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| bshanks@0 | 1 Specific aims
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| bshanks@15 | 2 Massive new datasets obtained with techniques such as in situ hybridization
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| bshanks@0 | 3 (ISH) and BAC-transgenics allow the expression levels of many genes at many
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| bshanks@0 | 4 locations to be compared. Our goal is to develop automated methods to relate
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| bshanks@0 | 5 spatial variation in gene expression to anatomy. We want to find marker genes
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| bshanks@0 | 6 for specific anatomical regions, and also to draw new anatomical maps based on
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| bshanks@0 | 7 gene expression patterns. We have three specific aims:
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| bshanks@17 | 8 (1) develop an algorithm to screen spatial gene expression data for combi-
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| bshanks@17 | 9 nations of marker genes which selectively target anatomical regions
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| bshanks@17 | 10 (2) develop an algorithm to suggest new ways of carving up a structure into
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| bshanks@17 | 11 anatomical subregions, based on spatial patterns in gene expression
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| bshanks@17 | 12 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that con-
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| bshanks@17 | 13 tains a flattened version of the Allen Mouse Brain Atlas ISH data, as well as
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| bshanks@17 | 14 the boundaries of cortical anatomical areas. Use this dataset to validate the
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| bshanks@17 | 15 methods developed in (1) and (2).
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| bshanks@0 | 16 In addition to validating the usefulness of the algorithms, the application of
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| bshanks@0 | 17 these methods to cerebral cortex will produce immediate benefits, because there
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| bshanks@0 | 18 are currently no known genetic markers for many cortical areas. The results
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| bshanks@0 | 19 of the project will support the development of new ways to selectively target
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| bshanks@0 | 20 cortical areas, and it will support the development of a method for identifying
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| bshanks@0 | 21 the cortical areal boundaries present in small tissue samples.
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| bshanks@0 | 22 All algorithms that we develop will be implemented in an open-source soft-
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| bshanks@0 | 23 ware toolkit. The toolkit, as well as the machine-readable datasets developed
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| bshanks@0 | 24 in aim (3), will be published and freely available for others to use.
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| bshanks@26 | 25 1
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| bshanks@26 | 26
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| bshanks@0 | 27 Background and significance
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| bshanks@0 | 28 Aim 1
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| bshanks@16 | 29 Machine learning terminology: supervised learning
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| bshanks@16 | 30 The task of looking for marker genes for anatomical subregions means that
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| bshanks@16 | 31 one is looking for a set of genes such that, if the expression level of those genes
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| bshanks@16 | 32 is known, then the locations of the subregions can be inferred.
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| bshanks@0 | 33 If we define the subregions so that they cover the entire anatomical structure
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| bshanks@0 | 34 to be divided, then instead of saying that we are using gene expression to find
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| bshanks@0 | 35 the locations of the subregions, we may say that we are using gene expression to
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| bshanks@0 | 36 determine to which subregion each voxel within the structure belongs. We call
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| bshanks@0 | 37 this a classification task, because each voxel is being assigned to a class (namely,
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| bshanks@0 | 38 its subregion).
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| bshanks@0 | 39 Therefore, an understanding of the relationship between the combination of
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| bshanks@0 | 40 their expression levels and the locations of the subregions may be expressed as
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| bshanks@16 | 41 a function. The input to this function is a voxel, along with the gene expression
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| bshanks@0 | 42 levels within that voxel; the output is the subregional identity of the target
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| bshanks@0 | 43 voxel, that is, the subregion to which the target voxel belongs. We call this
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| bshanks@0 | 44 function a classifier. In general, the input to a classifier is called an instance,
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| bshanks@15 | 45 and the output is called a label (or a class label).
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| bshanks@0 | 46 The object of aim 1 is not to produce a single classifier, but rather to develop
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| bshanks@0 | 47 an automated method for determining a classifier for any known anatomical
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| bshanks@0 | 48 structure. Therefore, we seek a procedure by which a gene expression dataset
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| bshanks@0 | 49 may be analyzed in concert with an anatomical atlas in order to produce a
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| bshanks@0 | 50 classifier. Such a procedure is a type of a machine learning procedure. The
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| bshanks@0 | 51 construction of the classifier is called training (also learning), and the initial
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| bshanks@0 | 52 gene expression dataset used in the construction of the classifier is called training
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| bshanks@0 | 53 data.
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| bshanks@0 | 54 In the machine learning literature, this sort of procedure may be thought
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| bshanks@28 | 55 of as a supervised learning task, defined as a task in which the goal is to learn
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| bshanks@0 | 56 a mapping from instances to labels, and the training data consists of a set of
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| bshanks@0 | 57 instances (voxels) for which the labels (subregions) are known.
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| bshanks@0 | 58 Each gene expression level is called a feature, and the selection of which
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| bshanks@29 | 59 genes1 to include is called feature selection. Feature selection is one component
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| bshanks@0 | 60 of the task of learning a classifier. Some methods for learning classifiers start
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| bshanks@0 | 61 out with a separate feature selection phase, whereas other methods combine
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| bshanks@0 | 62 feature selection with other aspects of training.
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| bshanks@0 | 63 One class of feature selection methods assigns some sort of score to each
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| bshanks@0 | 64 candidate gene. The top-ranked genes are then chosen. Some scoring measures
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| bshanks@0 | 65 can assign a score to a set of selected genes, not just to a single gene; in this
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| bshanks@0 | 66 case, a dynamic procedure may be used in which features are added and sub-
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| bshanks@0 | 67 tracted from the selected set depending on how much they raise the score. Such
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| bshanks@0 | 68 procedures are called “stepwise” or “greedy”.
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| bshanks@29 | 69 __________________________
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| bshanks@29 | 70 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.
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| bshanks@29 | 71 2
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| bshanks@29 | 72
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| bshanks@0 | 73 Although the classifier itself may only look at the gene expression data within
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| bshanks@0 | 74 each voxel before classifying that voxel, the learning algorithm which constructs
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| bshanks@0 | 75 the classifier may look over the entire dataset. We can categorize score-based
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| bshanks@0 | 76 feature selection methods depending on how the score of calculated. Often
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| bshanks@0 | 77 the score calculation consists of assigning a sub-score to each voxel, and then
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| bshanks@0 | 78 aggregating these sub-scores into a final score (the aggregation is often a sum or
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| bshanks@0 | 79 a sum of squares). If only information from nearby voxels is used to calculate a
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| bshanks@0 | 80 voxel’s sub-score, then we say it is a local scoring method. If only information
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| bshanks@0 | 81 from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a
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| bshanks@0 | 82 pointwise scoring method.
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| bshanks@0 | 83 Key questions when choosing a learning method are: What are the instances?
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| bshanks@0 | 84 What are the features? How are the features chosen? Here are four principles
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| bshanks@0 | 85 that outline our answers to these questions.
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| bshanks@29 | 86 Principle 1: Combinatorial gene expression It is too much to hope
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| bshanks@29 | 87 that every anatomical region of interest will be identified by a single gene. For
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| bshanks@29 | 88 example, in the cortex, there are some areas which are not clearly delineated
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| bshanks@29 | 89 by any gene included in the Allen Brain Atlas (ABA) dataset. However, at
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| bshanks@29 | 90 least some of these areas can be delineated by looking at combinations of genes
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| bshanks@29 | 91 (an example of an area for which multiple genes are necessary and sufficient
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| bshanks@29 | 92 is provided in Preliminary Results). Therefore, each instance should contain
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| bshanks@29 | 93 multiple features (genes).
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| bshanks@16 | 94 Principle 2: Only look at combinations of small numbers of genes
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| bshanks@29 | 95 When the classifier classifies a voxel, it is only allowed to look at the expression of
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| bshanks@29 | 96 the genes which have been selected as features. The more data that is available
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| bshanks@29 | 97 to a classifier, the better that it can do. For example, perhaps there are weak
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| bshanks@29 | 98 correlations over many genes that add up to a strong signal. So, why not include
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| bshanks@29 | 99 every gene as a feature? The reason is that we wish to employ the classifier in
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| bshanks@29 | 100 situations in which it is not feasible to gather data about every gene. For
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| bshanks@29 | 101 example, if we want to use the expression of marker genes as a trigger for some
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| bshanks@29 | 102 regionally-targeted intervention, then our intervention must contain a molecular
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| bshanks@29 | 103 mechanism to check the expression level of each marker gene before it triggers.
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| bshanks@29 | 104 It is currently infeasible to design a molecular trigger that checks the level of
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| bshanks@29 | 105 more than a handful of genes. Similarly, if the goal is to develop a procedure to
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| bshanks@29 | 106 do ISH on tissue samples in order to label their anatomy, then it is infeasible
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| bshanks@29 | 107 to label more than a few genes. Therefore, we must select only a few genes as
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| bshanks@29 | 108 features.
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| bshanks@16 | 109 Principle 3: Use geometry in feature selection
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| bshanks@16 | 110 When doing feature selection with score-based methods, the simplest thing
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| bshanks@16 | 111 to do would be to score the performance of each voxel by itself and then com-
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| bshanks@16 | 112 bine these scores (pointwise scoring). A more powerful approach is to also use
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| bshanks@16 | 113 information about the geometric relations between each voxel and its neighbors;
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| bshanks@16 | 114 this requires non-pointwise, local scoring methods. See Preliminary Results for
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| bshanks@16 | 115 evidence of the complementary nature of pointwise and local scoring methods.
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| bshanks@29 | 116 3
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| bshanks@29 | 117
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| bshanks@16 | 118 Principle 4: Work in 2-D whenever possible
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| bshanks@16 | 119 There are many anatomical structures which are commonly characterized in
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| bshanks@0 | 120 terms of a two-dimensional manifold. When it is known that the structure that
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| bshanks@0 | 121 one is looking for is two-dimensional, the results may be improved by allowing
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| bshanks@0 | 122 the analysis algorithm to take advantage of this prior knowledge. In addition,
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| bshanks@0 | 123 it is easier for humans to visualize and work with 2-D data.
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| bshanks@0 | 124 Therefore, when possible, the instances should represent pixels, not voxels.
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| bshanks@1 | 125 Aim 2
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| bshanks@16 | 126 Machine learning terminology: clustering
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| bshanks@16 | 127 If one is given a dataset consisting merely of instances, with no class labels,
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| bshanks@16 | 128 then analysis of the dataset is referred to as unsupervised learning in the jargon
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| bshanks@16 | 129 of machine learning. One thing that you can do with such a dataset is to group
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| bshanks@15 | 130 instances together. A set of similar instances is called a cluster, and the activity
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| bshanks@15 | 131 of finding grouping the data into clusters is called clustering or cluster analysis.
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| bshanks@15 | 132 The task of deciding how to carve up a structure into anatomical subregions
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| bshanks@15 | 133 can be put into these terms. The instances are once again voxels (or pixels)
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| bshanks@15 | 134 along with their associated gene expression profiles. We make the assumption
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| bshanks@15 | 135 that voxels from the same subregion have similar gene expression profiles, at
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| bshanks@15 | 136 least compared to the other subregions. This means that clustering voxels is
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| bshanks@15 | 137 the same as finding potential subregions; we seek a partitioning of the voxels
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| bshanks@15 | 138 into subregions, that is, into clusters of voxels with similar gene expression.
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| bshanks@15 | 139 It is desirable to determine not just one set of subregions, but also how
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| bshanks@15 | 140 these subregions relate to each other, if at all; perhaps some of the subregions
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| bshanks@15 | 141 are more similar to each other than to the rest, suggesting that, although at a
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| bshanks@15 | 142 fine spatial scale they could be considered separate, on a coarser spatial scale
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| bshanks@15 | 143 they could be grouped together into one large subregion. This suggests the
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| bshanks@15 | 144 outcome of clustering may be a hierarchial tree of clusters, rather than a single
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| bshanks@15 | 145 set of clusters which partition the voxels. This is called hierarchial clustering.
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| bshanks@16 | 146 Similarity scores
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| bshanks@18 | 147 A crucial choice when designing a clustering method is how to measure
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| bshanks@18 | 148 similarity, across either pairs of instances, or clusters, or both. There is much
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| bshanks@18 | 149 overlap between scoring methods for feature selection (discussed above under
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| bshanks@18 | 150 Aim 1) and scoring methods for similarity.
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| bshanks@16 | 151 Spatially contiguous clusters; image segmentation
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| bshanks@16 | 152 We have shown that aim 2 is a type of clustering task. In fact, it is a
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| bshanks@16 | 153 special type of clustering task because we have an additional constraint on
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| bshanks@16 | 154 clusters; voxels grouped together into a cluster must be spatially contiguous.
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| bshanks@16 | 155 In Preliminary Results, we show that one can get reasonable results without
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| bshanks@16 | 156 enforcing this constraint, however, we plan to compare these results against
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| bshanks@16 | 157 other methods which guarantee contiguous clusters.
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| bshanks@15 | 158 Perhaps the biggest source of continguous clustering algorithms is the field
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| bshanks@15 | 159 of computer vision, which has produced a variety of image segmentation algo-
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| bshanks@29 | 160 4
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| bshanks@29 | 161
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| bshanks@15 | 162 rithms. Image segmentation is the task of partitioning the pixels in a digital
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| bshanks@15 | 163 image into clusters, usually contiguous clusters. Aim 2 is similar to an image
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| bshanks@15 | 164 segmentation task. There are two main differences; in our task, there are thou-
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| bshanks@15 | 165 sands of color channels (one for each gene), rather than just three. There are
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| bshanks@15 | 166 imaging tasks which use more than three colors, however, for example multispec-
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| bshanks@15 | 167 tral imaging and hyperspectral imaging, which are often used to process satellite
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| bshanks@15 | 168 imagery. A more crucial difference is that there are various cues which are ap-
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| bshanks@15 | 169 propriate for detecting sharp object boundaries in a visual scene but which are
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| bshanks@15 | 170 not appropriate for segmenting abstract spatial data such as gene expression.
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| bshanks@15 | 171 Although many image segmentation algorithms can be expected to work well
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| bshanks@15 | 172 for segmenting other sorts of spatially arranged data, some of these algorithms
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| bshanks@15 | 173 are specialized for visual images.
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| bshanks@16 | 174 Dimensionality reduction
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| bshanks@16 | 175 Unlike aim 1, there is no externally-imposed need to select only a handful
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| bshanks@16 | 176 of informative genes for inclusion in the instances. However, some clustering
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| bshanks@16 | 177 algorithms perform better on small numbers of features. There are techniques
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| bshanks@15 | 178 which “summarize” a larger number of features using a smaller number of fea-
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| bshanks@15 | 179 tures; these techniques go by the name of feature extraction or dimensionality
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| bshanks@15 | 180 reduction. The small set of features that such a technique yields is called the
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| bshanks@15 | 181 reduced feature set. After the reduced feature set is created, the instances may
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| bshanks@15 | 182 be replaced by reduced instances, which have as their features the reduced fea-
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| bshanks@15 | 183 ture set rather than the original feature set of all gene expression levels. Note
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| bshanks@15 | 184 that the features in the reduced feature set do not necessarily correspond to
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| bshanks@15 | 185 genes; each feature in the reduced set may be any function of the set of gene
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| bshanks@15 | 186 expression levels.
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| bshanks@15 | 187 Another use for dimensionality reduction is to visualize the relationships
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| bshanks@15 | 188 between subregions. For example, one might want to make a 2-D plot upon
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| bshanks@15 | 189 which each subregion is represented by a single point, and with the property
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| bshanks@15 | 190 that subregions with similar gene expression profiles should be nearby on the
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| bshanks@15 | 191 plot (that is, the property that distance between pairs of points in the plot
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| bshanks@15 | 192 should be proportional to some measure of dissimilarity in gene expression). It
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| bshanks@15 | 193 is likely that no arrangement of the points on a 2-D plan will exactly satisfy
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| bshanks@15 | 194 this property – however, dimensionality reduction techniques allow one to find
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| bshanks@15 | 195 arrangements of points that approximately satisfy that property. Note that
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| bshanks@15 | 196 in this application, dimensionality reduction is being applied after clustering;
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| bshanks@15 | 197 whereas in the previous paragraph, we were talking about using dimensionality
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| bshanks@15 | 198 reduction before clustering.
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| bshanks@16 | 199 Clustering genes rather than voxels
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| bshanks@16 | 200 Although the ultimate goal is to cluster the instances (voxels or pixels), one
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| bshanks@15 | 201 strategy to achieve this goal is to first cluster the features (genes). There are
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| bshanks@15 | 202 two ways that clusters of genes could be used.
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| bshanks@15 | 203 Gene clusters could be used as part of dimensionality reduction: rather than
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| bshanks@15 | 204 have one feature for each gene, we could have one reduced feature for each gene
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| bshanks@15 | 205 cluster.
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| bshanks@29 | 206 5
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| bshanks@29 | 207
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| bshanks@15 | 208 Gene clusters could also be used to directly yield a clustering on instances.
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| bshanks@15 | 209 This is because many genes have an expression pattern which seems to pick
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| bshanks@15 | 210 out a single, spatially continguous subregion. Therefore, it seems likely that an
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| bshanks@15 | 211 anatomically interesting subregion will have multiple genes which each individ-
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| bshanks@29 | 212 ually pick it out2. This suggests the following procedure: cluster together genes
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| bshanks@15 | 213 which pick out similar subregions, and then to use the more popular common
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| bshanks@15 | 214 subregions as the final clusters. In the Preliminary Data we show that a num-
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| bshanks@15 | 215 ber of anatomically recognized cortical regions, as well as some “superregions”
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| bshanks@15 | 216 formed by lumping together a few regions, are associated with gene clusters in
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| bshanks@15 | 217 this fashion.
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| bshanks@0 | 218 Aim 3
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| bshanks@16 | 219 Background
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| bshanks@18 | 220 The cortex is divided into areas and layers. To a first approximation, the
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| bshanks@18 | 221 parcellation of the cortex into areas can be drawn as a 2-D map on the surface of
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| bshanks@18 | 222 the cortex. In the third dimension, the boundaries between the areas continue
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| bshanks@18 | 223 downwards into the cortical depth, perpendicular to the surface. The layer
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| bshanks@17 | 224 boundaries run parallel to the surface. One can picture an area of the cortex as
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| bshanks@17 | 225 a slice of many-layered cake.
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| bshanks@0 | 226 Although it is known that different cortical areas have distinct roles in both
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| bshanks@0 | 227 normal functioning and in disease processes, there are no known marker genes
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| bshanks@0 | 228 for many cortical areas. When it is necessary to divide a tissue sample into
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| bshanks@0 | 229 cortical areas, this is a manual process that requires a skilled human to combine
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| bshanks@0 | 230 multiple visual cues and interpret them in the context of their approximate
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| bshanks@0 | 231 location upon the cortical surface.
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| bshanks@0 | 232 Even the questions of how many areas should be recognized in cortex, and
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| bshanks@0 | 233 what their arrangement is, are still not completely settled. A proposed division
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| bshanks@0 | 234 of the cortex into areas is called a cortical map. In the rodent, the lack of a
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| bshanks@0 | 235 single agreed-upon map can be seen by contrasting the recent maps given by
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| bshanks@0 | 236 Swanson?? on the one hand, and Paxinos and Franklin?? on the other. While
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| bshanks@0 | 237 the maps are certainly very similar in their general arrangement, significant
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| bshanks@0 | 238 differences remain in the details.
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| bshanks@16 | 239 Significance
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| bshanks@16 | 240 The method developed in aim (1) will be applied to each cortical area to find
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| bshanks@0 | 241 a set of marker genes such that the combinatorial expression pattern of those
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| bshanks@29 | 242 genes uniquely picks out the target area. Finding marker genes will be useful
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| bshanks@29 | 243 for drug discovery as well as for experimentation because marker genes can be
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| bshanks@29 | 244 used to design interventions which selectively target individual cortical areas.
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| bshanks@27 | 245 __________________________
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| bshanks@29 | 246 2This would seem to contradict our finding in aim 1 that some cortical areas are combina-
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| bshanks@27 | 247 torially coded by multiple genes. However, it is possible that the currently accepted cortical
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| bshanks@27 | 248 maps divide the cortex into subregions which are unnatural from the point of view of gene
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| bshanks@27 | 249 expression; perhaps there is some other way to map the cortex for which each subregion can
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| bshanks@27 | 250 be identified by single genes.
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| bshanks@27 | 251 6
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| bshanks@27 | 252
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| bshanks@0 | 253 The application of the marker gene finding algorithm to the cortex will
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| bshanks@0 | 254 also support the development of new neuroanatomical methods. In addition to
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| bshanks@0 | 255 finding markers for each individual cortical areas, we will find a small panel
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| bshanks@0 | 256 of genes that can find many of the areal boundaries at once. This panel of
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| bshanks@0 | 257 marker genes will allow the development of an ISH protocol that will allow
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| bshanks@0 | 258 experimenters to more easily identify which anatomical areas are present in
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| bshanks@0 | 259 small samples of cortex.
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| bshanks@0 | 260 The method developed in aim (3) will provide a genoarchitectonic viewpoint
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| bshanks@0 | 261 that will contribute to the creation of a better map. The development of present-
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| bshanks@0 | 262 day cortical maps was driven by the application of histological stains. It is
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| bshanks@0 | 263 conceivable that if a different set of stains had been available which identified
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| bshanks@0 | 264 a different set of features, then the today’s cortical maps would have come out
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| bshanks@0 | 265 differently. Since the number of classes of stains is small compared to the number
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| bshanks@0 | 266 of genes, it is likely that there are many repeated, salient spatial patterns in
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| bshanks@0 | 267 the gene expression which have not yet been captured by any stain. Therefore,
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| bshanks@0 | 268 current ideas about cortical anatomy need to incorporate what we can learn
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| bshanks@0 | 269 from looking at the patterns of gene expression.
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| bshanks@0 | 270 While we do not here propose to analyze human gene expression data, it is
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| bshanks@0 | 271 conceivable that the methods we propose to develop could be used to suggest
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| bshanks@0 | 272 modifications to the human cortical map as well.
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| bshanks@0 | 273 Related work
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| bshanks@18 | 274 There does not appear to be much work on the automated analysis of spatial
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| bshanks@18 | 275 gene expression data.
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| bshanks@18 | 276 There is a substantial body of work on the analysis of gene expression data,
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| bshanks@18 | 277 however, most of this concerns gene expression data which is not fundamentally
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| bshanks@23 | 278 spatial.
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| bshanks@18 | 279 As noted above, there has been much work on both supervised learning and
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| bshanks@22 | 280 clustering, and there are many available algorithms for each. However, the
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| bshanks@22 | 281 completion of Aims 1 and 2 involves more than just choosing between a set of
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| bshanks@22 | 282 existing algorithms, and will constitute a substantial contribution to biology.
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| bshanks@22 | 283 The algorithms require the scientist to provide a framework for representing the
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| bshanks@22 | 284 problem domain, and the way that this framework is set up has a large impact
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| bshanks@22 | 285 on performance. Creating a good framework can require creatively reconcep-
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| bshanks@22 | 286 tualizing the problem domain, and is not merely a mechanical “fine-tuning”
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| bshanks@22 | 287 of numerical parameters. For example, we believe that domain-specific scoring
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| bshanks@22 | 288 measures (such as gradient similarity, which is discussed in Preliminary Work)
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| bshanks@22 | 289 may be necessary in order to achieve the best results in this application.
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| bshanks@20 | 290 We are aware of two existing efforts to relate spatial gene expression data to
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| bshanks@20 | 291 anatomy through computational methods.
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| bshanks@20 | 292 [?] describes an analysis of the anatomy of the hippocampus using the ABA
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| bshanks@20 | 293 dataset. In addition to manual analysis, two clustering methods were employed,
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| bshanks@20 | 294 a modified Non-negative Matrix Factorization (NNMF), and a hierarchial bifur-
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| bshanks@20 | 295 cation clustering scheme based on correlation as the similarity score. The paper
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| bshanks@20 | 296 yielded impressive results, proving the usefulness of such research. We have run
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| bshanks@29 | 297 7
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| bshanks@29 | 298
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| bshanks@20 | 299 NNMF on the cortical dataset and while the results are promising (see Prelim-
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| bshanks@29 | 300 inary Data), we think that it will be possible to find a better method3 (we also
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| bshanks@27 | 301 think that more automation of the parts that this paper’s authors did manually
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| bshanks@27 | 302 will be possible).
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| bshanks@27 | 303 and [?] describes AGEA. todo
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| bshanks@26 | 304 __________________________
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| bshanks@29 | 305 3We ran “vanilla” NNMF, whereas the paper under discussion used a modified method.
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| bshanks@26 | 306 Their main modification consisted of adding a soft spatial contiguity constraint. However,
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| bshanks@26 | 307 on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional
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| bshanks@26 | 308 constraint was needed. The paper under discussion mentions that they also tried a hierarchial
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| bshanks@26 | 309 variant of NNMF, but since they didn’t report its results, we assume that those result were
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| bshanks@26 | 310 not any more impressive than the results of the non-hierarchial variant.
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| bshanks@26 | 311 8
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| bshanks@26 | 312
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| bshanks@25 | 313 Preliminary work
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| bshanks@25 | 314 Format conversion between SEV, MATLAB, NIFTI
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| bshanks@25 | 315 todo
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| bshanks@25 | 316 Flatmap of cortex
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| bshanks@25 | 317 todo
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| bshanks@16 | 318 Using combinations of multiple genes is necessary and sufficient to
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| bshanks@15 | 319 delineate some cortical areas
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| bshanks@16 | 320 Here we give an example of a cortical area which is not marked by any
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| bshanks@16 | 321 single gene, but which can be identified combinatorially. according to logistic
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| bshanks@29 | 322 regression, gene wwc14 is the best fit single gene for predicting whether or not a
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| bshanks@16 | 323 pixel on the cortical surface belongs to the motor area (area MO). The upper-left
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| bshanks@0 | 324 picture in Figure shows wwc1’s spatial expression pattern over the cortex. The
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| bshanks@0 | 325 lower-right boundary of MO is represented reasonably well by this gene, however
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| bshanks@0 | 326 the gene overshoots the upper-left boundary. This flattened 2-D representation
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| bshanks@0 | 327 does not show it, but the area corresponding to the overshoot is the medial
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| bshanks@0 | 328 surface of the cortex. MO is only found on the lateral surface (todo).
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| bshanks@29 | 329 Gnee mtif25 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s
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| bshanks@0 | 330 upper-left boundary, but not its lower-right boundary. Mtif2 does not express
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| bshanks@0 | 331 very much on the medial surface. By adding together the values at each pixel
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| bshanks@16 | 332 in these two figures, we get the lower-left of Figure . This combination captures
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| bshanks@16 | 333 area MO much better than any single gene.
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| bshanks@17 | 334 Correlation todo
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| bshanks@17 | 335 Conditional entropy todo
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| bshanks@17 | 336 Gradient similarity todo
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| bshanks@16 | 337 Geometric and pointwise scoring methods provide complementary
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| bshanks@16 | 338 information
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| bshanks@16 | 339 To show that local geometry can provide useful information that cannot be
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| bshanks@16 | 340 detected via pointwise analyses, consider Fig. . The top row of Fig. displays the
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| bshanks@29 | 341 3 genes which most match area AUD, according to a pointwise method6. The
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| bshanks@21 | 342 bottom row displays the 3 genes which most match AUD according to a method
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| bshanks@29 | 343 which considers local geometry7 The pointwise method in the top row identifies
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| bshanks@26 | 344 __________________________
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| bshanks@29 | 345 4“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652
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| bshanks@29 | 346 5“mitochondrial translational initiation factor 2”; EntrezGene ID 76784
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| bshanks@29 | 347 6For each gene, a logistic regression in which the response variable was whether or not a
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| bshanks@21 | 348 surface pixel was within area AUD, and the predictor variable was the value of the expression
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| bshanks@21 | 349 of the gene underneath that pixel. The resulting scores were used to rank the genes in terms
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| bshanks@21 | 350 of how well they predict area AUD.
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| bshanks@29 | 351 7For each gene the gradient similarity (see section ??) between (a) a map of the expression
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| bshanks@22 | 352 of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this
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| bshanks@22 | 353 was used to rank the genes.
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| bshanks@26 | 354 9
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| bshanks@0 | 355
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| bshanks@0 | 356
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| bshanks@0 | 357
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| bshanks@0 | 358 Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2
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| bshanks@0 | 359 (each pixel’s value on the lower left is the sum of the corresponding pixels in
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| bshanks@0 | 360 the upper row). Within each picture, the vertical axis roughly corresponds to
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| bshanks@0 | 361 anterior at the top and posterior at the bottom, and the horizontal axis roughly
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| bshanks@0 | 362 corresponds to medial at the left and lateral at the right. The red outline is
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| bshanks@0 | 363 the boundary of region MO. Pixels are colored approximately according to the
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| bshanks@0 | 364 density of expressing cells underneath each pixel, with red meaning a lot of
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| bshanks@0 | 365 expression and blue meaning little.
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| bshanks@26 | 366 10
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| bshanks@26 | 367
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| bshanks@15 | 368
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| bshanks@15 | 369
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| bshanks@15 | 370 Figure 2: The top row shows the three genes which (individually) best predict
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| bshanks@15 | 371 area AUD, according to logistic regression. The bottom row shows the three
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| bshanks@15 | 372 genes which (individually) best match area AUD, according to gradient similar-
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| bshanks@15 | 373 ity. From left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a,
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| bshanks@15 | 374 Ptk7, Aph1a again, and Lepr
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| bshanks@27 | 375 genes which express more strongly in AUD than outside of it; its weakness is that
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| bshanks@27 | 376 this includes many areas which don’t have a salient border matching the areal
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| bshanks@27 | 377 border. The geometric method identifies genes whose salient expression border
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| bshanks@26 | 378 seems to partially line up with the border of AUD; its weakness is that this
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| bshanks@26 | 379 includes genes which don’t express over the entire area. Genes which have high
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| bshanks@26 | 380 rankings using both pointwise and border criteria, such as Aph1a in the example,
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| bshanks@26 | 381 may be particularly good markers. None of these genes are, individually, a
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| bshanks@26 | 382 perfect marker for AUD; we deliberately chose a “difficult” area in order to
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| bshanks@26 | 383 better contrast pointwise with geometric methods.
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| bshanks@26 | 384 Areas which can be identified by single genes
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| bshanks@26 | 385 todo
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| bshanks@18 | 386 Specific to Aim 1 (and Aim 3)
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| bshanks@17 | 387 Forward stepwise logistic regression todo
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| bshanks@17 | 388 SVM on all genes at once
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| bshanks@16 | 389 In order to see how well one can do when looking at all genes at once, we
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| bshanks@16 | 390 ran a support vector machine to classify cortical surface pixels based on their
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| bshanks@29 | 391 gene expression profiles. We achieved classification accuracy of about 81%8.
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| bshanks@16 | 392 As noted above, however, a classifier that looks at all the genes at once isn’t
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| bshanks@16 | 393 practically useful.
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| bshanks@27 | 394 ____________
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| bshanks@29 | 395 85-fold cross-validation.
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| bshanks@27 | 396 11
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| bshanks@27 | 397
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| bshanks@16 | 398 The requirement to find combinations of only a small number of genes limits
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| bshanks@16 | 399 us from straightforwardly applying many of the most simple techniques from
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| bshanks@17 | 400 the field of supervised machine learning. In the parlance of machine learning,
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| bshanks@17 | 401 our task combines feature selection with supervised learning.
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| bshanks@17 | 402 Decision trees
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| bshanks@17 | 403 todo
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| bshanks@18 | 404 Specific to Aim 2 (and Aim 3)
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| bshanks@18 | 405 Raw dimensionality reduction results
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| bshanks@20 | 406 todo
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| bshanks@20 | 407 (might want to incld nnMF since mentioned above)
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| bshanks@18 | 408 Dimensionality reduction plus K-means or spectral clustering
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| bshanks@18 | 409 Many areas are captured by clusters of genes
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| bshanks@16 | 410 todo
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| bshanks@15 | 411 todo
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| bshanks@26 | 412 12
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| bshanks@26 | 413
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| bshanks@15 | 414 Research plan
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| bshanks@18 | 415 todo amongst other things:
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| bshanks@16 | 416 Develop algorithms that find genetic markers for anatomical re-
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| bshanks@16 | 417 gions
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| bshanks@0 | 418 1. Develop scoring measures for evaluating how good individual genes are at
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| bshanks@0 | 419 marking areas: we will compare pointwise, geometric, and information-
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| bshanks@0 | 420 theoretic measures.
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| bshanks@0 | 421 2. Develop a procedure to find single marker genes for anatomical regions: for
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| bshanks@0 | 422 each cortical area, by using or combining the scoring measures developed,
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| bshanks@0 | 423 we will rank the genes by their ability to delineate each area.
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| bshanks@0 | 424 3. Extend the procedure to handle difficult areas by using combinatorial cod-
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| bshanks@0 | 425 ing: for areas that cannot be identified by any single gene, identify them
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| bshanks@0 | 426 with a handful of genes. We will consider both (a) algorithms that incre-
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| bshanks@0 | 427 mentally/greedily combine single gene markers into sets, such as forward
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| bshanks@0 | 428 stepwise regression and decision trees, and also (b) supervised learning
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| bshanks@0 | 429 techniques which use soft constraints to minimize the number of features,
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| bshanks@0 | 430 such as sparse support vector machines.
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| bshanks@0 | 431 4. Extend the procedure to handle difficult areas by combining or redrawing
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| bshanks@0 | 432 the boundaries: An area may be difficult to identify because the bound-
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| bshanks@0 | 433 aries are misdrawn, or because it does not “really” exist as a single area,
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| bshanks@0 | 434 at least on the genetic level. We will develop extensions to our procedure
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| bshanks@0 | 435 which (a) detect when a difficult area could be fit if its boundary were
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| bshanks@0 | 436 redrawn slightly, and (b) detect when a difficult area could be combined
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| bshanks@0 | 437 with adjacent areas to create a larger area which can be fit.
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| bshanks@16 | 438 Apply these algorithms to the cortex
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| bshanks@0 | 439 1. Create open source format conversion tools: we will create tools to bulk
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| bshanks@0 | 440 download the ABA dataset and to convert between SEV, NIFTI and MAT-
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| bshanks@0 | 441 LAB formats.
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| bshanks@0 | 442 2. Flatmap the ABA cortex data: map the ABA data onto a plane and draw
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| bshanks@0 | 443 the cortical area boundaries onto it.
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| bshanks@0 | 444 3. Find layer boundaries: cluster similar voxels together in order to auto-
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| bshanks@0 | 445 matically find the cortical layer boundaries.
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| bshanks@0 | 446 4. Run the procedures that we developed on the cortex: we will present, for
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| bshanks@0 | 447 each area, a short list of markers to identify that area; and we will also
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| bshanks@0 | 448 present lists of “panels” of genes that can be used to delineate many areas
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| bshanks@0 | 449 at once.
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| bshanks@27 | 450 13
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| bshanks@27 | 451
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| bshanks@16 | 452 Develop algorithms to suggest a division of a structure into anatom-
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| bshanks@0 | 453 ical parts
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| bshanks@0 | 454 1. Explore dimensionality reduction algorithms applied to pixels: including
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| bshanks@0 | 455 TODO
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| bshanks@0 | 456 2. Explore dimensionality reduction algorithms applied to genes: including
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| bshanks@0 | 457 TODO
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| bshanks@0 | 458 3. Explore clustering algorithms applied to pixels: including TODO
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| bshanks@0 | 459 4. Explore clustering algorithms applied to genes: including gene shaving,
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| bshanks@0 | 460 TODO
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| bshanks@0 | 461 5. Develop an algorithm to use dimensionality reduction and/or hierarchial
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| bshanks@0 | 462 clustering to create anatomical maps
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| bshanks@0 | 463 6. Run this algorithm on the cortex: present a hierarchial, genoarchitectonic
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| bshanks@0 | 464 map of the cortex
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| bshanks@26 | 465 ______________________________________________
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| bshanks@26 | 466 stuff i dunno where to put yet (there is more scattered through grant-
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| bshanks@15 | 467 oldtext):
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| bshanks@16 | 468 Principle 4: Work in 2-D whenever possible
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| bshanks@21 | 469 In anatomy, the manifold of interest is usually either defined by a combina-
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| bshanks@21 | 470 tion of two relevant anatomical axes (todo), or by the surface of the structure
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| bshanks@21 | 471 (as is the case with the cortex). In the former case, the manifold of interest is
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| bshanks@21 | 472 a plane, but in the latter case it is curved. If the manifold is curved, there are
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| bshanks@21 | 473 various methods for mapping the manifold into a plane.
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| bshanks@22 | 474 The method that we will develop will begin by mapping the data into a
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| bshanks@22 | 475 2-D plane. Although the manifold that characterized cortical areas is known
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| bshanks@22 | 476 to be the cortical surface, it remains to be seen which method of mapping the
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| bshanks@22 | 477 manifold into a plane is optimal for this application. We will compare mappings
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| bshanks@22 | 478 which attempt to preserve size (such as the one used by Caret??) with mappings
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| bshanks@22 | 479 which preserve angle (conformal maps).
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| bshanks@22 | 480 Although there is much 2-D organization in anatomy, there are also struc-
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| bshanks@22 | 481 tures whose shape is fundamentally 3-dimensional. If possible, we would like
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| bshanks@22 | 482 the method we develop to include a statistical test that warns the user if the
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| bshanks@22 | 483 assumption of 2-D structure seems to be wrong.
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| bshanks@22 | 484 if we need citations for aim 3 significance, http://www.sciencedirect.
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| bshanks@22 | 485 com/science?_ob=ArticleURL&_udi=B6WSS-4V70FHY-9&_user=4429&_coverDate=
|
| bshanks@25 | 486 12%2F26%2F2008&_rdoc=1&_fmt=full&_orig=na&_cdi=7054&_docanchor=&_acct=
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| bshanks@25 | 487 C000059602&_version=1&_urlVersion=0&_userid=4429&md5=551eccc743a2bfe6e992eee0c3194203#
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| bshanks@25 | 488 app2 has examples of genetic targeting to specific anatomical regions
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| bshanks@25 | 489 —
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| bshanks@25 | 490 note:
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| bshanks@29 | 491 do we need to cite: no known markers, impressive results?
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| bshanks@26 | 492 14
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| bshanks@26 | 493
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| bshanks@26 | 494
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