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2.1 --- a/grant.html Mon Apr 20 16:23:22 2009 -0700 2.2 +++ b/grant.html Mon Apr 20 16:57:54 2009 -0700 2.3 @@ -581,15 +581,27 @@ 2.4 but as a sample, PCA, NNMF, and landmark 2.5 Isomap are shown in the first, second, and third 2.6 rows of Figure 6. 2.7 -After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we have tried 2.8 -k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last 2.9 -row of Figure 6. To compare, the leftmost picture on the bottom row of Figure 6 shows some of the major subdivisions of 2.10 -cortex. These results clearly show that different dimensionality reduction techniques capture different aspects of the data 2.11 -and lead to different clusterings, indicating the utility of our proposal to produce a detailed comparion of these techniques 2.12 -as applied to the domain of genomic anatomy. 2.13 -Many areas are captured by clusters of genes 2.14 -todo 2.15 -todo 2.16 + 2.17 +Figure 7: Prototypes corresponding to sample gene clusters, clustered by 2.18 +gradient similarity. Region boundaries for the region that most matches 2.19 +each prototype are overlayed. After applying the dimensionality reduc- 2.20 + tion, we ran clustering algorithms on the re- 2.21 + duced data. To date we have tried k-means and 2.22 + spectral clustering. The results of k-means after 2.23 + PCA, NNMF, and landmark Isomap are shown 2.24 + in the last row of Figure 6. To compare, the 2.25 + leftmost picture on the bottom row of Figure 2.26 + 6 shows some of the major subdivisions of cor- 2.27 + tex. These results clearly show that different di- 2.28 + mensionality reduction techniques capture dif- 2.29 + ferent aspects of the data and lead to differ- 2.30 + ent clusterings, indicating the utility of our pro- 2.31 + posal to produce a detailed comparion of these 2.32 + techniques as applied to the domain of genomic 2.33 + anatomy. 2.34 +Many areas are captured by clusters of genes We also clustered the genes using gradient similarity to see if the 2.35 +spatial regions defined by any clusters matched known anatomical regions. Figure 7 shows, for ten sample gene clusters, 2.36 +each cluster’s average expression pattern, compared to a known anatomical boundary. 2.37 _________________________________________ 2.38 195-fold cross-validation. 2.39 Research plan

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5.1 --- a/grant.txt Mon Apr 20 16:23:22 2009 -0700 5.2 +++ b/grant.txt Mon Apr 20 16:57:54 2009 -0700 5.3 @@ -397,7 +397,7 @@ 5.4 5.5 \begin{wrapfigure}{L}{0.6\textwidth}\centering 5.6 \includegraphics[scale=1]{merge3_norm_hv_PCA_ndims50_prototypes_collage_sm_border.eps} 5.7 -\includegraphics[scale=1]{nnmf_ndims7_collage_border.eps} 5.8 +\includegraphics[scale=.96]{nnmf_ndims7_collage_border.eps} 5.9 \includegraphics[scale=1]{merge3_norm_hv_k150_LandmarkIsomap_ndims7_prototypes_collage_sm_border.eps} 5.10 \\ 5.11 \includegraphics[scale=.24]{paint_merge3_major.eps}\includegraphics[scale=.22]{merge3_norm_hv_PCA_ndims50_kmeans_7clust.eps}\includegraphics[scale=.24]{norm_hv_NNMF_6_norm_kmeans_7clust.eps}\includegraphics[scale=.22]{merge3_norm_hv_k150_LandmarkIsomap_ndims7_kmeans_7clust.eps} 5.12 @@ -417,25 +417,18 @@ 5.13 5.14 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 first, second, and third rows of Figure \ref{dimReduc}. 5.15 5.16 +\begin{wrapfigure}{L}{0.6\textwidth}\centering 5.17 +\includegraphics[scale=.2]{cosine_similarity1_rearrange_colorize.eps} 5.18 +\caption{Prototypes corresponding to sample gene clusters, clustered by gradient similarity. Region boundaries for the region that most matches each prototype are overlayed.} 5.19 +\label{geneClusters}\end{wrapfigure} 5.20 + 5.21 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 leftmost picture on the bottom 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. 5.22 5.23 5.24 5.25 \vspace{0.3cm}**Many areas are captured by clusters of genes** 5.26 - 5.27 -todo 5.28 - 5.29 - 5.30 - 5.31 - 5.32 - 5.33 - 5.34 - 5.35 - 5.36 - 5.37 - 5.38 - 5.39 -todo 5.40 +We also clustered the genes using gradient similarity to see if the spatial regions defined by any clusters matched known anatomical regions. Figure \ref{geneClusters} shows, for ten sample gene clusters, each cluster's average expression pattern, compared to a known anatomical boundary. This suggests that it is worth attempting to cluster genes, and then to use the results to cluster voxels. 5.41 + 5.42 5.43 5.44