1 Specific aims

2 Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in situ transgenic

3 reporter, microarray voxelation, and others, allow the expression levels of many genes at many locations to be compared.

4 Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker

5 genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have

6 three specific aims:

7 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target

8 anatomical regions

9 (2) develop an algorithm to suggest new ways of carving up a structure into anatomically distinct regions, based on

10 spatial patterns in gene expression

11 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse

12 Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of

13 Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).

14 Although our particular application involves the 3D spatial distribution of gene expression, we anticipate that the methods

15 developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located in a low-dimensional

16 space. In particular, our method could be applied to genome-wide sequencing data derived from sets of tissues and disease

17 states.

18 In terms of the application of the methods to cerebral cortex, aim (1) is to go from cortical areas to marker genes,

19 and aim (2) is to let the gene profile define the cortical areas. In addition to validating the usefulness of the algorithms,

20 the application of these methods to cortex will produce immediate benefits, because there are currently no known genetic

21 markers for most cortical areas. The results of the project will support the development of new ways to selectively target

22 cortical areas, and it will support the development of a method for identifying the cortical areal boundaries present in small

23 tissue samples.

24 All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well as the

25 machine-readable datasets developed in aim (3), will be published and freely available for others to use.

26 The challenge topic

27 This proposal addresses challenge topic 06-HG-101. Massive new datasets obtained with techniques such as in situ hybridiza-

28 tion (ISH), immunohistochemistry, in situ transgenic reporter, microarray voxelation, and others, allow the expression levels

29 of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial variation in

30 gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical

31 maps based on gene expression patterns.

32 The Challenge and Potential impact

33 Each of our three aims will be discussed in turn. For each aim, we will develop a conceptual framework for thinking about

34 the task, and we will present our strategy for solving it. Next we will discuss related work. At the conclusion of each section,

35 we will summarize why our strategy is different from what has been done before. At the end of this section, we will describe

36 the potential impact.

37 Aim 1: Given a map of regions, find genes that mark the regions

38 Machine learning terminology: classifiers The task of looking for marker genes for known anatomical regions means

39 that one is looking for a set of genes such that, if the expression level of those genes is known, then the locations of the

40 regions can be inferred.

41 If we define the regions so that they cover the entire anatomical structure to be subdivided, we may say that we are

42 using gene expression in each voxel to assign that voxel to the proper area. We call this a classification task, because each

43 voxel is being assigned to a class (namely, its region). An understanding of the relationship between the combination of

44 their expression levels and the locations of the regions may be expressed as a function. The input to this function is a voxel,

45 along with the gene expression levels within that voxel; the output is the regional identity of the target voxel, that is, the

46 region to which the target voxel belongs. We call this function a classifier. In general, the input to a classifier is called an

47 instance, and the output is called a label (or a class label).

48 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a

49 classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be

50 analyzed in concert with an anatomical atlas in order to produce a classifier. The initial gene expression dataset used in

51 the construction of the classifier is called training data. In the machine learning literature, this sort of procedure may be

52 thought of as a supervised learning task, defined as a task in which the goal is to learn a mapping from instances to labels,

53 and the training data consists of a set of instances (voxels) for which the labels (regions) are known.

54 Each gene expression level is called a feature, and the selection of which genes1 to include is called feature selection.

55 Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with

56 a separate feature selection phase, whereas other methods combine feature selection with other aspects of training.

57 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then

58 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

59 procedure may be used in which features are added and subtracted from the selected set depending on how much they raise

60 the score. Such procedures are called “stepwise” or “greedy”.

61 Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the

62 algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature selection

63 methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to each voxel,

64 and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares or average). If

65 only information from nearby voxels is used to calculate a voxel’s sub-score, then we say it is a local scoring method. If only

66 information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.

67 Both gene expression data and anatomical atlases have errors, due to a variety of factors. Individual subjects have

68 idiosyncratic anatomy. Subjects may be improperly registred to the atlas. The method used to measure gene expression

69 may be noisy. The atlas may have errors. It is even possible that some areas in the anatomical atlas are “wrong” in that

70 they do not have the same shape as the natural domains of gene expression to which they correspond. These sources of error

71 can affect the displacement and the shape of both the gene expression data and the anatomical target areas. Therefore, it

72 is important to use feature selection methods which are robust to these kinds of errors.

73 Our strategy for Aim 1

74 Key questions when choosing a learning method are: What are the instances? What are the features? How are the features

75 chosen? Here are four principles that outline our answers to these questions.

76 _________________________________________

77 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.

78 Principle 1: Combinatorial gene expression

79 It istoo much to hope that every anatomical region of interest will be identified by a single gene. For example, in the

80 cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset.

81 However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for

82 which multiple genes are necessary and sufficient is provided in Preliminary Studies, Figure 4). Therefore, each instance

83 should contain multiple features (genes).

84 Principle 2: Only look at combinations of small numbers of genes

85 When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have been selected

86 as features. The more data that are available to a classifier, the better that it can do. For example, perhaps there are weak

87 correlations over many genes that add up to a strong signal. So, why not include every gene as a feature? The reason is that

88 we wish to employ the classifier in situations in which it is not feasible to gather data about every gene. For example, if we

89 want to use the expression of marker genes as a trigger for some regionally-targeted intervention, then our intervention must

90 contain a molecular mechanism to check the expression level of each marker gene before it triggers. It is currently infeasible

91 to design a molecular trigger that checks the level of more than a handful of genes. Similarly, if the goal is to develop a

92 procedure to do ISH on tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes.

93 Therefore, we must select only a few genes as features.

94 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many

95 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task

96 combines feature selection with supervised learning.

97 Principle 3: Use geometry in feature selection

98 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of

99 each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information

100 about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See

101 Preliminary Studies, figure 3 for evidence of the complementary nature of pointwise and local scoring methods.

102 Principle 4: Work in 2-D whenever possible

103 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When

104 it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis

105 algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D

106 data. Therefore, when possible, the instances should represent pixels, not voxels.

107 Related work

108 There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data

109 which are not fundamentally spatial2.

110 As noted above, there has been much work on both supervised learning and there are many available algorithms for

111 each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the

112 way that this framework is set up has a large impact on performance. Creating a good framework can require creatively

113 reconceptualizing the problem domain, and is not merely a mechanical “fine-tuning” of numerical parameters. For example,

114 we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Studies) may

115 be necessary in order to achieve the best results in this application.

116 We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods.

117 [12 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of

118 interest, computing what proportion of this structure is covered by the gene’s spatial region.

119 GeneAtlas[5] and EMAGE [25] allow the user to construct a search query by demarcating regions and then specifing

120 either the strength of expression or the name of another gene or dataset whose expression pattern is to be matched. For the

121 similiarity score (match score) between two images (in this case, the query and the gene expression images), GeneAtlas uses

122 the sum of a weighted L1-norm distance between vectors whose components represent the number of cells within a pixel3

123 whose expression is within four discretization levels. EMAGE uses Jaccard similarity4. Neither GeneAtlas nor EMAGE

124 allow one to search for combinations of genes that define a region in concert but not separately.

125 [14 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The user

126 selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) yields a list of genes which are

127 overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of overexpressed genes for selected

128 structures). Correlation: The user selects a seed voxel and the system then shows the user how much correlation there is

129 between the gene expression profile of the seed voxel and every other voxel. Clusters: will be described later

130 _________________________________________

131 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not

132 just data which have only a few different locations or which is indexed by anatomical label.

133 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.

134 4the number of true pixels in the intersection of the two images, divided by the number of pixels in their union.

135 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we

136 will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also

137 search for underexpression. Third, Gene Finder uses a simple pointwise score5, whereas we will also use geometric scores

138 such as gradient similarity (described in Preliminary Studies). Figures 4, 2, and 3 in the Preliminary Studies section contains

139 evidence that each of our three choices is the right one.

140 [6 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni

141 correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA,

142 this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for

143 underexpression, and does not look for combinations of genes.

144 [10 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary

145 algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their

146 match score is Jaccard similarity.

147 In summary, there has been fruitful work on finding marker genes, but only one of the previous projects explores

148 combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or

149 scoring methods.

150 Aim 2: From gene expression data, discover a map of regions

151 Machine learning terminology: clustering

152 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as

153 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances

154 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called

155 clustering or cluster analysis.

156 The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances

157 are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels

158 from the same anatomical region have similar gene expression profiles, at least compared to the other regions. This means

159 that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into

160 clusters of voxels with similar gene expression.

161 It is desirable to determine not just one set of regions, but also how these regions relate to each other. The outcome of

162 clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. This is called

163 hierarchial clustering.

164 Similarity scores A crucial choice when designing a clustering method is how to measure similarity, across either pairs

165 of instances, or clusters, or both. There is much overlap between scoring methods for feature selection (discussed above

166 under Aim 1) and scoring methods for similarity.

167 Spatially contiguous clusters; image segmentation We have shown that aim 2 is a type of clustering task. In fact,

168 it is a special type of clustering task because we have an additional constraint on clusters; voxels grouped together into a

169 cluster must be spatially contiguous. In Preliminary Studies, we show that one can get reasonable results without enforcing

170 this constraint; however, we plan to compare these results against other methods which guarantee contiguous clusters.

171 Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous clusters. Aim

172 2 is similar to an image segmentation task. There are two main differences; in our task, there are thousands of color channels

173 (one for each gene), rather than just three6. A more crucial difference is that there are various cues which are appropriate

174 for detecting sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data

175 such as gene expression. Although many image segmentation algorithms can be expected to work well for segmenting other

176 sorts of spatially arranged data, some of these algorithms are specialized for visual images.

177 Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression feature

178 vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying data.

179 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the

180 instances. However, some clustering algorithms perform better on small numbers of features7. There are techniques which

181 “summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature

182 extraction or dimensionality reduction. The small set of features that such a technique yields is called the reduced feature

183 set. Note that the features in the reduced feature set do not necessarily correspond to genes; each feature in the reduced set

184 may be any function of the set of gene expression levels.

185 _________________________________________

186 5“Expression energy ratio”, which captures overexpression.

187 6There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are often

188 used to process satellite imagery.

189 7First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering algorithms

190 may be much less. Second, it is thought that some clustering algorithms may give better results on reduced data.

191 Clustering genes rather than voxels Although the ultimate goal is to cluster the instances (voxels or pixels), one

192 strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes could be used.

193 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could

194 have one reduced feature for each gene cluster.

195 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression

196 pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically

197 interesting region will have multiple genes which each individually pick it out8. This suggests the following procedure:

198 cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters.

199 In Preliminary Studies, Figure 7, we show that a number of anatomically recognized cortical regions, as well as some

200 “superregions” formed by lumping together a few regions, are associated with gene clusters in this fashion.

201 The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering

202 algorithms.

203 Related work

204 Some researchers have attempted to parcellate cortex on the basis of non-gene expression data. For example, [17], [2], [18],

205 and [1 ] associate spots on the cortex with the radial profile9 of response to some stain ([11] uses MRI), extract features from

206 this profile, and then use similarity between surface pixels to cluster. Features used include statistical moments, wavelets,

207 and the excess mass functional. Some of these features are motivated by the presence of tangential lines of stain intensity

208 which correspond to laminar structure. Some methods use standard clustering procedures, whereas others make use of the

209 spatial nature of the data to look for sudden transitions, which are identified as areal borders.

210 [22 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,

211 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive

212 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving

213 the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset10 and while the results are

214 promising, they also demonstrate that NNMF is not necessarily the best dimensionality reduction method for this application

215 (see Preliminary Studies, Figure 6).

216 AGEA[14] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation

217 as the similarity metric. EMAGE[25] allows the user to select a dataset from among a large number of alternatives, or by

218 running a search query, and then to cluster the genes within that dataset. EMAGE clusters via hierarchial complete linkage

219 clustering with un-centred correlation as the similarity score.

220 [6 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and which were

221 highly correlated with many other genes. They computed the matrix of (rank) correlations between pairs of these genes, and

222 ordered the rows of this matrix as follows: “the first row of the matrix was chosen to show the strongest contrast between

223 the highest and lowest correlation coefficient for that row. The remaining rows were then arranged in order of decreasing

224 similarity using a least squares metric”. The resulting matrix showed four clusters. For each cluster, prototypical spatial

225 expression patterns were created by averaging the genes in the cluster. The prototypes were analyzed manually, without

226 clustering voxels.

227 [10 ] applies their technique for finding combinations of marker genes for the purpose of clustering genes around a “seed

228 gene”. They do this by using the pattern of expression of the seed gene as the target image, and then searching for other

229 genes which can be combined to reproduce this pattern. Other genes which are found are considered to be related to the

230 seed. The same team also describes a method[24] for finding “association rules” such as, “if this voxel is expressed in by

231 any gene, then that voxel is probably also expressed in by the same gene”. This could be useful as part of a procedure for

232 clustering voxels.

233 In summary, although these projects obtained clusterings, there has not been much comparison between different algo-

234 rithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found. The

235 projects using gene expression on cortex did not attempt to make use of the radial profile of gene expression. Also, none of

236 these projects did a separate dimensionality reduction step before clustering pixels, none tried to cluster genes first in order

237 to guide automated clustering of pixels into spatial regions, and none used co-clustering algorithms.

238 _________________________________________

239 8This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is

240 possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression;

241 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

242 the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.

243 9A radial profile is a profile along a line perpendicular to the cortical surface.

244 10We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft

245 spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was

246 needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.

247 Aim 3: apply the methods developed to the cerebral cortex

248 Background

249 The cortex is divided into areas and layers. Because of the cortical columnar organization, the parcellation of the cortex

250 into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the

251 areas continue downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the

252 surface. One can picture an area of the cortex as a slice of a six-layered cake11.

253 It is known that different cortical areas have distinct roles in both normal functioning and in disease processes, yet there

254 are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample into cortical areas, this is

255 a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of their

256 approximate location upon the cortical surface.

257 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not

258 completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a single

259 agreed-upon map can be seen by contrasting the recent maps given by Swanson[21] on the one hand, and Paxinos and

260 Franklin[16] on the other. While the maps are certainly very similar in their general arrangement, significant differences

261 remain.

262 The Allen Mouse Brain Atlas dataset

263 The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male, 56-day-old

264 C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed

265 to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial resolution

266 is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different mouse

267 brains were needed in order to measure the expression of many genes.

268 An automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate

269 system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 = 159,326

270 voxels in the 3D coordinate system, of which 51,533 are in the brain[14].

271 Mus musculus is thought to contain about 22,000 protein-coding genes[27]. The ABA contains data on about 20,000

272 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our dataset is derived from

273 only the coronal subset of the ABA12.

274 The ABA is not the only large public spatial gene expression dataset13. With the exception of the ABA, GenePaint, and

275 EMAGE, most of the other resources have not (yet) extracted the expression intensity from the ISH images and registered

276 the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of data available for public

277 download from the website14. Many of these resources focus on developmental gene expression.

278 Related work

279 [14 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations

280 between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either

281 of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of

282 the other components of AGEA can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes

283 for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas15.

284 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, (b) there has

285 been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally

286 finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo

287 from gene expression data.

288 ___________________

289 11Outside of isocortex, the number of layers varies.

290 12The sagittal data do not cover the entire cortex, and also have greater registration error[14]. Genes were selected by the Allen Institute for

291 coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression

292 pattern”[14].

293 13Other such resources include GENSAT[8], GenePaint[26], its sister project GeneAtlas[5], BGEM[13], EMAGE[25], EurExpress (http:

294 //www.eurexpress.org/ee/; EurExpress data are also entered into EMAGE), EADHB (http://www.ncl.ac.uk/ihg/EADHB/database/$EADHB_

295 {database}$.html), MAMEP (http://mamep.molgen.mpg.de/index.php), Xenbase (http://xenbase.org/), ZFIN[20], Aniseed (http://

296 aniseed-ibdm.univ-mrs.fr/), VisiGene (http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some of the other listed data

297 sources), GEISHA[4], Fruitfly.org[23], COMPARE (http://compare.ibdml.univ-mrs.fr/), GXD[19], GEO[3] (GXD and GEO contain spatial

298 data but also non-spatial data. All GXD spatial data are also in EMAGE.)

299 14without prior offline registration

300 15In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are often stronger

301 than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel correlation

302 clustering algorithm will tend to create clusters representing cortical layers, not areas (there may be clusters which presumably correspond to the

303 intersection of a layer and an area, but since one area will have many layer-area intersection clusters, further work is needed to make sense of

304 these). The reason that Gene Finder cannot the find marker genes for cortical areas is that, although the user chooses a seed voxel, Gene Finder

305 chooses the ROI for which genes will be found, and it creates that ROI by (pairwise voxel correlation) clustering around the seed.

306 Our project is guided by a concrete application with a well-specified criterion of success (how well we can find marker

307 genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods.

308 Significance

309

310

311 Figure 1: Top row: Genes Nfic and

312 A930001M12Rik are the most correlated

313 with area SS (somatosensory cortex). Bot-

314 tom row: Genes C130038G02Rik and

315 Cacna1i are those with the best fit using

316 logistic regression. Within each picture, the

317 vertical axis roughly corresponds to anterior

318 at the top and posterior at the bottom, and

319 the horizontal axis roughly corresponds to

320 medial at the left and lateral at the right.

321 The red outline is the boundary of region

322 SS. Pixels are colored according to correla-

323 tion, with red meaning high correlation and

324 blue meaning low. The method developed in aim (1) will be applied to each cortical area to find

325 a set of marker genes such that the combinatorial expression pattern of those

326 genes uniquely picks out the target area. Finding marker genes will be useful

327 for drug discovery as well as for experimentation because marker genes can be

328 used to design interventions which selectively target individual cortical areas.

329 The application of the marker gene finding algorithm to the cortex will

330 also support the development of new neuroanatomical methods. In addition

331 to finding markers for each individual cortical areas, we will find a small panel

332 of genes that can find many of the areal boundaries at once. This panel of

333 marker genes will allow the development of an ISH protocol that will allow

334 experimenters to more easily identify which anatomical areas are present in

335 small samples of cortex.

336 The method developed in aim (2) will provide a genoarchitectonic viewpoint

337 that will contribute to the creation of a better map. The development of

338 present-day cortical maps was driven by the application of histological stains.

339 If a different set of stains had been available which identified a different set of

340 features, then today’s cortical maps may have come out differently. It is likely

341 that there are many repeated, salient spatial patterns in the gene expression

342 which have not yet been captured by any stain. Therefore, cortical anatomy

343 needs to incorporate what we can learn from looking at the patterns of gene

344 expression.

345 While we do not here propose to analyze human gene expression data, it is

346 conceivable that the methods we propose to develop could be used to suggest

347 modifications to the human cortical map as well. In fact, the methods we will

348 develop will be applicable to other datasets beyond the brain. We will provide

349 an open-source toolbox to allow other researchers to easily use our methods.

350 With these methods, researchers with gene expression for any area of the body

351 will be able to efficiently find marker genes for anatomical regions, or to use

352 gene expression to discover new anatomical patterning. As described above,

353 marker genes have a variety of uses in the development of drugs and experimental manipulations, and in the anatomical

354 characterization of tissue samples. The discovery of new ways to carve up anatomical structures into regions may lead to

355 the discovery of new anatomical subregions in various structures, which will widely impact all areas of biology.

356

357 Figure 2: Gene Pitx2

358 is selectively underex-

359 pressed in area SS. Although our particular application involves the 3D spatial distribution of gene expression, we

360 anticipate that the methods developed in aims (1) and (2) will not be limited to gene expression

361 data, but rather will generalize to any sort of high-dimensional data over points located in a

362 low-dimensional space.

363 The approach: Preliminary Studies

364 Format conversion between SEV, MATLAB, NIFTI

365 We have created software to (politely) download all of the SEV files16 from the Allen Institute

366 website. We have also created software to convert between the SEV, MATLAB, and NIFTI file

367 formats, as well as some of Caret’s file formats.

368 Flatmap of cortex

369 We downloaded the ABA data and applied a mask to select only those voxels which belong to

370 cerebral cortex. We divided the cortex into hemispheres.

371 Using Caret[7], we created a mesh representation of the surface of the selected voxels. For each gene, and for each node

372 of the mesh, we calculated an average of the gene expression of the voxels “underneath” that mesh node. We then flattened

373 the cortex, creating a two-dimensional mesh.

374 ____

375 16SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.

376

377

378

379 Figure 3: The top row shows the two genes

380 which (individually) best predict area AUD,

381 according to logistic regression. The bot-

382 tom row shows the two genes which (indi-

383 vidually) best match area AUD, according

384 to gradient similarity. From left to right and

385 top to bottom, the genes are Ssr1, Efcbp1,

386 Ptk7, and Aph1a. We sampled the nodes of the irregular, flat mesh in order to create a regular

387 grid of pixel values. We converted this grid into a MATLAB matrix.

388 We manually traced the boundaries of each of 49 cortical areas from the

389 ABA coronal reference atlas slides. We then converted these manual traces

390 into Caret-format regional boundary data on the mesh surface. We projected

391 the regions onto the 2-d mesh, and then onto the grid, and then we converted

392 the region data into MATLAB format.

393 At this point, the data are in the form of a number of 2-D matrices, all in

394 registration, with the matrix entries representing a grid of points (pixels) over

395 the cortical surface:

396 ∙ A 2-D matrix whose entries represent the regional label associated with

397 each surface pixel

398 ∙ For each gene, a 2-D matrix whose entries represent the average expres-

399 sion level underneath each surface pixel

400 We created a normalized version of the gene expression data by subtracting

401 each gene’s mean expression level (over all surface pixels) and dividing the

402 expression level of each gene by its standard deviation.

403 The features and the target area are both functions on the surface pix-

404 els. They can be referred to as scalar fields over the space of surface pixels;

405 alternately, they can be thought of as images which can be displayed on the

406 flatmapped surface.

407 To move beyond a single average expression level for each surface pixel, we

408 plan to create a separate matrix for each cortical layer to represent the average expression level within that layer. Cortical

409 layers are found at different depths in different parts of the cortex. In preparation for extracting the layer-specific datasets,

410 we have extended Caret with routines that allow the depth of the ROI for volume-to-surface projection to vary.

411 In the Research Plan, we describe how we will automatically locate the layer depths. For validation, we have manually

412 demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex.

413 Feature selection and scoring methods

414 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a marker. See,

415 for example, Figure 2.

416

417

418 Figure 4: Upper left: wwc1. Upper right:

419 mtif2. Lower left: wwc1 + mtif2 (each

420 pixel’s value on the lower left is the sum of

421 the corresponding pixels in the upper row). Correlation Recall that the instances are surface pixels, and consider the

422 problem of attempting to classify each instance as either a member of a partic-

423 ular anatomical area, or not. The target area can be represented as a boolean

424 mask over the surface pixels.

425 One class of feature selection scoring methods contains methods which cal-

426 culate some sort of “match” between each gene image and the target image.

427 Those genes which match the best are good candidates for features.

428 One of the simplest methods in this class is to use correlation as the match

429 score. We calculated the correlation between each gene and each cortical area.

430 The top row of Figure 1 shows the three genes most correlated with area SS.

431 Conditional entropy An information-theoretic scoring method is to find

432 features such that, if the features (gene expression levels) are known, uncer-

433 tainty about the target (the regional identity) is reduced. Entropy measures

434 uncertainty, so what we want is to find features such that the conditional dis-

435 tribution of the target has minimal entropy. The distribution to which we are

436 referring is the probability distribution over the population of surface pixels.

437 The simplest way to use information theory is on discrete data, so we

438 discretized our gene expression data by creating, for each gene, five thresholded

439 boolean masks of the gene data. For each gene, we created a boolean mask

440 of its expression levels using each of these thresholds: the mean of that gene, the mean minus one standard deviation, the

441 mean minus two standard deviations, the mean plus one standard deviation, the mean plus two standard deviations.

442 Now, for each region, we created and ran a forward stepwise procedure which attempted to find pairs of gene expression

443 boolean masks such that the conditional entropy of the target area’s boolean mask, conditioned upon the pair of gene

444 expression boolean masks, is minimized.

445 This finds pairs of genes which are most informative (at least at these discretization thresholds) relative to the question,

446 “Is this surface pixel a member of the target area?”. Its advantage over linear methods such as logistic regression is that it

447 takes account of arbitrarily nonlinear relationships; for example, if the XOR of two variables predicts the target, conditional

448 entropy would notice, whereas linear methods would not.

449

450

451

452

453 Figure 5: From left to right and top

454 to bottom, single genes which roughly

455 identify areas SS (somatosensory primary

456 + supplemental), SSs (supplemental so-

457 matosensory), PIR (piriform), FRP (frontal

458 pole), RSP (retrosplenial), COApm (Corti-

459 cal amygdalar, posterior part, medial zone).

460 Grouping some areas together, we have

461 also found genes to identify the groups

462 ACA+PL+ILA+DP+ORB+MO (anterior

463 cingulate, prelimbic, infralimbic, dorsal pe-

464 duncular, orbital, motor), posterior and lat-

465 eral visual (VISpm, VISpl, VISI, VISp; pos-

466 teromedial, posterolateral, lateral, and pri-

467 mary visual; the posterior and lateral vi-

468 sual area is distinguished from its neigh-

469 bors, but not from the entire rest of the

470 cortex). The genes are Pitx2, Aldh1a2,

471 Ppfibp1, Slco1a5, Tshz2, Trhr, Col12a1,

472 Ets1. Gradient similarity We noticed that the previous two scoring methods,

473 which are pointwise, often found genes whose pattern of expression did not

474 look similar in shape to the target region. For this reason we designed a

475 non-pointwise local scoring method to detect when a gene had a pattern of

476 expression which looked like it had a boundary whose shape is similar to the

477 shape of the target region. We call this scoring method “gradient similarity”.

478 One might say that gradient similarity attempts to measure how much the

479 border of the area of gene expression and the border of the target region over-

480 lap. However, since gene expression falls off continuously rather than jumping

481 from its maximum value to zero, the spatial pattern of a gene’s expression often

482 does not have a discrete border. Therefore, instead of looking for a discrete

483 border, we look for large gradients. Gradient similarity is a symmetric function

484 over two images (i.e. two scalar fields). It is is high to the extent that matching

485 pixels which have large values and large gradients also have gradients which

486 are oriented in a similar direction. The formula is:

487 ∑

488 pixel<img src="cmsy7-32.png" alt="&#x2208;" />pixels cos(abs(&#x2220;&#x2207;1 -&#x2220;&#x2207;2)) &#x22C5;|&#x2207;1| + |&#x2207;2|

489 2 &#x22C5; pixel_value1 + pixel_value2

490 2

491 where &#x2207;1 and &#x2207;2 are the gradient vectors of the two images at the current

492 pixel; &#x2220;&#x2207;i is the angle of the gradient of image i at the current pixel; |&#x2207;i| is

493 the magnitude of the gradient of image i at the current pixel; and pixel_valuei

494 is the value of the current pixel in image i.

495 The intuition is that we want to see if the borders of the pattern in the

496 two images are similar; if the borders are similar, then both images will have

497 corresponding pixels with large gradients (because this is a border) which are

498 oriented in a similar direction (because the borders are similar).

499 Most of the genes in Figure 5 were identified via gradient similarity.

500 Gradient similarity provides information complementary to cor-

501 relation

502 To show that gradient similarity can provide useful information that cannot

503 be detected via pointwise analyses, consider Fig. 3. The top row of Fig. 3

504 displays the 3 genes which most match area AUD, according to a pointwise

505 method17. The bottom row displays the 3 genes which most match AUD ac-

506 cording to a method which considers local geometry18 The pointwise method

507 in the top row identifies genes which express more strongly in AUD than out-

508 side of it; its weakness is that this includes many areas which don&#8217;t have a

509 salient border matching the areal border. The geometric method identifies

510 genes whose salient expression border seems to partially line up with the bor-

511 der of AUD; its weakness is that this includes genes which don&#8217;t express over

512 the entire area. Genes which have high rankings using both pointwise and bor-

513 der criteria, such as Aph1a in the example, may be particularly good markers.

514 None of these genes are, individually, a perfect marker for AUD; we deliberately

515 chose a &#8220;difficult&#8221; area in order to better contrast pointwise with geometric

516 methods.

517 Areas which can be identified by single genes Using gradient simi-

518 larity, we have already found single genes which roughly identify some areas

519 and groupings of areas. For each of these areas, an example of a gene which roughly identifies it is shown in Figure 5. We

520 have not yet cross-verified these genes in other atlases.

521 _________________________________________

522 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

523 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

524 they predict area AUD.

525 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,

526 was calculated, and this was used to rank the genes.

527 In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior part of

528 cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate), VIS

529 (visual), AUD (auditory).

530 These results validate our expectation that the ABA dataset can be exploited to find marker genes for many cortical

531 areas, while also validating the relevancy of our new scoring method, gradient similarity.

532 Combinations of multiple genes are useful and necessary for some areas

533 In Figure 4, we give an example of a cortical area which is not marked by any single gene, but which can be identified

534 combinatorially. Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a

535 pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure 4 shows wwc1&#8217;s spatial

536 expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, but the

537 gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding

538 to the overshoot is the medial surface of the cortex. MO is only found on the dorsal surface. Gene mtif2 is shown in the

539 upper-right. Mtif2 captures MO&#8217;s upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much

540 on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left image. This

541 combination captures area MO much better than any single gene.

542 This shows that our proposal to develop a method to find combinations of marker genes is both possible and necessary.

543 Feature selection integrated with prediction As noted earlier, in general, any classifier can be used for feature

544 selection by running it inside a stepwise wrapper. Also, some learning algorithms integrate soft constraints on number of

545 features used. Examples of both of these will be seen in the section &#8220;Multivariate supervised learning&#8221;.

546 Multivariate supervised learning

547

548

549

550

551 Figure 6: First row: the first 6 reduced dimensions, using PCA. Second

552 row: the first 6 reduced dimensions, using NNMF. Third row: the first

553 six reduced dimensions, using landmark Isomap. Bottom row: examples

554 of kmeans clustering applied to reduced datasets to find 7 clusters. Left:

555 19 of the major subdivisions of the cortex. Second from left: PCA. Third

556 from left: NNMF. Right: Landmark Isomap. Additional details: In the

557 third and fourth rows, 7 dimensions were found, but only 6 displayed. In

558 the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions

559 were used; for landmark Isomap, 7 dimensions were used. Forward stepwise logistic regression Lo-

560 gistic regression is a popular method for pre-

561 dictive modeling of categorial data. As a pi-

562 lot run, for five cortical areas (SS, AUD, RSP,

563 VIS, and MO), we performed forward stepwise

564 logistic regression to find single genes, pairs of

565 genes, and triplets of genes which predict areal

566 identify. This is an example of feature selec-

567 tion integrated with prediction using a stepwise

568 wrapper. Some of the single genes found were

569 shown in various figures throughout this doc-

570 ument, and Figure 4 shows a combination of

571 genes which was found.

572 We felt that, for single genes, gradient simi-

573 larity did a better job than logistic regression at

574 capturing our subjective impression of a &#8220;good

575 gene&#8221;.

576 SVM on all genes at once

577 In order to see how well one can do when

578 looking at all genes at once, we ran a support

579 vector machine to classify cortical surface pix-

580 els based on their gene expression profiles. We

581 achieved classification accuracy of about 81%19.

582 This shows that the genes included in the ABA

583 dataset are sufficient to define much of cortical

584 anatomy. However, as noted above, a classifier

585 that looks at all the genes at once isn&#8217;t as prac-

586 tically useful as a classifier that uses only a few

587 genes.

588 _________________________________________

589 195-fold cross-validation.

590 Data-driven redrawing of the cor-

591 tical map

592 We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene expression

593 profile associated with each voxel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional Scaling

594 (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment (LTSA), Hessian locally linear

595 embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic Proximity Embedding (SPE), Fast Maximum

596 Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing

597 many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the first, second, and third rows of

598 Figure 6.

599 After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we have tried

600 k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last

601 row of Figure 6. To compare, the leftmost picture on the bottom row of Figure 6 shows some of the major subdivisions of

602 cortex. These results clearly show that different dimensionality reduction techniques capture different aspects of the data

603 and lead to different clusterings, indicating the utility of our proposal to produce a detailed comparion of these techniques

604 as applied to the domain of genomic anatomy.

605

606 Figure 7: Prototypes corresponding to sample gene clusters,

607 clustered by gradient similarity. Region boundaries for the

608 region that most matches each prototype are overlayed. Many areas are captured by clusters of genes We

609 also clustered the genes using gradient similarity to see if

610 the spatial regions defined by any clusters matched known

611 anatomical regions. Figure 7 shows, for ten sample gene

612 clusters, each cluster&#8217;s average expression pattern, compared

613 to a known anatomical boundary. This suggests that it is

614 worth attempting to cluster genes, and then to use the re-

615 sults to cluster voxels.

616 The approach: what we plan to do

617 Flatmap cortex and segment cortical layers

618 There are multiple ways to flatten 3-D data into 2-D. We

619 will compare mappings from manifolds to planes which at-

620 tempt to preserve size (such as the one used by Caret[7])

621 with mappings which preserve angle (conformal maps). Our

622 method will include a statistical test that warns the user if

623 the assumption of 2-D structure seems to be wrong.

624 We have not yet made use of radial profiles. While the radial profiles may be used &#8220;raw&#8221;, for laminar structures like the

625 cortex another strategy is to group together voxels in the same cortical layer; each surface pixel would then be associated

626 with one expression level per gene per layer. We will develop a segmentation algorithm to automatically identify the layer

627 boundaries.

628 Develop algorithms that find genetic markers for anatomical regions

629 We will develop scoring methods for evaluating how good individual genes are at marking areas. We will compare pointwise,

630 geometric, and information-theoretic measures. We already developed one entirely new scoring method (gradient similarity),

631 but we may develop more. Scoring measures that we will explore will include the L1 norm, correlation, expression energy

632 ratio, conditional entropy, gradient similarity, Jaccard similarity, Dice similarity, Hough transform, and statistical tests such

633 as Student&#8217;s t-test, and the Mann-Whitney U test (a non-parametric test). In addition, any classifier induces a scoring

634 measure on genes by taking the prediction error when using that gene to predict the target.

635 Using some combination of these measures, we will develop a procedure to find single marker genes for anatomical regions:

636 for each cortical area, we will rank the genes by their ability to delineate each area. We will quantitatively compare the list

637 of single genes generated by our method to the lists generated by previous methods which are mentioned in Aim 1 Related

638 Work.

639 Some cortical areas have no single marker genes but can be identified by combinatorial coding. This requires multivariate

640 scoring measures and feature selection procedures. Many of the measures, such as expression energy, gradient similarity,

641 Jaccard, Dice, Hough, Student&#8217;s t, and Mann-Whitney U are univariate. We will extend these scoring measures for use

642 in multivariate feature selection, that is, for scoring how well combinations of genes, rather than individual genes, can

643 distinguish a target area. There are existing multivariate forms of some of the univariate scoring measures, for example,

644 Hotelling&#8217;s T-square is a multivariate analog of Student&#8217;s t.

645 We will develop a feature selection procedure for choosing the best small set of marker genes for a given anatomical

646 area. In addition to using the scoring measures that we develop, we will also explore (a) feature selection using a stepwise

647 wrapper over &#8220;vanilla&#8221; classifiers such as logistic regression, (b) supervised learning methods such as decision trees which

648 incrementally/greedily combine single gene markers into sets, and (c) supervised learning methods which use soft constraints

649 to minimize number of features used, such as sparse support vector machines.

650 Since errors of displacement and of shape may cause genes and target areas to match less than they should, we will

651 consider the robustness of feature selection methods in the presence of error. Some of these methods, such as the Hough

652 transform, are designed to be resistant in the presence of error, but many are not. We will consider extensions to scoring

653 measures that may improve their robustness; for example, a wrapper that runs a scoring method on small displacements

654 and distortions of the data adds robustness to registration error at the expense of computation time.

655 An area may be difficult to identify because the boundaries are misdrawn in the atlas, or because the shape of the natural

656 domain of gene expression corresponding to the area is different from the shape of the area as recognized by anatomists.

657 We will extend our procedure to handle difficult areas by combining areas or redrawing their boundaries. We will develop

658 extensions to our procedure which (a) detect when a difficult area could be fit if its boundary were redrawn slightly, and (b)

659 detect when a difficult area could be combined with adjacent areas to create a larger area which can be fit.

660 A future publication on the method that we develop in Aim 1 will review the scoring measures and quantitatively compare

661 their performance in order to provide a foundation for future research of methods of marker gene finding. We will measure

662 the robustness of the scoring measures as well as their absolute performance on our dataset.

663 Classifiers

664 We will explore and compare different classifiers. As noted above, this activity is not separate from the previous one,

665 because some supervised learning algorithms include feature selection, and any classifier can be combined with a stepwise

666 wrapper for use as a feature selection method. We will explore logistic regression (including spatial models[15]), decision

667 trees20 , sparse SVMs, generative mixture models (including naive bayes), kernel density estimation, instance-based learning

668 methods (such as k-nearest neighbor), genetic algorithms, and artificial neural networks.

669 Application to cortical areas

670 # confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting, two hemis

671 Develop algorithms to suggest a division of a structure into anatomical parts

672 1.Explore dimensionality reduction algorithms applied to pixels: including TODO

673 2.Explore dimensionality reduction algorithms applied to genes: including TODO

674 3.Explore clustering algorithms applied to pixels: including TODO

675 4.Explore clustering algorithms applied to genes: including gene shaving[9], TODO

676 5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps

677 6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex

678 # Linear discriminant analysis

679 # jbt, coclustering

680 # self-organizing map

681 # Linear discriminant analysis

682 # compare using clustering scores

683 # multivariate gradient similarity

684 # deep belief nets

685 Apply these algorithms to the cortex

686 Using the methods developed in Aim 1, we will present, for each cortical area, a short list of markers to identify that

687 area; and we will also present lists of &#8220;panels&#8221; of genes that can be used to delineate many areas at once. Using the methods

688 developed in Aim 2, we will present one or more hierarchial cortical maps. We will identify and explain how the statistical

689 structure in the gene expression data led to any unexpected or interesting features of these maps, and we will provide

690 biological hypotheses to interpret any new cortical areas, or groupings of areas, which are discovered.

691 _________________________________________

692 20Actually, we have already begun to explore decision trees. For each cortical area, we have used the C4.5 algorithm to find a decision tree for

693 that area. We achieved good classification accuracy on our training set, but the number of genes that appeared in each tree was too large. We

694 plan to implement a pruning procedure to generate trees that use fewer genes.

695 Timeline and milestones

696 Finding marker genes

697 &#x2219;September-November 2009: Develop an automated mechanism for segmenting the cortical voxels into layers

698 &#x2219;November 2009 (milestone): Have completed construction of a flatmapped, cortical dataset with information for each

699 layer

700 &#x2219;October 2009-April 2010: Develop scoring methods and to test them in various supervised learning frameworks. Also

701 test out various dimensionality reduction schemes in combination with supervised learning. create or extend supervised

702 learning frameworks which use multivariate versions of the best scoring methods.

703 &#x2219;January 2010 (milestone): Submit a publication on single marker genes for cortical areas

704 &#x2219;February-July 2010: Continue to develop scoring methods and supervised learning frameworks. Explore the best way

705 to integrate radial profiles with supervised learning. Explore the best way to make supervised learning techniques

706 robust against incorrect labels (i.e. when the areas drawn on the input cortical map are slightly off). Quantitatively

707 compare the performance of different supervised learning techniques. Validate marker genes found in the ABA dataset

708 by checking against other gene expression datasets. Create documentation and unit tests for software toolbox for Aim

709 1. Respond to user bug reports for Aim 1 software toolbox.

710 &#x2219;June 2010 (milestone): Submit a paper describing a method fulfilling Aim 1. Release toolbox.

711 &#x2219;July 2010 (milestone): Submit a paper describing combinations of marker genes for each cortical area, and a small

712 number of marker genes that can, in combination, define most of the areas at once

713 Revealing new ways to parcellate a structure into regions

714 &#x2219;June 2010-March 2011: Explore dimensionality reduction algorithms for Aim 2. Explore standard hierarchial clus-

715 tering algorithms, used in combination with dimensionality reduction, for Aim 2. Explore co-clustering algorithms.

716 Think about how radial profile information can be used for Aim 2. Adapt clustering algorithms to use radial profile

717 information. Quantitatively compare the performance of different dimensionality reduction and clustering techniques.

718 Quantitatively compare the value of different flatmapping methods and ways of representing radial profiles.

719 &#x2219;March 2011 (milestone): Submit a paper describing a method fulfilling Aim 2. Release toolbox.

720 &#x2219;February-May 2011: Using the methods developed for Aim 2, explore the genomic anatomy of the cortex. If new ways

721 of organizing the cortex into areas are discovered, read the literature and talk to people to learn about research related

722 to interpreting our results. Create documentation and unit tests for software toolbox for Aim 2. Respond to user bug

723 reports for Aim 2 software toolbox.

724 &#x2219;May 2011 (milestone): Submit a paper on the genomic anatomy of the cortex, using the methods developed in Aim 2

725 &#x2219;May-August 2011: Revisit Aim 1 to see if what was learned during Aim 2 can improve the methods for Aim 1. Follow

726 up on responses to our papers. Possibly submit another paper.

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