1.1 Binary file grant.pdf has changed

2.1 --- a/grant.txt Mon Apr 20 17:19:47 2009 -0700 2.2 +++ b/grant.txt Mon Apr 20 17:32:13 2009 -0700 2.3 @@ -47,7 +47,7 @@ 2.4 2.5 2.6 \vspace{0.3cm}**Principle 1: Combinatorial gene expression** 2.7 -It is too much to hope that every anatomical region of interest will be identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary Results). Therefore, each instance should contain multiple features (genes). 2.8 +It is too much to hope that every anatomical region of interest will be identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary Studies, Figure \ref{MOcombo}). Therefore, each instance should contain multiple features (genes). 2.9 2.10 2.11 \vspace{0.3cm}**Principle 2: Only look at combinations of small numbers of genes** 2.12 @@ -58,7 +58,7 @@ 2.13 2.14 \vspace{0.3cm}**Principle 3: Use geometry in feature selection** 2.15 2.16 -When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods. 2.17 +When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See Preliminary Studies, figure \ref{AUDgeometry} for evidence of the complementary nature of pointwise and local scoring methods. 2.18 2.19 2.20 2.21 @@ -73,7 +73,7 @@ 2.22 === Related work === 2.23 There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data which is not fundamentally spatial\footnote{By "__fundamentally__ spatial" we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not just data which has only a few different locations or which is indexed by anatomical label.}. 2.24 2.25 -As noted above, there has been much work on both supervised learning and there are many available algorithms for each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the way that this framework is set up has a large impact on performance. Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical "fine-tuning" of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Work) may be necessary in order to achieve the best results in this application. 2.26 +As noted above, there has been much work on both supervised learning and there are many available algorithms for each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the way that this framework is set up has a large impact on performance. Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical "fine-tuning" of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Studies) may be necessary in order to achieve the best results in this application. 2.27 2.28 We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods. 2.29 2.30 @@ -99,7 +99,7 @@ 2.31 \item Clusters: will be described later 2.32 \end{itemize} 2.33 2.34 -Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also search for underexpression. Third, Gene Finder uses a simple pointwise score\footnote{"Expression energy ratio", which captures overexpression.}, whereas we will also use geometric scores such as gradient similarity. The Preliminary Data section contains evidence that each of our three choices is the right one. 2.35 +Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also search for underexpression. Third, Gene Finder uses a simple pointwise score\footnote{"Expression energy ratio", which captures overexpression.}, whereas we will also use geometric scores such as gradient similarity. Figures \ref{MOcombo}, \ref{hole}, and \ref{AUDgeometry} in Preliminary Studies section contains evidence that each of our three choices is the right one. 2.36 2.37 \cite{chin_genome-scale_2007} looks at the mean expression level of genes within anatomical regions, and applies a Student's t-test with Bonferroni correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA, this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for underexpression, and does not look for combinations of genes. 2.38 2.39 @@ -129,7 +129,7 @@ 2.40 \vspace{0.3cm}**Spatially contiguous clusters; image segmentation** 2.41 2.42 2.43 -We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary Results, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these results against other methods which guarantee contiguous clusters. 2.44 +We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary Studies, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these results against other methods which guarantee contiguous clusters. 2.45 2.46 Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these algorithms are specialized for visual images. 2.47 2.48 @@ -151,7 +151,7 @@ 2.49 2.50 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could have one reduced feature for each gene cluster. 2.51 2.52 -Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically interesting region will have multiple genes which each individually pick it out\footnote{This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression; perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another possibility is that, although the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.}. This suggests the following procedure: cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some "superregions" formed by lumping together a few regions, are associated with gene clusters in this fashion. 2.53 +Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically interesting region will have multiple genes which each individually pick it out\footnote{This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression; perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another possibility is that, although the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.}. This suggests the following procedure: cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters. In Preliminary Studies, Figure \ref{geneClusters}, we show that a number of anatomically recognized cortical regions, as well as some "superregions" formed by lumping together a few regions, are associated with gene clusters in this fashion. 2.54 2.55 The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering algorithms. 2.56 2.57 @@ -161,7 +161,7 @@ 2.58 \cite{thompson_genomic_2008} describes an analysis of the anatomy of 2.59 the hippocampus using the ABA dataset. In addition to manual analysis, 2.60 two clustering methods were employed, a modified Non-negative Matrix 2.61 -Factorization (NNMF), and a hierarchial recursive bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset\footnote{We ran "vanilla" NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.} and while the results are promising (see Preliminary Data), we think that it will be possible to find an even better method. 2.62 +Factorization (NNMF), and a hierarchial recursive bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset\footnote{We ran "vanilla" NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.} and while the results are promising, they also demonstrate that NNMF is not necessarily the best dimensionality reduction method for this application (see Preliminary Studies, Figure \ref{dimReduc}). 2.63 2.64 %% In addition, this paper described a visual screening of the data, specifically, a visual analysis of 6000 genes with the primary purpose of observing how the spatial pattern of their expression coincided with the regions that had been identified by NNMF. We propose to do this sort of screening automatically, which would yield an objective, quantifiable result, rather than qualitative observations. 2.65 2.66 @@ -227,7 +227,7 @@ 2.67 2.68 \newpage 2.69 2.70 -== Preliminary work == 2.71 +== Preliminary Studies == 2.72 \begin{wrapfigure}{L}{0.4\textwidth}\centering 2.73 %%\includegraphics[scale=.31]{singlegene_SS_corr_top_1_2365_jet.eps}\includegraphics[scale=.31]{singlegene_SS_corr_top_2_242_jet.eps}\includegraphics[scale=.31]{singlegene_SS_corr_top_3_654_jet.eps} 2.74 %%\\ 2.75 @@ -435,7 +435,7 @@ 2.76 2.77 2.78 \newpage 2.79 -== Research plan == 2.80 +== Research Design and Methods == 2.81 2.82 2.83 \vspace{0.3cm}**Further work on flatmapping**