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2.1 --- a/grant.html Mon Apr 20 14:33:20 2009 -0700 2.2 +++ b/grant.html Mon Apr 20 15:08:40 2009 -0700 2.3 @@ -426,21 +426,21 @@ 2.4 In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior part of 2.5 cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate), VIS 2.6 (visual), AUD (auditory). 2.7 +These results validate our expectation that the ABA dataset can be exploited to find marker genes for many cortical 2.8 +areas, while also validating the relevancy of our new scoring method, gradient similarity. 2.9 Combinations of multiple genes are useful and necessary for some areas 2.10 In Figure 5, we give an example of a cortical area which is not marked by any single gene, but which can be identified 2.11 -combinatorially. 2.12 +combinatorially. This shows that our proposal to develop a method to find combinations of marker genes is both possible 2.13 +and necessary. 2.14 Feature selection integrated with prediction As noted earlier, in general, any predictive method can be used for 2.15 feature selection by running it inside a stepwise wrapper. Also, some predictive methods integrate soft constraints on number 2.16 of features used. Examples of both of these will be seen in the section “Multivariate Predictive methods”. 2.17 Multivariate Predictive methods 2.18 -Forward stepwise logistic regression As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed 2.19 -forward stepwise logistic regression to find single genes, pairs of genes, and triplets of genes which predict areal identify. 2.20 -This is an example of feature selection integrated with prediction using a stepwise wrapper. Some of the single genes found 2.21 -were shown in various figures throughout this document, and Figure 5 shows a combination of genes which was found. 2.22 -We felt that, for single genes, gradient similarity did a better job than logistic regression at capturing our subjective 2.23 -impression of a “good gene”. 2.24 -SVM on all genes at once 2.25 -In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical 2.26 +Forward stepwise logistic regression Logistic regression is a popular method for predictive modeling of categorial data. 2.27 +As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise logistic regression to 2.28 +find single genes, pairs of genes, and triplets of genes which predict areal identify. This is an example of feature selection 2.29 +integrated with prediction using a stepwise wrapper. Some of the single genes found were shown in various figures throughout 2.30 +this document, and Figure 5 shows a combination of genes which was found. 2.31 _________________________________________ 2.32 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 2.33 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 2.34 @@ -468,6 +468,33 @@ 2.35 Gene mtif2 is shown in the upper-right. Mtif2 captures MO’s upper-left boundary, but not its lower-right boundary. Mtif2 2.36 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get 2.37 the lower-left image. This combination captures area MO much better than any single gene. 2.38 +We felt that, for single genes, gradient similarity did a better job than logistic regression at capturing our subjective 2.39 +impression of a “good gene”. 2.40 +SVM on all genes at once 2.41 +In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical 2.42 +surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%19. This shows that 2.43 +the genes included in the ABA dataset are sufficient to define much of cortical anatomy. As noted above, however, a classifier 2.44 +that looks at all the genes at once isn’t as practically useful as a classifier that uses only a few genes. 2.45 +Data-driven redrawing of the cortical map 2.46 +We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene expression 2.47 +profile associated with each voxel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional Scaling 2.48 +(MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment (LTSA), Hessian locally linear 2.49 +embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic Proximity Embedding (SPE), Fast Maximum 2.50 +Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing 2.51 +many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the second, third, and fourth rows 2.52 +of Figure 6. 2.53 +After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we have tried 2.54 +k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last 2.55 +row of Figure 6. To compare, the first row of Figure 6 shows some of the major subdivisions of cortex. These results 2.56 +clearly show that different dimensionality reduction techniques capture different aspects of the data and lead to different 2.57 +clusterings, indicating the utility of our proposal to produce a detailed comparion of these techniques as applied to the 2.58 +domain of genomic anatomy. 2.59 +todo: nnmf 7 2.60 +Many areas are captured by clusters of genes 2.61 +todo 2.62 +todo 2.63 +_________________________________________ 2.64 + 195-fold cross-validation. 2.65 2.66 2.67 2.68 @@ -480,25 +507,6 @@ 2.69 NNMF. Right: Landmark Isomap. Additional details: In the third and fourth rows, 7 dimensions were found, but only 6 2.70 displayed. In the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions were used; for landmark Isomap, 7 2.71 dimensions were used. 2.72 -surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%19. As noted above, 2.73 -however, a classifier that looks at all the genes at once isn’t as practically useful as a classifier that uses only a few genes. 2.74 -Data-driven redrawing of the cortical map 2.75 -We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene expression 2.76 -profile associated with each voxel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional Scaling 2.77 -(MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment (LTSA), Hessian locally linear 2.78 -embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic Proximity Embedding (SPE), Fast Maximum 2.79 -Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing 2.80 -many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the second, third, and fourth rows 2.81 -of Figure 6. 2.82 -After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we have tried 2.83 -k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last 2.84 -row of Figure 6. To compare, the first row of Figure 6 shows some of the major subdivisions of cortex. 2.85 -todo: nnmf 7 2.86 -Many areas are captured by clusters of genes 2.87 -todo 2.88 -todo 2.89 -_________________________________________ 2.90 - 195-fold cross-validation. 2.91 Research plan 2.92 Further work on flatmapping 2.93 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo),

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5.1 --- a/grant.txt Mon Apr 20 14:33:20 2009 -0700 5.2 +++ b/grant.txt Mon Apr 20 15:08:40 2009 -0700 5.3 @@ -339,6 +339,7 @@ 5.4 5.5 In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior part of cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate), VIS (visual), AUD (auditory). 5.6 5.7 +These results validate our expectation that the ABA dataset can be exploited to find marker genes for many cortical areas, while also validating the relevancy of our new scoring method, gradient similarity. 5.8 5.9 \begin{figure}\centering 5.10 \includegraphics[scale=.31]{singlegene_example_2682_Pitx2_SS_jet.eps} 5.11 @@ -357,7 +358,7 @@ 5.12 5.13 \vspace{0.3cm}**Combinations of multiple genes are useful and necessary for some areas** 5.14 5.15 -In Figure \ref{MOcombo}, we give an example of a cortical area which is not marked by any single gene, but which can be identified combinatorially. 5.16 +In Figure \ref{MOcombo}, we give an example of a cortical area which is not marked by any single gene, but which can be identified combinatorially. This shows that our proposal to develop a method to find combinations of marker genes is both possible and necessary. 5.17 5.18 %% wwc1\footnote{"WW, C2 and coiled-coil domain containing 1"; EntrezGene ID 211652} 5.19 %% mtif2\footnote{"mitochondrial translational initiation factor 2"; EntrezGene ID 76784} 5.20 @@ -376,25 +377,20 @@ 5.21 5.22 5.23 5.24 - 5.25 - 5.26 - 5.27 - 5.28 - 5.29 \vspace{0.3cm}**Feature selection integrated with prediction** 5.30 As noted earlier, in general, any predictive method can be used for feature selection by running it inside a stepwise wrapper. Also, some predictive methods integrate soft constraints on number of features used. Examples of both of these will be seen in the section "Multivariate Predictive methods". 5.31 5.32 5.33 === Multivariate Predictive methods === 5.34 \vspace{0.3cm}**Forward stepwise logistic regression** 5.35 -As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise logistic regression to find single genes, pairs of genes, and triplets of genes which predict areal identify. This is an example of feature selection integrated with prediction using a stepwise wrapper. Some of the single genes found were shown in various figures throughout this document, and Figure \ref{MOcombo} shows a combination of genes which was found. 5.36 +Logistic regression is a popular method for predictive modeling of categorial data. As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise logistic regression to find single genes, pairs of genes, and triplets of genes which predict areal identify. This is an example of feature selection integrated with prediction using a stepwise wrapper. Some of the single genes found were shown in various figures throughout this document, and Figure \ref{MOcombo} shows a combination of genes which was found. 5.37 5.38 We felt that, for single genes, gradient similarity did a better job than logistic regression at capturing our subjective impression of a "good gene". 5.39 5.40 5.41 \vspace{0.3cm}**SVM on all genes at once** 5.42 5.43 -In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%\footnote{5-fold cross-validation.}. As noted above, however, a classifier that looks at all the genes at once isn't as practically useful as a classifier that uses only a few genes. 5.44 +In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%\footnote{5-fold cross-validation.}. This shows that the genes included in the ABA dataset are sufficient to define much of cortical anatomy. As noted above, however, a classifier that looks at all the genes at once isn't as practically useful as a classifier that uses only a few genes. 5.45 5.46 5.47 5.48 @@ -404,7 +400,7 @@ 5.49 5.50 We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene expression profile associated with each voxel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional Scaling (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment (LTSA), Hessian locally linear embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic Proximity Embedding (SPE), Fast Maximum Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the second, third, and fourth rows of Figure \ref{dimReduc}. 5.51 5.52 -After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last row of Figure \ref{dimReduc}. To compare, the first row of Figure \ref{dimReduc} shows some of the major subdivisions of cortex. 5.53 +After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last row of Figure \ref{dimReduc}. To compare, the first row of Figure \ref{dimReduc} shows some of the major subdivisions of cortex. These results clearly show that different dimensionality reduction techniques capture different aspects of the data and lead to different clusterings, indicating the utility of our proposal to produce a detailed comparion of these techniques as applied to the domain of genomic anatomy. 5.54 5.55 \begin{figure}\centering 5.56 \includegraphics[scale=.31]{paint_merge3_major.eps}