1 Specific aims

2 Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in

3 situ transgenic reporter, microarray voxelation, and others, allow the expression levels of many genes at many

4 locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expres-

5 sion to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical

6 maps based on gene expression patterns. We have three specific aims:

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

8 selectively target anatomical regions

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

10 based on 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

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

13 the functionality of Caret, an existing open-source scientific imaging program. Use this dataset to validate the

14 methods developed in (1) and (2).

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

16 the methods developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located

17 in a low-dimensional space. In particular, our method could be applied to genome-wide sequencing data derived

18 from sets of tissues and disease states.

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

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

21 of the algorithms, the application of these methods to cortex will produce immediate benefits, because there

22 are currently no known genetic markers for most cortical areas. The results of the project will support the

23 development of new ways to selectively target cortical areas, and it will support the development of a method for

24 identifying the cortical areal boundaries present in small tissue samples.

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

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

27 The challenge topic

28 This proposal addresses challenge topic 06-HG-101. Massive new datasets obtained with techniques such as

29 in situ hybridization (ISH), immunohistochemistry, in situ transgenic reporter, microarray voxelation, and others,

30 allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated

31 methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific

32 anatomical regions, and also to draw new anatomical maps based on gene expression patterns.

33 The Challenge and Potential impact

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

35 thinking about the task, and we will present our strategy for solving it. Next we will discuss related work. At the

36 conclusion of each section, we will summarize why our strategy is different from what has been done before. At

37 the end of this section, we will describe the potential impact.

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

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

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

41 locations of the regions can be inferred.

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

43 we are using gene expression in each voxel to assign that voxel to the proper area. We call this a classification

44 task, because each voxel is being assigned to a class (namely, its region). An understanding of the relationship

45 between the combination of their expression levels and the locations of the regions may be expressed as a

46 function. The input to this function is a voxel, along with the gene expression levels within that voxel; the output is

47 the regional identity of the target voxel, that is, the region to which the target voxel belongs. We call this function

48 a classifier. In general, the input to a classifier is called an instance, and the output is called a label (or a class

49 label).

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

51 determining a classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene

52 expression dataset may be analyzed in concert with an anatomical atlas in order to produce a classifier. The

53 initial gene expression dataset used in the construction of the classifier is called training data. In the machine

54 learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a task in

55 which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances

56 (voxels) for which the labels (regions) are known.

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

58 selection. Feature selection is one component of the task of learning a classifier. Some methods for learning

59 classifiers start out with a separate feature selection phase, whereas other methods combine feature selection

60 with other aspects of training.

61 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked

62 genes are then chosen. Some scoring measures can assign a score to a set of selected genes, not just to a

63 single gene; in this case, a dynamic procedure may be used in which features are added and subtracted from the

64 selected set depending on how much they raise the score. Such procedures are called “stepwise” or “greedy”.

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

66 that voxel, the algorithm which constructs the classifier may look over the entire dataset. We can categorize

67 score-based feature selection methods depending on how the score of calculated. Often the score calculation

68 consists of assigning a sub-score to each voxel, and then aggregating these sub-scores into a final score (the

69 aggregation is often a sum or a sum of squares or average). If only information from nearby voxels is used to

70 calculate a voxel’s sub-score, then we say it is a local scoring method. If only information from the voxel itself is

71 used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.

72 _________________________________________

73 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.

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

75 have idiosyncratic anatomy. Subjects may be improperly registred to the atlas. The method used to measure

76 gene expression may be noisy. The atlas may have errors. It is even possible that some areas in the anatomical

77 atlas are “wrong” in that they do not have the same shape as the natural domains of gene expression to which

78 they correspond. These sources of error can affect the displacement and the shape of both the gene expression

79 data and the anatomical target areas. Therefore, it is important to use feature selection methods which are

80 robust to these kinds of errors.

81 Our strategy for Aim 1

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

83 the features chosen? Here are four principles that outline our answers to these questions.

84 Principle 1: Combinatorial gene expression

85 It is too much to hope that every anatomical region of interest will be identified by a single gene. For example,

86 in the cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas

87 (ABA) dataset. However, at least some of these areas can be delineated by looking at combinations of genes

88 (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary Studies,

89 Figure 4). Therefore, each instance should contain multiple features (genes).

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

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

92 been selected as features. The more data that are available to a classifier, the better that it can do. For example,

93 perhaps there are weak correlations over many genes that add up to a strong signal. So, why not include every

94 gene as a feature? The reason is that we wish to employ the classifier in situations in which it is not feasible to

95 gather data about every gene. For example, if we want to use the expression of marker genes as a trigger for

96 some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the

97 expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that

98 checks the level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on

99 tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we

100 must select only a few genes as features.

101 The requirement to find combinations of only a small number of genes limits us from straightforwardly ap-

102 plying many of the most simple techniques from the field of supervised machine learning. In the parlance of

103 machine learning, our task combines feature selection with supervised learning.

104 Principle 3: Use geometry in feature selection

105 When doing feature selection with score-based methods, the simplest thing to do would be to score the per-

106 formance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach

107 is to also use information about the geometric relations between each voxel and its neighbors; this requires non-

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

109 pointwise and local scoring methods.

110 Principle 4: Work in 2-D whenever possible

111 There are many anatomical structures which are commonly characterized in terms of a two-dimensional

112 manifold. When it is known that the structure that one is looking for is two-dimensional, the results may be

113 improved by allowing the analysis algorithm to take advantage of this prior knowledge. In addition, it is easier for

114 humans to visualize and work with 2-D data. Therefore, when possible, the instances should represent pixels,

115 not voxels.

116 Related work

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

118 sion data which are not fundamentally spatial2.

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

120 algorithms for each. However, the algorithms require the scientist to provide a framework for representing the

121 problem domain, and the way that this framework is set up has a large impact on performance. Creating a

122 good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical

123 “fine-tuning” of numerical parameters. For example, we believe that domain-specific scoring measures (such

124 as gradient similarity, which is discussed in Preliminary Studies) may be necessary in order to achieve the best

125 results in this application.

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

127 methods.

128 [13 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical

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

130 GeneAtlas[5] and EMAGE [26] allow the user to construct a search query by demarcating regions and then

131 specifing either the strength of expression or the name of another gene or dataset whose expression pattern

132 is to be matched. For the similiarity score (match score) between two images (in this case, the query and the

133 gene expression images), GeneAtlas uses the sum of a weighted L1-norm distance between vectors whose

134 components represent the number of cells within a pixel3 whose expression is within four discretization levels.

135 EMAGE uses Jaccard similarity4. Neither GeneAtlas nor EMAGE allow one to search for combinations of genes

136 that define a region in concert but not separately.

137 [15 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The

138 user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) yields a list

139 of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of

140 overexpressed genes for selected structures). Correlation: The user selects a seed voxel and the system then

141 shows the user how much correlation there is between the gene expression profile of the seed voxel and every

142 other voxel. Clusters: will be described later

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

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

145 marker, whereas we will also search for underexpression. Third, Gene Finder uses a simple pointwise score5,

146 whereas we will also use geometric scores such as gradient similarity (described in Preliminary Studies). Figures

147 4, 2, and 3 in the Preliminary Studies section contains evidence that each of our three choices is the right one.

148 [6 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test

149 with Bonferroni correction to determine whether the mean expression level of a gene is significantly higher in

150 the target region. Like AGEA, this is a pointwise measure (only the mean expression level per pixel is being

151 analyzed), it is not being used to look for underexpression, and does not look for combinations of genes.

152 [10 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use

153 an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) images in order to

154 match a target image. Their match score is Jaccard similarity.

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

156 explores combinations of marker genes, and none of these publications compare the results obtained by using

157 different algorithms or scoring methods.

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

159 Machine learning terminology: clustering

160 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates;

161 not just data which have only a few different locations or which is indexed by anatomical label.

162 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.

163 4the number of true pixels in the intersection of the two images, divided by the number of pixels in their union.

164 5“Expression energy ratio”, which captures overexpression.

165 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is

166 referred to as unsupervised learning in the jargon of machine learning. One thing that you can do with such a

167 dataset is to group instances together. A set of similar instances is called a cluster, and the activity of finding

168 grouping the data into clusters is called clustering or cluster analysis.

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

170 instances are once again voxels (or pixels) along with their associated gene expression profiles. We make

171 the assumption that voxels from the same anatomical region have similar gene expression profiles, at least

172 compared to the other regions. This means that clustering voxels is the same as finding potential regions; we

173 seek a partitioning of the voxels into regions, that is, into clusters of voxels with similar gene expression.

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

175 outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the

176 voxels. This is called hierarchial clustering.

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

178 either pairs of instances, or clusters, or both. There is much overlap between scoring methods for feature

179 selection (discussed above under Aim 1) and scoring methods for similarity.

180 Spatially contiguous clusters; image segmentation We have shown that aim 2 is a type of clustering

181 task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels

182 grouped together into a cluster must be spatially contiguous. In Preliminary Studies, we show that one can get

183 reasonable results without enforcing this constraint; however, we plan to compare these results against other

184 methods which guarantee contiguous clusters.

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

186 clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are

187 thousands of color channels (one for each gene), rather than just three6. A more crucial difference is that there

188 are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not

189 appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation

190 algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these

191 algorithms are specialized for visual images.

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

193 feature vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying

194 data.

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

196 in the instances. However, some clustering algorithms perform better on small numbers of features7. There are

197 techniques which “summarize” a larger number of features using a smaller number of features; these techniques

198 go by the name of feature extraction or dimensionality reduction. The small set of features that such a technique

199 yields is called the reduced feature set. Note that the features in the reduced feature set do not necessarily

200 correspond to genes; each feature in the reduced set may be any function of the set of gene expression levels.

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

202 one strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes

203 could be used.

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

205 we could have one reduced feature for each gene cluster.

206 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes

207 have an expression pattern which seems to pick out a single, spatially continguous region. Therefore, it seems

208 likely that an anatomically interesting region will have multiple genes which each individually pick it out8. This

209 _________________________________________

210 6There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are

211 often used to process satellite imagery.

212 7First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering

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

214 8This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However,

215 it is possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene

216 expression; perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another

217 suggests the following procedure: cluster together genes which pick out similar regions, and then to use the

218 more popular common regions as the final clusters. In Preliminary Studies, Figure 7, we show that a number

219 of anatomically recognized cortical regions, as well as some “superregions” formed by lumping together a few

220 regions, are associated with gene clusters in this fashion.

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

222 co-clustering algorithms.

223 Related work

224 Some researchers have attempted to parcellate cortex on the basis of non-gene expression data. For example,

225 [18 ], [2 ], [19], and [1] associate spots on the cortex with the radial profile9 of response to some stain ([12] uses

226 MRI), extract features from this profile, and then use similarity between surface pixels to cluster. Features used

227 include statistical moments, wavelets, and the excess mass functional. Some of these features are motivated

228 by the presence of tangential lines of stain intensity which correspond to laminar structure. Some methods use

229 standard clustering procedures, whereas others make use of the spatial nature of the data to look for sudden

230 transitions, which are identified as areal borders.

231 [23 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual

232 analysis, two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and

233 a hierarchial recursive bifurcation clustering scheme based on correlation as the similarity score. The paper

234 yielded impressive results, proving the usefulness of computational genomic anatomy. We have run NNMF on

235 the cortical dataset10 and while the results are promising, they also demonstrate that NNMF is not necessarily

236 the best dimensionality reduction method for this application (see Preliminary Studies, Figure 6).

237 AGEA[15] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with

238 correlation as the similarity metric. EMAGE[26] allows the user to select a dataset from among a large number

239 of alternatives, or by running a search query, and then to cluster the genes within that dataset. EMAGE clusters

240 via hierarchial complete linkage clustering with un-centred correlation as the similarity score.

241 [6 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and

242 which were highly correlated with many other genes. They computed the matrix of (rank) correlations between

243 pairs of these genes, and ordered the rows of this matrix as follows: “the first row of the matrix was chosen to

244 show the strongest contrast between the highest and lowest correlation coefficient for that row. The remaining

245 rows were then arranged in order of decreasing similarity using a least squares metric”. The resulting matrix

246 showed four clusters. For each cluster, prototypical spatial expression patterns were created by averaging the

247 genes in the cluster. The prototypes were analyzed manually, without clustering voxels.

248 [10 ] applies their technique for finding combinations of marker genes for the purpose of clustering genes

249 around a “seed gene”. They do this by using the pattern of expression of the seed gene as the target image, and

250 then searching for other genes which can be combined to reproduce this pattern. Other genes which are found

251 are considered to be related to the seed. The same team also describes a method[25] for finding “association

252 rules” such as, “if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the

253 same gene”. This could be useful as part of a procedure for clustering voxels.

254 In summary, although these projects obtained clusterings, there has not been much comparison between

255 different algorithms or scoring methods, so it is likely that the best clustering method for this application has not

256 yet been found. The projects using gene expression on cortex did not attempt to make use of the radial profile

257 of gene expression. Also, none of these projects did a separate dimensionality reduction step before clustering

258 pixels, none tried to cluster genes first in order to guide automated clustering of pixels into spatial regions, and

259 none used co-clustering algorithms.

260 ________

261 possibility is that, although the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the

262 prototype.

263 9A radial profile is a profile along a line perpendicular to the cortical surface.

264 10We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding

265 a soft spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional

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

267 tried.

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

269 Background

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

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

272 boundaries between the areas continue downwards into the cortical depth, perpendicular to the surface. The

273 layer boundaries run parallel to the surface. One can picture an area of the cortex as a slice of a six-layered

274 cake11 .

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

276 yet there are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample

277 into cortical areas, this is a manual process that requires a skilled human to combine multiple visual cues and

278 interpret them in the context of their approximate location upon the cortical surface.

279 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are

280 still not completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent,

281 the lack of a single agreed-upon map can be seen by contrasting the recent maps given by Swanson[22] on the

282 one hand, and Paxinos and Franklin[17] on the other. While the maps are certainly very similar in their general

283 arrangement, significant differences remain.

284 The Allen Mouse Brain Atlas dataset

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

286 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-

287 automatically analyzed to create a digital measurement of gene expression levels at each location in each slice.

288 Per slice, cellular spatial resolution is achieved. Using this method, a single physical slice can only be used

289 to measure one single gene; many different mouse brains were needed in order to measure the expression of

290 many genes.

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

292 coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are

293 67x41x58 = 159,326 voxels in the 3D coordinate system, of which 51,533 are in the brain[15].

294 Mus musculus is thought to contain about 22,000 protein-coding genes[28]. The ABA contains data on about

295 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our

296 dataset is derived from only the coronal subset of the ABA12.

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

298 GenePaint, and EMAGE, most of the other resources have not (yet) extracted the expression intensity from the

299 ISH images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE

300 make this form of data available for public download from the website14. Many of these resources focus on

301 developmental gene expression.

302 Related work

303 [15 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure

304 of correlations between voxel gene expression profiles within a handful of cortical areas. However, this sort

305 of analysis is not related to either of our aims, as it neither finds marker genes, nor does it suggest a cortical

306 map based on gene expression data. Neither of the other components of AGEA can be applied to cortical

307 _________________________________________

308 11Outside of isocortex, the number of layers varies.

309 12The sagittal data do not cover the entire cortex, and also have greater registration error[15]. Genes were selected by the Allen

310 Institute for coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc identification of a marked

311 non-ubiquitous expression pattern”[15].

312 13Other such resources include GENSAT[8], GenePaint[27], its sister project GeneAtlas[5], BGEM[14], EMAGE[26], EurExpress

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

314 database/EADHB_database.html), MAMEP (http://mamep.molgen.mpg.de/index.php), Xenbase (http://xenbase.org/), ZFIN[21],

315 Aniseed (http://aniseed-ibdm.univ-mrs.fr/), VisiGene (http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some

316 of the other listed data sources), GEISHA[4], Fruitfly.org[24], COMPARE (http://compare.ibdml.univ-mrs.fr/), GXD[20], GEO[3]

317 (GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.)

318 14without prior offline registration

319 areas; AGEA’s Gene Finder cannot be used to find marker genes for the cortical areas; and AGEA’s hierarchial

320 clustering does not produce clusters corresponding to the cortical areas15.

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

322 (b) there has been almost no comparison of different algorithms or scoring methods, and (c) there has been no

323 work on computationally finding marker genes for cortical areas, or on finding a hierarchial clustering that will

324 yield a map of cortical areas de novo from gene expression data.

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

326 find marker genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing

327 different methods.

328 Significance

329

330

331 Figure 1: Top row: Genes Nfic

332 and A930001M12Rik are the most

333 correlated with area SS (somatosen-

334 sory cortex). Bottom row: Genes

335 C130038G02Rik and Cacna1i are

336 those with the best fit using logistic

337 regression. Within each picture, the

338 vertical axis roughly corresponds to

339 anterior at the top and posterior at the

340 bottom, and the horizontal axis roughly

341 corresponds to medial at the left and

342 lateral at the right. The red outline is

343 the boundary of region SS. Pixels are

344 colored according to correlation, with

345 red meaning high correlation and blue

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

347 find a set of marker genes such that the combinatorial expression pat-

348 tern of those genes uniquely picks out the target area. Finding marker

349 genes will be useful for drug discovery as well as for experimentation

350 because marker genes can be used to design interventions which se-

351 lectively target individual cortical areas.

352 The application of the marker gene finding algorithm to the cortex

353 will also support the development of new neuroanatomical methods. In

354 addition to finding markers for each individual cortical areas, we will

355 find a small panel of genes that can find many of the areal boundaries

356 at once. This panel of marker genes will allow the development of an

357 ISH protocol that will allow experimenters to more easily identify which

358 anatomical areas are present in small samples of cortex.

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

360 viewpoint that will contribute to the creation of a better map. The de-

361 velopment of present-day cortical maps was driven by the application

362 of histological stains. If a different set of stains had been available

363 which identified a different set of features, then today’s cortical maps

364 may have come out differently. It is likely that there are many repeated,

365 salient spatial patterns in the gene expression which have not yet been

366 captured by any stain. Therefore, cortical anatomy needs to incorpo-

367 rate what we can learn from looking at the patterns of gene expression.

368 While we do not here propose to analyze human gene expression

369 data, it is conceivable that the methods we propose to develop could

370 be used to suggest modifications to the human cortical map as well. In

371 fact, the methods we will develop will be applicable to other datasets

372 beyond the brain. We will provide an open-source toolbox to allow

373 other researchers to easily use our methods. With these methods, re-

374 searchers with gene expression for any area of the body will be able to

375 efficiently find marker genes for anatomical regions, or to use gene expression to discover new anatomical pat-

376 terning. As described above, marker genes have a variety of uses in the development of drugs and experimental

377 manipulations, and in the anatomical characterization of tissue samples. The discovery of new ways to carve up

378 anatomical structures into regions may lead to the discovery of new anatomical subregions in various structures,

379 _________________________________________

380 15In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer

381 are often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a

382 pairwise voxel correlation clustering algorithm will tend to create clusters representing cortical layers, not areas (there may be clusters

383 which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area intersection

384 clusters, further work is needed to make sense of these). The reason that Gene Finder cannot the find marker genes for cortical areas

385 is that, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found, and it creates that ROI by

386 (pairwise voxel correlation) clustering around the seed.

387 which will widely impact all areas of biology.

388

389 Figure 2: Gene Pitx2

390 is selectively underex-

391 pressed in area SS. Although our particular application involves the 3D spatial distribution of gene ex-

392 pression, we anticipate that the methods developed in aims (1) and (2) will not be limited

393 to gene expression data, but rather will generalize to any sort of high-dimensional data

394 over points located in a low-dimensional space.

395 The approach: Preliminary Studies

396 Format conversion between SEV, MATLAB, NIFTI

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

398 Institute website. We have also created software to convert between the SEV, MATLAB,

399 and NIFTI file formats, as well as some of Caret’s file formats.

400 Flatmap of cortex

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

402 belong to cerebral cortex. We divided the cortex into hemispheres.

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

404 for each node of the mesh, we calculated an average of the gene expression of the voxels “underneath” that

405 mesh node. We then flattened the cortex, creating a two-dimensional mesh.

406

407

408 Figure 3: The top row shows the two

409 genes which (individually) best predict

410 area AUD, according to logistic regres-

411 sion. The bottom row shows the two

412 genes which (individually) best match

413 area AUD, according to gradient sim-

414 ilarity. From left to right and top to

415 bottom, the genes are Ssr1, Efcbp1,

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

417 a regular grid of pixel values. We converted this grid into a MATLAB

418 matrix.

419 We manually traced the boundaries of each of 49 cortical areas

420 from the ABA coronal reference atlas slides. We then converted these

421 manual traces into Caret-format regional boundary data on the mesh

422 surface. We projected the regions onto the 2-d mesh, and then onto

423 the grid, and then we converted the region data into MATLAB format.

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

425 all in registration, with the matrix entries representing a grid of points

426 (pixels) over the cortical surface:

427 ∙ A 2-D matrix whose entries represent the regional label associ-

428 ated with each surface pixel

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

430 expression level underneath each surface pixel

431 We created a normalized version of the gene expression data by

432 subtracting each gene’s mean expression level (over all surface pixels)

433 and dividing the expression level of each gene by its standard deviation.

434 The features and the target area are both functions on the surface

435 pixels. They can be referred to as scalar fields over the space of sur-

436 face pixels; alternately, they can be thought of as images which can be

437 displayed on the flatmapped surface.

438 To move beyond a single average expression level for each surface pixel, we plan to create a separate matrix

439 for each cortical layer to represent the average expression level within that layer. Cortical layers are found at

440 different depths in different parts of the cortex. In preparation for extracting the layer-specific datasets, we have

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

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

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

444 _________________________________________

445 16SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.

446 Feature selection and scoring methods

447 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a

448 marker. See, for example, Figure 2.

449

450

451 Figure 4: Upper left: wwc1. Upper

452 right: mtif2. Lower left: wwc1 + mtif2

453 (each pixel’s value on the lower left is

454 the sum of the corresponding pixels in

455 the upper row). Correlation Recall that the instances are surface pixels, and con-

456 sider the problem of attempting to classify each instance as either a

457 member of a particular anatomical area, or not. The target area can be

458 represented as a boolean mask over the surface pixels.

459 One class of feature selection scoring methods contains methods

460 which calculate some sort of “match” between each gene image and

461 the target image. Those genes which match the best are good candi-

462 dates for features.

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

464 the match score. We calculated the correlation between each gene

465 and each cortical area. The top row of Figure 1 shows the three genes

466 most correlated with area SS.

467 Conditional entropy An information-theoretic scoring method is

468 to find features such that, if the features (gene expression levels) are

469 known, uncertainty about the target (the regional identity) is reduced.

470 Entropy measures uncertainty, so what we want is to find features such

471 that the conditional distribution of the target has minimal entropy. The

472 distribution to which we are referring is the probability distribution over

473 the population of surface pixels.

474 The simplest way to use information theory is on discrete data, so we discretized our gene expression data

475 by creating, for each gene, five thresholded boolean masks of the gene data. For each gene, we created a

476 boolean mask of its expression levels using each of these thresholds: the mean of that gene, the mean minus

477 one standard deviation, the mean minus two standard deviations, the mean plus one standard deviation, the

478 mean plus two standard deviations.

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

480 expression boolean masks such that the conditional entropy of the target area’s boolean mask, conditioned upon

481 the pair of gene expression boolean masks, is minimized.

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

483 question, “Is this surface pixel a member of the target area?”. Its advantage over linear methods such as logistic

484 regression is that it takes account of arbitrarily nonlinear relationships; for example, if the XOR of two variables

485 predicts the target, conditional entropy would notice, whereas linear methods would not.

486 Gradient similarity We noticed that the previous two scoring methods, which are pointwise, often found

487 genes whose pattern of expression did not look similar in shape to the target region. For this reason we designed

488 a non-pointwise local scoring method to detect when a gene had a pattern of expression which looked like it had

489 a boundary whose shape is similar to the shape of the target region. We call this scoring method “gradient

490 similarity”.

491 One might say that gradient similarity attempts to measure how much the border of the area of gene expres-

492 sion and the border of the target region overlap. However, since gene expression falls off continuously rather

493 than jumping from its maximum value to zero, the spatial pattern of a gene’s expression often does not have a

494 discrete border. Therefore, instead of looking for a discrete border, we look for large gradients. Gradient similarity

495 is a symmetric function over two images (i.e. two scalar fields). It is is high to the extent that matching pixels

496 which have large values and large gradients also have gradients which are oriented in a similar direction. The

497 formula is:

498 ∑

499 pixel<img src="cmsy8-32.png" alt="&#x2208;" />pixels cos(abs(&#x2220;&#x2207;1 -&#x2220;&#x2207;2)) &#x22C5;|&#x2207;1| + |&#x2207;2|

500 2 &#x22C5; pixel_value1 + pixel_value2

501 2

502

503

504

505

506

507 Figure 5: From left to right and top

508 to bottom, single genes which roughly

509 identify areas SS (somatosensory pri-

510 mary + supplemental), SSs (supple-

511 mental somatosensory), PIR (piriform),

512 FRP (frontal pole), RSP (retrosple-

513 nial), COApm (Cortical amygdalar, pos-

514 terior part, medial zone). Grouping

515 some areas together, we have also

516 found genes to identify the groups

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

518 cingulate, prelimbic, infralimbic, dor-

519 sal peduncular, orbital, motor), poste-

520 rior and lateral visual (VISpm, VISpl,

521 VISI, VISp; posteromedial, posterolat-

522 eral, lateral, and primary visual; the

523 posterior and lateral visual area is dis-

524 tinguished from its neighbors, but not

525 from the entire rest of the cortex). The

526 genes are Pitx2, Aldh1a2, Ppfibp1,

527 Slco1a5, Tshz2, Trhr, Col12a1, Ets1. where &#x2207;1 and &#x2207;2 are the gradient vectors of the two images at the

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

529 pixel; |&#x2207;i| is the magnitude of the gradient of image i at the current

530 pixel; and pixel_valuei is the value of the current pixel in image i.

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

532 the two images are similar; if the borders are similar, then both images

533 will have corresponding pixels with large gradients (because this is a

534 border) which are oriented in a similar direction (because the borders

535 are similar).

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

537 Gradient similarity provides information complementary to

538 correlation

539 To show that gradient similarity can provide useful information that

540 cannot be detected via pointwise analyses, consider Fig. 3. The top

541 row of Fig. 3 displays the 3 genes which most match area AUD, ac-

542 cording to a pointwise method17. The bottom row displays the 3 genes

543 which most match AUD according to a method which considers local

544 geometry18 The pointwise method in the top row identifies genes which

545 express more strongly in AUD than outside of it; its weakness is that

546 this includes many areas which don&#8217;t have a salient border matching

547 the areal border. The geometric method identifies genes whose salient

548 expression border seems to partially line up with the border of AUD;

549 its weakness is that this includes genes which don&#8217;t express over the

550 entire area. Genes which have high rankings using both pointwise and

551 border criteria, such as Aph1a in the example, may be particularly good

552 markers. None of these genes are, individually, a perfect marker for

553 AUD; we deliberately chose a &#8220;difficult&#8221; area in order to better contrast

554 pointwise with geometric methods.

555 Areas which can be identified by single genes Using gradient

556 similarity, we have already found single genes which roughly identify

557 some areas and groupings of areas. For each of these areas, an ex-

558 ample of a gene which roughly identifies it is shown in Figure 5. We

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

560 In addition, there are a number of areas which are almost identified

561 by single genes: COAa+NLOT (anterior part of cortical amygdalar area,

562 nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral

563 anterior cingulate), VIS (visual), AUD (auditory).

564 These results validate our expectation that the ABA dataset can

565 be exploited to find marker genes for many cortical areas, while also

566 validating the relevancy of our new scoring method, gradient similarity.

567 Combinations of multiple genes are useful and necessary for

568 some areas

569 In Figure 4, we give an example of a cortical area which is not

570 marked by any single gene, but which can be identified combinatorially.

571 Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a pixel on

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

573 _________________________________________

574 17For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the

575 predictor variable was the value of the expression of the gene underneath that pixel. The resulting scores were used to rank the genes

576 in terms of how well they predict area AUD.

577 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

578 area AUD, was calculated, and this was used to rank the genes.

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

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

581 area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the dorsal surface.

582 Gene mtif2 is shown in the upper-right. Mtif2 captures MO&#8217;s upper-left boundary, but not its lower-right boundary.

583 Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these

584 two figures, we get the lower-left image. This combination captures area MO much better than any single gene.

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

586 necessary.

587 Feature selection integrated with prediction As noted earlier, in general, any classifier can be used for fea-

588 ture selection by running it inside a stepwise wrapper. Also, some learning algorithms integrate soft constraints

589 on number of features used. Examples of both of these will be seen in the section &#8220;Multivariate supervised

590 learning&#8221;.

591 Multivariate supervised learning

592

593

594

595

596 Figure 6: First row: the first 6 reduced dimensions, using PCA. Sec-

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

598 the first six reduced dimensions, using landmark Isomap. Bottom

599 row: examples of kmeans clustering applied to reduced datasets

600 to find 7 clusters. Left: 19 of the major subdivisions of the cortex.

601 Second from left: PCA. Third from left: NNMF. Right: Landmark

602 Isomap. Additional details: In the third and fourth rows, 7 dimen-

603 sions were found, but only 6 displayed. In the last row: for PCA,

604 50 dimensions were used; for NNMF, 6 dimensions were used; for

605 landmark Isomap, 7 dimensions were used. Forward stepwise logistic regression

606 Logistic regression is a popular method

607 for predictive modeling of categorial data.

608 As a pilot run, for five cortical areas (SS,

609 AUD, RSP, VIS, and MO), we performed

610 forward stepwise logistic regression to find

611 single genes, pairs of genes, and triplets

612 of genes which predict areal identify. This

613 is an example of feature selection inte-

614 grated with prediction using a stepwise

615 wrapper. Some of the single genes found

616 were shown in various figures throughout

617 this document, and Figure 4 shows a com-

618 bination of genes which was found.

619 We felt that, for single genes, gradi-

620 ent similarity did a better job than logistic

621 regression at capturing our subjective im-

622 pression of a &#8220;good gene&#8221;.

623 SVM on all genes at once

624 In order to see how well one can do

625 when looking at all genes at once, we ran

626 a support vector machine to classify corti-

627 cal surface pixels based on their gene ex-

628 pression profiles. We achieved classifica-

629 tion accuracy of about 81%19. This shows

630 that the genes included in the ABA dataset

631 are sufficient to define much of cortical

632 anatomy. However, as noted above, a clas-

633 sifier that looks at all the genes at once isn&#8217;t

634 as practically useful as a classifier that uses only a few genes.

635 _________________________________________

636 195-fold cross-validation.

637 Data-driven redrawing of the cortical map

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

639 expression profile associated with each pixel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-

640 Dimensional Scaling (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment

641 (LTSA), Stochastic Proximity Embedding (SPE), Fast Maximum Variance Unfolding (FastMVU), Non-negative

642 Matrix Factorization (NNMF). Space constraints prevent us from showing many of the results, but as a sample,

643 PCA, NNMF, and landmark Isomap are shown in the first, second, and third rows of Figure 6.

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

645 have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are

646 shown in the last row of Figure 6. To compare, the leftmost picture on the bottom row of Figure 6 shows some

647 of the major subdivisions of cortex. These results clearly show that different dimensionality reduction techniques

648 capture different aspects of the data and lead to different clusterings, indicating the utility of our proposal to

649 produce a detailed comparion of these techniques as applied to the domain of genomic anatomy.

650

651 Figure 7: Prototypes corresponding to sample gene

652 clusters, clustered by gradient similarity. Region bound-

653 aries for the region that most matches each prototype

654 are overlayed. Many areas are captured by clusters of genes

655 We also clustered the genes using gradient similarity

656 to see if the spatial regions defined by any clusters

657 matched known anatomical regions. Figure 7 shows,

658 for ten sample gene clusters, each cluster&#8217;s average

659 expression pattern, compared to a known anatomical

660 boundary. This suggests that it is worth attempting to

661 cluster genes, and then to use the results to cluster

662 pixels.

663 The approach: what we plan to do

664 Flatmap cortex and segment cortical layers

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

666 We will compare mappings from manifolds to planes

667 which attempt to preserve size (such as the one used

668 by Caret[7]) with mappings which preserve angle (conformal maps). Our method will include a statistical test

669 that warns the user if the assumption of 2-D structure seems to be wrong.

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

671 like the cortex another strategy is to group together voxels in the same cortical layer; each surface pixel would

672 then be associated with one expression level per gene per layer. We will develop a segmentation algorithm to

673 automatically identify the layer boundaries.

674 Develop algorithms that find genetic markers for anatomical regions

675 Scoring measures and feature selection We will develop scoring methods for evaluating how good individual

676 genes are at marking areas. We will compare pointwise, geometric, and information-theoretic measures. We

677 already developed one entirely new scoring method (gradient similarity), but we may develop more. Scoring

678 measures that we will explore will include the L1 norm, correlation, expression energy ratio, conditional entropy,

679 gradient similarity, Jaccard similarity, Dice similarity, Hough transform, and statistical tests such as Student&#8217;s t-

680 test, and the Mann-Whitney U test (a non-parametric test). In addition, any classifier induces a scoring measure

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

682 Using some combination of these measures, we will develop a procedure to find single marker genes for

683 anatomical regions: for each cortical area, we will rank the genes by their ability to delineate each area. We

684 will quantitatively compare the list of single genes generated by our method to the lists generated by previous

685 methods which are mentioned in Aim 1 Related Work.

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

687 multivariate scoring measures and feature selection procedures. Many of the measures, such as expression

688 energy, gradient similarity, Jaccard, Dice, Hough, Student&#8217;s t, and Mann-Whitney U are univariate. We will extend

689 these scoring measures for use in multivariate feature selection, that is, for scoring how well combinations of

690 genes, rather than individual genes, can distinguish a target area. There are existing multivariate forms of some

691 of the univariate scoring measures, for example, Hotelling&#8217;s T-square is a multivariate analog of Student&#8217;s t.

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

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

694 selection using a stepwise wrapper over &#8220;vanilla&#8221; classifiers such as logistic regression, (b) supervised learning

695 methods such as decision trees which incrementally/greedily combine single gene markers into sets, and (c)

696 supervised learning methods which use soft constraints to minimize number of features used, such as sparse

697 support vector machines.

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

699 we will consider the robustness of feature selection methods in the presence of error. Some of these methods,

700 such as the Hough transform, are designed to be resistant in the presence of error, but many are not. We will

701 consider extensions to scoring measures that may improve their robustness; for example, a wrapper that runs a

702 scoring method on small displacements and distortions of the data adds robustness to registration error at the

703 expense of computation time.

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

705 of the natural domain of gene expression corresponding to the area is different from the shape of the area as

706 recognized by anatomists. We will extend our procedure to handle difficult areas by combining areas or redrawing

707 their boundaries. We will develop extensions to our procedure which (a) detect when a difficult area could be

708 fit if its boundary were redrawn slightly20, and (b) detect when a difficult area could be combined with adjacent

709 areas to create a larger area which can be fit.

710 A future publication on the method that we develop in Aim 1 will review the scoring measures and quantita-

711 tively compare their performance in order to provide a foundation for future research of methods of marker gene

712 finding. We will measure the robustness of the scoring measures as well as their absolute performance on our

713 dataset.

714 Classifiers We will explore and compare different classifiers. As noted above, this activity is not separate

715 from the previous one, because some supervised learning algorithms include feature selection, and any clas-

716 sifier can be combined with a stepwise wrapper for use as a feature selection method. We will explore logistic

717 regression (including spatial models[16]), decision trees21, sparse SVMs, generative mixture models (including

718 naive bayes), kernel density estimation, instance-based learning methods (such as k-nearest neighbor), genetic

719 algorithms, and artificial neural networks.

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

721 Explore dimensionality reduction on gene expression profiles We have already described the application

722 of ten dimensionality reduction algorithms for the purpose of replacing the gene expression profiles, which are

723 vectors of about 4000 gene expression levels, with a smaller number of features. We plan to further explore

724 and interpret these results, as well as to apply other unsupervised learning algorithms, including independent

725 components analysis, self-organizing maps, and generative models such as deep Boltzmann machines. We

726 will explore ways to quantitatively compare the relevance of the different dimensionality reduction methods for

727 identifying cortical areal boundaries.

728 Explore dimensionality reduction on pixels Instead of applying dimensionality reduction to the gene ex-

729 _________________________________________

730 20Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene expression by

731 multiple sources of evidence. Interestingly, the need to detect &#8220;natural spatial domains of gene expression&#8221; in a data-driven fashion

732 means that the methods of Aim 2 might be useful in achieving Aim 1, as well &#8211; particularly discriminative dimensionality reduction.

733 21Actually, we have already begun to explore decision trees. For each cortical area, we have used the C4.5 algorithm to find a decision

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

735 too large. We plan to implement a pruning procedure to generate trees that use fewer genes.

736 pression profiles, the same techniques can be applied instead to the pixels22. It is possible that the features

737 generated in this way by some dimensionality reduction techniques will directly correspond to interesting spatial

738 regions.

739 Explore clustering and segmentation algorithms on pixels We will explore clustering and segmenta-

740 tion algorithms in order to segment the pixels into regions. We will explore k-means, spectral clustering, gene

741 shaving[9], recursive division clustering, multivariate generalizations of edge detectors, multivariate generaliza-

742 tions of watershed transformations, region growing, active contours, graph partitioning methods, and recursive

743 agglomerative clustering with various linkage functions. These methods can be combined with dimensionality

744 reduction.

745 Explore clustering on genes We have already shown that the procedure of clustering genes according to

746 gradient similarity, and then creating an averaged prototype of each cluster&#8217;s expression pattern, yields some

747 spatial patterns which match cortical areas. We will further explore the clustering of genes.

748 In addition to using the cluster expression prototypes directly to identify spatial regions, this might be useful

749 as a component of dimensionality reduction. For example, one could imagine clustering similar genes and then

750 replacing their expression levels with a single average expression level, thereby removing some redundancy from

751 the gene expression profiles. One could then perform clustering on pixels (possibly after a second dimensionality

752 reduction step) in order to identify spatial regions. It remains to be seen whether removal of redundancy would

753 help or hurt the ultimate goal of identifying interesting spatial regions.

754 Explore co-clustering There are some algorithms which simultaineously incorporate clustering on instances

755 and on features (in our case, genes and pixels), for example, IRM[11]. These are called co-clustering or biclus-

756 tering algorithms.

757 Quantitatively compare different methods In order to tell which method is best for genomic anatomy, for

758 each experimental method we will compare the cortical map found by unsupervised learning to a cortical map

759 derived from the Allen Reference Atlas. In order to compare the experimental clustering with the reference

760 clustering, we will explore various quantitative metrics that purport to measure how similar two clusterings are,

761 such as Jaccard, Rand index, Fowlkes-Mallows, variation of information, Larsen, Van Dongen, and others.

762 Discriminative dimensionality reduction In addition to using a purely data-driven approach to identify

763 spatial regions, it might be useful to see how well the known regions can be reconstructed from a small number

764 of features, even if those features are chosen by using knowledge of the regions. For example, linear discriminant

765 analysis could be used as a dimensionality reduction technique in order to identify a few features which are the

766 best linear summary of gene expression profiles for the purpose of discriminating between regions. This reduced

767 feature set could then be used to cluster pixels into regions. Perhaps the resulting clusters will be similar to the

768 reference atlas, yet more faithful to natural spatial domains of gene expression than the reference atlas is.

769 Apply the new methods to the cortex

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

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

772 Because in most cases the ABA coronal dataset only contains one ISH per gene, it is possible for an unrelated

773 combination of genes to seem to identify an area when in fact it is only coincidence. There are two ways we will

774 validate our marker genes to guard against this. First, we will confirm that putative combinations of marker genes

775 express the same pattern in both hemispheres. Second, we will manually validate our final results on other gene

776 expression datasets such as EMAGE, GeneAtlas, and GENSAT.

777 Using the methods developed in Aim 2, we will present one or more hierarchial cortical maps. We will identify

778 and explain how the statistical structure in the gene expression data led to any unexpected or interesting features

779 _________________________________________

780 22Consider a matrix whose rows represent pixel locations, and whose columns represent genes. An entry in this matrix represents the

781 gene expression level at a given pixel. One can look at this matrix as a collection of pixels, each corresponding to a vector of many gene

782 expression levels; or one can look at it as a collection of genes, each corresponding to a vector giving that gene&#8217;s expression at each

783 pixel. Similarly, dimensionality reduction can be used to replace a large number of genes with a small number of features, or it can be

784 used to replace a large number of pixels with a small number of features.

785 of these maps, and we will provide biological hypotheses to interpret any new cortical areas, or groupings of

786 areas, which are discovered.

787 Timeline and milestones

788 Finding marker genes

789 September-November 2009: Develop an automated mechanism for segmenting the cortical voxels into layers

790 November 2009 (milestone): Have completed construction of a flatmapped, cortical dataset with information

791 for each layer

792 October 2009-April 2010: Develop scoring methods and to test them in various supervised learning frameworks.

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

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

795 January 2010 (milestone): Submit a publication on single marker genes for cortical areas

796 February-July 2010: Continue to develop scoring methods and supervised learning frameworks. Explore the

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

798 techniques robust against incorrect labels (i.e. when the areas drawn on the input cortical map are slightly

799 off). Quantitatively compare the performance of different supervised learning techniques. Validate marker genes

800 found in the ABA dataset by checking against other gene expression datasets. Create documentation and unit

801 tests for software toolbox for Aim 1. Respond to user bug reports for Aim 1 software toolbox.

802 June 2010 (milestone): Submit a paper describing a method fulfilling Aim 1. Release toolbox.

803 July 2010 (milestone): Submit a paper describing combinations of marker genes for each cortical area, and a

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

805 Revealing new ways to parcellate a structure into regions

806 June 2010-March 2011: Explore dimensionality reduction algorithms for Aim 2. Explore standard hierarchial

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

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

809 profile information. Quantitatively compare the performance of different dimensionality reduction and clustering

810 techniques. Quantitatively compare the value of different flatmapping methods and ways of representing radial

811 profiles.

812 March 2011 (milestone): Submit a paper describing a method fulfilling Aim 2. Release toolbox.

813 February-May 2011: Using the methods developed for Aim 2, explore the genomic anatomy of the cortex. If

814 new ways of organizing the cortex into areas are discovered, read the literature and talk to people to learn about

815 research related to interpreting our results. Create documentation and unit tests for software toolbox for Aim 2.

816 Respond to user bug reports for Aim 2 software toolbox.

817 May 2011 (milestone): Submit a paper on the genomic anatomy of the cortex, using the methods developed in

818 Aim 2

819 May-August 2011: Revisit Aim 1 to see if what was learned during Aim 2 can improve the methods for Aim 1.

820 Follow up on responses to our papers. Possibly submit another paper.

821 Bibliography &amp; References Cited

822 [1]Chris Adamson, Leigh Johnston, Terrie Inder, Sandra Rees, Iven Mareels, and Gary Egan. A Tracking

823 Approach to Parcellation of the Cerebral Cortex, volume Volume 3749/2005 of Lecture Notes in Computer

824 Science, pages 294&#8211;301. Springer Berlin / Heidelberg, 2005.

825 [2]J. Annese, A. Pitiot, I. D. Dinov, and A. W. Toga. A myelo-architectonic method for the structural classification

826 of cortical areas. NeuroImage, 21(1):15&#8211;26, 2004.

827 [3]Tanya Barrett, Dennis B. Troup, Stephen E. Wilhite, Pierre Ledoux, Dmitry Rudnev, Carlos Evangelista,

828 Irene F. Kim, Alexandra Soboleva, Maxim Tomashevsky, and Ron Edgar. NCBI GEO: mining tens of millions

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