1.1 --- a/grant.html Mon Apr 20 13:08:18 2009 -0700 1.2 +++ b/grant.html Mon Apr 20 14:33:20 2009 -0700 1.3 @@ -333,9 +333,9 @@ 1.4 the cortex, creating a two-dimensional mesh. 1.5 We sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this grid 1.6 into a MATLAB matrix. 1.7 -We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted 1.8 -these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d 1.9 -mesh, and then onto the grid, and then we converted the region data into MATLAB format. 1.10 +We manually traced the boundaries of each of 49 cortical areas from the ABA coronal reference atlas slides. We then 1.11 +converted these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions 1.12 +onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format. 1.13 At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing 1.14 a grid of points (pixels) over the cortical surface: 1.15 ∙A 2-D matrix whose entries represent the regional label associated with each surface pixel 1.16 @@ -469,22 +469,31 @@ 1.17 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get 1.18 the lower-left image. This combination captures area MO much better than any single gene. 1.19 1.20 + 1.21 1.22 1.23 1.24 - 1.25 - Figure 6: todo liso 1.26 + 1.27 +Figure 6: Top row: 19 of the major subdivisions of the cortex. Second row: the first 6 reduced dimensions, using PCA. 1.28 +Third row: the first 6 reduced dimensions, using NNMF. Fourth row: the first six reduced dimensions, using landmark 1.29 +Isomap. Bottom row: examples of kmeans clustering applied to reduced datasets to find 7 clusters. Left: PCA. Middle: 1.30 +NNMF. Right: Landmark Isomap. Additional details: In the third and fourth rows, 7 dimensions were found, but only 6 1.31 +displayed. In the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions were used; for landmark Isomap, 7 1.32 +dimensions were used. 1.33 surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%19. As noted above, 1.34 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. 1.35 Data-driven redrawing of the cortical map 1.36 -Raw dimensionality reduction We have applied the following dimensionality reduction algorithms to reduce the di- 1.37 -mensionality of the gene expression profile associated with each voxel: Principal Components Analysis (PCA), Simple 1.38 -PCA (SPCA), Multi-Dimensional Scaling (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space 1.39 -Alignment (LTSA), Hessian locally linear embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic 1.40 -Proximity Embedding (SPE), Fast Maximum Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). 1.41 -todo 1.42 -(might want to incld nnMF since mentioned above) 1.43 -Dimensionality reduction plus K-means or spectral clustering 1.44 +We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene expression 1.45 +profile associated with each voxel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional Scaling 1.46 +(MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment (LTSA), Hessian locally linear 1.47 +embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic Proximity Embedding (SPE), Fast Maximum 1.48 +Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing 1.49 +many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the second, third, and fourth rows 1.50 +of Figure 6. 1.51 +After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we have tried 1.52 +k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last 1.53 +row of Figure 6. To compare, the first row of Figure 6 shows some of the major subdivisions of cortex. 1.54 +todo: nnmf 7 1.55 Many areas are captured by clusters of genes 1.56 todo 1.57 todo