From 8957a68c1916206bb261ec1a4d145b504487493c Mon Sep 17 00:00:00 2001
From: jona <yablee@gmail.com>
Date: Wed, 27 May 2020 16:21:00 +0200
Subject: [PATCH] Add index terms

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 11-multiomics-analysis.Rmd | 28 ++++++++++++++--------------
 1 file changed, 14 insertions(+), 14 deletions(-)

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@@ -18,11 +18,11 @@ Chapter Author: Jonathan Ronen
 
 
 
-Living cells are a symphony of complex processes. Modern sequencing technology has lead to many comprehensive assays being routinely available to experimenters, giving us different ways to peek at the internal doings of the cells, each experiment revealing a different part of some underlying processes. As an example, most cells have the same DNA, but sequencing the genome of a cell allows us to find mutations and structural alterations that drive tumerogenesis in cancer. If we treat the DNA with bisulfite prior to sequencing, cytosine residues are converted to uracil, but 5-methylcytosine residues are unaffected. This allows us to probe the methylation patterns of the genome, or its methylome. By sequencing the mRNA molecules in a cell, we can calculate the abundance, in different samples, of different mRNA transcripts, or uncover its transcriptome. Performing different experiments on the same samples, for instance RNA-seq, DNA-seq, and BS-seq, results in multi-dimensional omics datasets, which enable the study of relationships between different biological processes, e.g. DNA methylation, mutations, and gene expression, and the leveraging of multiple data types to draw inferences about biological systems. This chapter provides an overview of some of the available methods for such analyses, focusing on matrix factorization approaches. In the examples in this chapter we will demonstrate how these methods are applicable to cancer subtyping, i.e. finding tumors which are driven by the same oncogenic processes.
+\index{multi-omics}Living cells are a symphony of complex processes. Modern sequencing technology has lead to many comprehensive assays being routinely available to experimenters, giving us different ways to peek at the internal doings of the cells, each experiment revealing a different part of some underlying processes. As an example, most cells have the same DNA, but sequencing the genome of a cell allows us to find mutations and structural alterations that drive tumerogenesis in cancer. If we treat the DNA with bisulfite prior to sequencing, cytosine residues are converted to uracil, but 5-methylcytosine residues are unaffected. This allows us to probe the methylation patterns of the genome, or its methylome. By sequencing the mRNA molecules in a cell, we can calculate the abundance, in different samples, of different mRNA transcripts, or uncover its transcriptome. Performing different experiments on the same samples, for instance RNA-seq, DNA-seq, and BS-seq, results in multi-dimensional omics datasets, which enable the study of relationships between different biological processes, e.g. DNA methylation, mutations, and gene expression, and the leveraging of multiple data types to draw inferences about biological systems. This chapter provides an overview of some of the available methods for such analyses, focusing on matrix factorization approaches. In the examples in this chapter we will demonstrate how these methods are applicable to cancer subtyping, i.e. finding tumors which are driven by the same oncogenic processes.
 
 ### Use case: Multi-omics data from colorectal cancer
 
-The examples in this chapter will use the following data: a set of 121 tumors from the TCGA [@tcga_pan_cancer] cohorts of Colon and Rectum adenocarcinoma. The tumors have been profiled for gene expression using RNA-seq, mutations using Exome-seq, and copy number variations using genotyping arrays. Projects such as TCGA have turbocharged efforts to sub-divide cancer into subtypes. Although two tumors arise in the colon, they may have distinct molecular profiles, which is important for treatment decisions. The subset of tumors used in this chapter belong to two distinct molecular subtypes defined by the Colorectal Cancer Subtyping Consortium [@cmscc], _CMS1_ and _CMS3_. The following code snippets load this multi-omics data from the companion package.
+\index{multi-omics}\index{colorectal cancer}The examples in this chapter will use the following data: a set of 121 tumors from the TCGA [@tcga_pan_cancer] cohorts of Colon and Rectum adenocarcinoma. The tumors have been profiled for gene expression using RNA-seq, mutations using Exome-seq, and copy number variations using genotyping arrays. Projects such as TCGA have turbocharged efforts to sub-divide cancer into subtypes. Although two tumors arise in the colon, they may have distinct molecular profiles, which is important for treatment decisions. The subset of tumors used in this chapter belong to two distinct molecular subtypes defined by the Colorectal Cancer Subtyping Consortium [@cmscc], _CMS1_ and _CMS3_. The following code snippets load this multi-omics data from the companion package.
 
 ```{r,moloadMultiomicsGE, tidy=FALSE}
 csvfile <- system.file("extdata", "multi-omics", "COREAD_CMS13_gex.csv", 
@@ -94,11 +94,11 @@ The interpretation of Figure \@ref(fig:moCNVHeatmap) is left as an exercise for
 
 ## Latent variable models for multi-omics integration
 
-Unupervised multi-omics integration methods are methods that look for patterns within and across data types, in a label-agnostic fashion, i.e. without knowledge of the identity or label of the analyzed samples (e.g. cell type, tumor/normal). This chapter focuses on latent variable models, a form of dimensionality reduction technique (see Chapter 4, Unsupervised Learning). Latent variable models make an assumption that the high dimensional data we observe (e.g. counts of tens of thousands of mRNA molecules) arrise from a lower dimension description. The variables in that lower dimensional description are termed _Latent Variables_, as they are believed to be latent in the data, but not directly observable through experimentation. Therefore, there is a need for methods to infer the latent variables from the data. For instance, (see Chapter 8, RNA-seq analysis) the relative abundance of different mRNA molecules in a cell is largely determined by the cell type. There are other experiments which may be used to discern the cell type of cells (e.g. looking at them under a microscope), but an RNA-seq experiment does not, directly, reveal whether the analyzed sample was taken from one organ or another. A latent variable model would set the cell type as a latent variable, and the observable abundance of mRNA molecules to be dependent on the value of the latent variable (e.g. if the latent variable is "Regulatory T-cell", we would expect to find high expression of CD4, FOXP3, and CD25).
+\index{unsupervised learning}Unupervised multi-omics integration methods are methods that look for patterns within and across data types, in a label-agnostic fashion, i.e. without knowledge of the identity or label of the analyzed samples (e.g. cell type, tumor/normal). This chapter focuses on latent variable models, a form of dimensionality reduction technique (see Chapter 4, Unsupervised Learning). Latent variable models make an assumption that the high dimensional data we observe (e.g. counts of tens of thousands of mRNA molecules) arrise from a lower dimension description. The variables in that lower dimensional description are termed _Latent Variables_, as they are believed to be latent in the data, but not directly observable through experimentation. Therefore, there is a need for methods to infer the latent variables from the data. For instance, (see Chapter 8, RNA-seq analysis) the relative abundance of different mRNA molecules in a cell is largely determined by the cell type. There are other experiments which may be used to discern the cell type of cells (e.g. looking at them under a microscope), but an RNA-seq experiment does not, directly, reveal whether the analyzed sample was taken from one organ or another. A latent variable model would set the cell type as a latent variable, and the observable abundance of mRNA molecules to be dependent on the value of the latent variable (e.g. if the latent variable is "Regulatory T-cell", we would expect to find high expression of CD4, FOXP3, and CD25).
   
 ## Matrix factorization methods for unsupervised multi-omics data integration
 
-Matrix factorization techniques attempt to infer a set of latent variables from the data by finding factors of a data matrix. Principal Component Analysis (Chapter 4) is a form of matrix factorization which finds factors based on the covariance structure of the data. Generally, matrix factorization methods may be formulated as
+\index{dimensionality reduction}\index{matrix factorization}Matrix factorization techniques attempt to infer a set of latent variables from the data by finding factors of a data matrix. Principal Component Analysis (introduced in Chapter \@ref(unsupervisedLearning)) is a form of matrix factorization which finds factors based on the covariance structure of the data. Generally, matrix factorization methods may be formulated as
 
 
 $$
@@ -110,7 +110,7 @@ $$
 min~\|X-WH\|,
 $$
 
-which may be further subject to some constraints or regularization terms. As we normally seek a latent variable model with a considerably lower dimensionality than $X$, this is the more common case.
+which may be further subject to some constraints or regularization terms\index{loss function}\index{optimization}. As we normally seek a latent variable model with a considerably lower dimensionality than $X$, this is the more common case.
 
 ```{r,momatrixFactorization,fig.cap="General matrix factorization framework. The data matrix on the left hand side is decomposed into factors on the right hand side. The equality may be an approximation as some matrix factorization methods are lossless (exact), while others are an approximation.",fig.align = 'center',out.width='75%',echo=FALSE}
 knitr::include_graphics("images/matrix_factorization.png" )
@@ -120,7 +120,7 @@ In Figure \@ref(fig:momatrixFactorization), the $5 \times 4$ data matrix $X$ is
 
 ### Multiple Factor Analysis
 
-Multiple factor analysis is a natural starting point for a discussion about matrix factorization methods for intergrating multiple data types. It is a straightforward extension of PCA into the domain of multiple data types [^mfamca].
+\index{multiple factor analysis}Multiple factor analysis is a natural starting point for a discussion about matrix factorization methods for intergrating multiple data types. It is a straightforward extension of PCA into the domain of multiple data types [^mfamca].
 
 Figure \@ref(fig:moMFA) sketches a naive extension of PCA to a multi-omics context.
 
@@ -191,7 +191,7 @@ Figure \@ref(fig:momfaheatmap) shows that indeed, when tumors are clustered and
 
 ### Joint Non-negative Matrix Factorization
 
-NMF (Non-negative Matrix Factorization) is an algorithm from 2000 that seeks to find a non-negative additive decomposition for a non-negative data matrix. It takes the familiar form $X \approx WH$, with $X \ge 0$, $W \ge 0$, and $H \ge 0$. The non-negative constraints make a lossless decomposition (i.e. $X=WH$) generally impossible. Hence, NMF attempts to find a solution which minimizes the Frobenius norm of the reconstruction:
+\index{non-negative matrix factorization}NMF (Non-negative Matrix Factorization) is an algorithm from 2000 that seeks to find a non-negative additive decomposition for a non-negative data matrix. It takes the familiar form $X \approx WH$, with $X \ge 0$, $W \ge 0$, and $H \ge 0$. The non-negative constraints make a lossless decomposition (i.e. $X=WH$) generally impossible. Hence, NMF attempts to find a solution which minimizes the Frobenius norm of the reconstruction:
 
 $$
 min~\|X-WH\|_F \\
@@ -365,7 +365,7 @@ pheatmap::pheatmap(t(nmf_df[,1:2]),
 
 ### iCluster
 
-iCluster takes a Bayesian approach to the latent variable model. In Bayesian statistics, we infer distributions over model parameters, rather than finding a single maximum-likelihood parameter estimate. In iCluster, we model the data as 
+\index{iCluster}iCluster takes a Bayesian approach to the latent variable model. In Bayesian statistics, we infer distributions over model parameters, rather than finding a single maximum-likelihood parameter estimate. In iCluster, we model the data as 
 
 $$
 X_{(i)} = W_{(i)}Z + \epsilon_i,
@@ -391,7 +391,7 @@ $$
 \ell_{iC}(W,\Sigma) = -\frac{1}{2} \bigg( \sum_{i=1}^L \ln (|\Sigma|) + X^T\Sigma^{-1}X + p_i \ln (2 \pi) \bigg)
 $$
 
-where $p_i$ is the number of features in omics data type $i$. Because this model has more parameters than we typically have samples, we need to push the model to use fewer parameters than it has at its disposal, by using regularization. iCluster uses Lasso regularization, which is a direct penalty on the absolute value of the parameters. I.e., instead of optimizing $\ell_{iC}(W,\Sigma)$, we will optimize the regularized log-likelihood:
+where $p_i$ is the number of features in omics data type $i$. Because this model has more parameters than we typically have samples, we need to push the model to use fewer parameters than it has at its disposal, by using regularization. iCluster uses Lasso regularization, which is a direct penalty on the absolute value of the parameters. I.e., instead of optimizing $\ell_{iC}(W,\Sigma)$, we will optimize the regularized log-likelihood:\index{loss function}
 
 $$
 \ell = \ell_{iC}(W,\Sigma) - \lambda\|W\|_1.
@@ -463,7 +463,7 @@ pheatmap::pheatmap(t(icp_df[,1:2]),
 
 ## Clustering using latent factors
 
-A common analysis in biological investigations is clustering. This is often interesting in cancer studies as one hopes to find groups of tumors (clusters) which behave similarly, i.e. have similar risks and/or respond to the same drugs. PCA is a common step in clustering analyses, and so it is easy to see how the latent variable models above may all be a useful pre-processing step before clustering. In the examples below, we will use the latent variables inferred by the algorithms in the previous section on the set of Colorectal cancer tumors from the TCGA.
+\index{clustering}\index{unsupervised learning}A common analysis in biological investigations is clustering. This is often interesting in cancer studies as one hopes to find groups of tumors (clusters) which behave similarly, i.e. have similar risks and/or respond to the same drugs. PCA is a common step in clustering analyses, and so it is easy to see how the latent variable models above may all be a useful pre-processing step before clustering. In the examples below, we will use the latent variables inferred by the algorithms in the previous section on the set of Colorectal cancer tumors from the TCGA. For a more complete introduction to clustering, see Chapter \@ref(unsupervisedLearning).
 
 ### One-hot clustering
 
@@ -491,7 +491,7 @@ The one-hot clustering method does not lend itself very well to the other method
 
 ### K-means clustering
 
-K-means clustering was introduced in Chapter 4. K-means is a special case of the EM algorithm, and indeed iCluster was originally conceived as an extension of K-means from binary cluster assignments to real-valued latent variables. The iCluster algorithm, as it is so named, calls for application of K-means clustering on its latent variables, after the inference step. The following code snippet shows how to pull K-means clusters out of the iCluster results, and produces the heatmap in Figure \@ref(fig:moiClusterHeatmap), which shows how well these clusters correspond to cancer subtypes.
+K-means clustering was introduced in Chapter \@ref(unsupervisedLearning). K-means is a special case of the EM algorithm, and indeed iCluster was originally conceived as an extension of K-means from binary cluster assignments to real-valued latent variables. The iCluster algorithm, as it is so named, calls for application of K-means clustering on its latent variables, after the inference step. The following code snippet shows how to pull K-means clusters out of the iCluster results, and produces the heatmap in Figure \@ref(fig:moiClusterHeatmap), which shows how well these clusters correspond to cancer subtypes.
 
 ```{r,moiClusterHeatmap,fig.cap="K-means clustering on iCluster+ factors largely recapitulates the CMS sub-types."}
 rownames(icluster.z) <- rownames(covariates)
@@ -542,11 +542,11 @@ Inspection of the factor coefficients in the heatmap above reveals that Joint NM
 
 #### Disentangled representations
 
-The property displayed above, where each feature is predominantly associated with only a single factor, is termed _disentangledness_, i.e., it leads to _disentangled_ latent variable representations, as changing one input feature only affects a single latent variable. This property is very desirable as it greatly simplifies the biological interpretation of modules. Here, we have two modules with a set of co-occurring molecular signatures which merit deeper investigation into the mechanisms by which these different omics features are related. For this reason, NMF is widely used in computational biology today.
+\index{disentangled representations}The property displayed above, where each feature is predominantly associated with only a single factor, is termed _disentangledness_, i.e., it leads to _disentangled_ latent variable representations, as changing one input feature only affects a single latent variable. This property is very desirable as it greatly simplifies the biological interpretation of modules. Here, we have two modules with a set of co-occurring molecular signatures which merit deeper investigation into the mechanisms by which these different omics features are related. For this reason, NMF is widely used in computational biology today.
 
 ### Making sense of factors using enrichment analysis
 
-In order to investigate the oncogenic processes that drive the differences between tumors, we may draw upon biological prior knowledge by looking for overlaps between genes that drive certain tumors, and genes involved in familiar biological processes.
+\index{enrichment analysis}In order to investigate the oncogenic processes that drive the differences between tumors, we may draw upon biological prior knowledge by looking for overlaps between genes that drive certain tumors, and genes involved in familiar biological processes.
 
 #### Enrichment analysis
 
@@ -558,7 +558,7 @@ $$
 P(k) = \frac{{\binom{K}{k}} - \binom{N-K}{n-k}}{\binom{N}{n}}.
 $$
 
-the **hypergeometric test** uses the hypergeometric distribution to assess the statistical significance of the presense of genes belonging to a gene set in the latent factor. The null hypothesis is that there is no relationship between genes in a gene set, and genes in a latent factor. When testing for over-representation of gene set genes in a latent factor, the P value from the hypergeometric test is the probability of getting $k$ or more genes from a gene set in a latent factor
+the **hypergeometric test** \index{statistical test} uses the hypergeometric distribution to assess the statistical significance of the presense of genes belonging to a gene set in the latent factor. The null hypothesis is that there is no relationship between genes in a gene set, and genes in a latent factor. When testing for over-representation of gene set genes in a latent factor, the P value from the hypergeometric test is the probability of getting $k$ or more genes from a gene set in a latent factor
 
 $$
 p = \sum_{i=k}^K P(k=i).
-- 
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