,
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| bshanks@62 | 449 was calculated, and this was used to rank the genes.
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| bshanks@60 | 450
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| bshanks@62 | 451
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| bshanks@62 | 452
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| bshanks@64 | 453 Figure 4: From left to right and top to bottom, single genes which roughly identify areas SS (somatosensory primary +
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| bshanks@62 | 454 supplemental), SSs (supplemental somatosensory), PIR (piriform), FRP (frontal pole), RSP (retrosplenial), COApm (Corti-
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| bshanks@62 | 455 cal amygdalar, posterior part, medial zone). Grouping some areas together, we have also found genes to identify the groups
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| bshanks@62 | 456 ACA+PL+ILA+DP+ORB+MO (anterior cingulate, prelimbic, infralimbic, dorsal peduncular, orbital, motor), posterior
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| bshanks@62 | 457 and lateral visual (VISpm, VISpl, VISI, VISp; posteromedial, posterolateral, lateral, and primary visual; the posterior and
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| bshanks@62 | 458 lateral visual area is distinguished from its neighbors, but not from the entire rest of the cortex). The genes are Pitx2,
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| bshanks@62 | 459 Aldh1a2, Ppfibp1, Slco1a5, Tshz2, Trhr, Col12a1, Ets1.
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| bshanks@64 | 460
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| bshanks@64 | 461
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| bshanks@64 | 462 Figure 5: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 (each pixel’s value on the lower left is the
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| bshanks@64 | 463 sum of the corresponding pixels in the upper row). Acccording to logistic regression, gene wwc1 is the best fit single gene
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| bshanks@64 | 464 for predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in
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| bshanks@64 | 465 Figure 5 shows wwc1’s spatial expression pattern over the cortex. The lower-right boundary of MO is represented reasonably
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| bshanks@64 | 466 well by this gene, however the gene overshoots the upper-left boundary. This flattened 2-D representation does not show
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| bshanks@64 | 467 it, but the area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the lateral surface.
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| bshanks@64 | 468 Gene mtif2 is shown in the upper-right. Mtif2 captures MO’s upper-left boundary, but not its lower-right boundary. Mtif2
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| bshanks@64 | 469 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get
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| bshanks@64 | 470 the lower-left image. This combination captures area MO much better than any single gene.
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| bshanks@66 | 471
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| bshanks@66 | 472
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| bshanks@66 | 473
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| bshanks@66 | 474
|
| bshanks@66 | 475
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| bshanks@66 | 476 Figure 6: todo liso
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| bshanks@64 | 477 surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%19. As noted above,
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| bshanks@64 | 478 however, a classifier that looks at all the genes at once isn’t as practically useful as a classifier that uses only a few genes.
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| bshanks@64 | 479 Data-driven redrawing of the cortical map
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| bshanks@64 | 480 Raw dimensionality reduction We have applied the following dimensionality reduction algorithms to reduce the di-
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| bshanks@64 | 481 mensionality of the gene expression profile associated with each voxel: Principal Components Analysis (PCA), Simple
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| bshanks@64 | 482 PCA (SPCA), Multi-Dimensional Scaling (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space
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| bshanks@64 | 483 Alignment (LTSA), Hessian locally linear embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic
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| bshanks@64 | 484 Proximity Embedding (SPE), Fast Maximum Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF).
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| bshanks@64 | 485 todo
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| bshanks@64 | 486 (might want to incld nnMF since mentioned above)
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| bshanks@64 | 487 Dimensionality reduction plus K-means or spectral clustering
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| bshanks@30 | 488 Many areas are captured by clusters of genes
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| bshanks@40 | 489 todo
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| bshanks@61 | 490 todo
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| bshanks@64 | 491 _________________________________________
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| bshanks@64 | 492 195-fold cross-validation.
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| bshanks@30 | 493 Research plan
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| bshanks@42 | 494 Further work on flatmapping
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| bshanks@42 | 495 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo),
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| bshanks@42 | 496 or by the surface of the structure (as is the case with the cortex). In the former case, the manifold of interest is a plane, but
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| bshanks@42 | 497 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane.
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| bshanks@42 | 498 In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal
|
| bshanks@53 | 499 for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret[5]) with
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| bshanks@42 | 500 mappings which preserve angle (conformal maps).
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| bshanks@42 | 501 Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional.
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| bshanks@42 | 502 If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D
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| bshanks@42 | 503 structure seems to be wrong.
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| bshanks@30 | 504 todo amongst other things:
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| bshanks@63 | 505 layerfinding
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| bshanks@30 | 506 Develop algorithms that find genetic markers for anatomical regions
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| bshanks@30 | 507 1.Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise,
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| bshanks@30 | 508 geometric, and information-theoretic measures.
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| bshanks@30 | 509 2.Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining
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| bshanks@30 | 510 the scoring measures developed, we will rank the genes by their ability to delineate each area.
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| bshanks@30 | 511 3.Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any
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| bshanks@30 | 512 single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily
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| bshanks@30 | 513 combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised
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| bshanks@33 | 514 learning techniques which use soft constraints to minimize the number of features, such as sparse support vector
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| bshanks@30 | 515 machines.
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| bshanks@33 | 516 4.Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult
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| bshanks@33 | 517 to identify because the boundaries are misdrawn, or because it does not “really” exist as a single area, at least on the
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| bshanks@30 | 518 genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its
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| bshanks@30 | 519 boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create
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| bshanks@30 | 520 a larger area which can be fit.
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| bshanks@51 | 521 # Linear discriminant analysis
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| bshanks@64 | 522 Decision trees todo
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| bshanks@64 | 523 For each cortical area, we used the C4.5 algorithm to find a pruned decision tree and ruleset for that area. We achieved
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| bshanks@64 | 524 estimated classification accuracy of more than 99.6% on each cortical area (as evaluated on the training data without
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| bshanks@64 | 525 cross-validation; so actual accuracy is expected to be lower). However, the resulting decision trees each made use of many
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| bshanks@64 | 526 genes.
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| bshanks@30 | 527 Apply these algorithms to the cortex
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| bshanks@30 | 528 1.Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert
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| bshanks@30 | 529 between SEV, NIFTI and MATLAB formats.
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| bshanks@30 | 530 2.Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it.
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| bshanks@30 | 531 3.Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries.
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| bshanks@30 | 532 4.Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify
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| bshanks@30 | 533 that area; and we will also present lists of “panels” of genes that can be used to delineate many areas at once.
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| bshanks@30 | 534 Develop algorithms to suggest a division of a structure into anatomical parts
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| bshanks@60 | 535 # mixture models, etc
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| bshanks@30 | 536 1.Explore dimensionality reduction algorithms applied to pixels: including TODO
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| bshanks@30 | 537 2.Explore dimensionality reduction algorithms applied to genes: including TODO
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| bshanks@30 | 538 3.Explore clustering algorithms applied to pixels: including TODO
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| bshanks@30 | 539 4.Explore clustering algorithms applied to genes: including gene shaving, TODO
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| bshanks@30 | 540 5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps
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| bshanks@30 | 541 6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex
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| bshanks@51 | 542 # Linear discriminant analysis
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| bshanks@51 | 543 # jbt, coclustering
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| bshanks@51 | 544 # self-organizing map
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| bshanks@53 | 545 # confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting
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| bshanks@53 | 546 # compare using clustering scores
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| bshanks@64 | 547 # multivariate gradient similarity
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| bshanks@66 | 548 # deep belief nets
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| bshanks@66 | 549 # note: slice artifact
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| bshanks@33 | 550 Bibliography & References Cited
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| bshanks@33 | 639
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| bshanks@33 | 640 _______________________________________________________________________________________________________
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| bshanks@30 | 641 stuff i dunno where to put yet (there is more scattered through grant-oldtext):
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| bshanks@16 | 642 Principle 4: Work in 2-D whenever possible
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| bshanks@33 | 643 —
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| bshanks@33 | 644 note:
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| bshanks@36 | 645 two hemis
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| bshanks@33 | 646
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| bshanks@33 | 647
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