1.1 --- a/grant.txt Mon Apr 20 13:08:18 2009 -0700 1.2 +++ b/grant.txt Mon Apr 20 14:33:20 2009 -0700 1.3 @@ -237,7 +237,7 @@ 1.4 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 into a MATLAB matrix. 1.6 1.7 -We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format. 1.8 +We manually traced the boundaries of each of 49 cortical areas from the ABA coronal reference atlas slides. We then converted these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format. 1.9 1.10 At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing a grid of points (pixels) over the cortical surface: 1.11 1.12 @@ -402,29 +402,24 @@ 1.13 1.14 === Data-driven redrawing of the cortical map === 1.15 1.16 -\vspace{0.3cm}**Raw dimensionality reduction** 1.17 -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). 1.18 - 1.19 - 1.20 -todo 1.21 - 1.22 -(might want to incld nnMF since mentioned above) 1.23 - 1.24 - 1.25 +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}. 1.26 + 1.27 +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. 1.28 1.29 \begin{figure}\centering 1.30 +\includegraphics[scale=.31]{paint_merge3_major.eps} 1.31 +\\ 1.32 \includegraphics[scale=1]{merge3_norm_hv_PCA_ndims50_prototypes_collage_sm_border.eps} 1.33 \includegraphics[scale=1]{nnmf_ndims7_collage_border.eps} 1.34 \includegraphics[scale=1]{merge3_norm_hv_k150_LandmarkIsomap_ndims7_prototypes_collage_sm_border.eps} 1.35 \\ 1.36 +\includegraphics[scale=.31]{merge3_norm_hv_PCA_ndims50_kmeans_7clust.eps} 1.37 \includegraphics[scale=.31]{norm_hv_NNMF_3_norm_kmeans_4clust.eps} 1.38 -\caption{todo liso} 1.39 -\label{lisomap}\end{figure} 1.40 - 1.41 - 1.42 -\vspace{0.3cm}**Dimensionality reduction plus K-means or spectral clustering** 1.43 - 1.44 - 1.45 +\includegraphics[scale=.31]{merge3_norm_hv_k150_LandmarkIsomap_ndims7_kmeans_7clust.eps} 1.46 +\caption{Top row: 19 of the major subdivisions of the cortex. Second row: the first 6 reduced dimensions, using PCA. Third row: the first 6 reduced dimensions, using NNMF. Fourth row: the first six reduced dimensions, using landmark Isomap. Bottom row: examples of kmeans clustering applied to reduced datasets to find 7 clusters. Left: PCA. Middle: NNMF. Right: Landmark Isomap. Additional details: In the third and fourth rows, 7 dimensions were found, but only 6 displayed. In the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions were used; for landmark Isomap, 7 dimensions were used.} 1.47 +\label{dimReduc}\end{figure} 1.48 + 1.49 +todo: nnmf 7 1.50 1.51 \vspace{0.3cm}**Many areas are captured by clusters of genes** 1.52