Exploring high-dimensional biological data with sparse contrastive principal component analysis

Boileau, Philippe; Hejazi, Nima S.; Dudoit, Sandrine

doi:10.1093/bioinformatics/btaa176

Cited by 31 publications

(14 citation statements)

References 41 publications

(26 reference statements)

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“…When applying ULCA to such a dataset, many of the attributes (e.g., 100 attributes) could significantly contribute to embedding axes. To avoid using many attributes when constructing the embedding axes, various sparse DR methods, such as sparse PCA [98], sparse LDA [15], and space cPCA [7], have been developed. These methods produce a sparse projection matrix by penalizing a case where an embedding uses many attributes.…”

Section: Discussionmentioning

confidence: 99%

Interactive Dimensionality Reduction for Comparative Analysis

Fujiwara,

Wei,

Zhao

et al. 2021

Preprint

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Finding the similarities and differences between two or more groups of datasets is a fundamental analysis task. For high-dimensional data, dimensionality reduction (DR) methods are often used to find the characteristics of each group. However, existing DR methods provide limited capability and flexibility for such comparative analysis as each method is designed only for a narrow analysis target, such as identifying factors that most differentiate groups. In this work, we introduce an interactive DR framework where we integrate our new DR method, called ULCA (unified linear comparative analysis), with an interactive visual interface. ULCA unifies two DR schemes, discriminant analysis and contrastive learning, to support various comparative analysis tasks. To provide flexibility for comparative analysis, we develop an optimization algorithm that enables analysts to interactively refine ULCA results. Additionally, we provide an interactive visualization interface to examine ULCA results with a rich set of analysis libraries. We evaluate ULCA and the optimization algorithm to show their efficiency as well as present multiple case studies using real-world datasets to demonstrate the usefulness of our framework.

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Section: Discussionmentioning

confidence: 99%

Interactive Dimensionality Reduction for Comparative Analysis

Fujiwara,

Wei,

Zhao

et al. 2021

Preprint

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“…A sparse version of CPCA was recently developed, which allows for greater interpretability of the estimated components, especially in high-dimensional settings (Boileau et al, 2020). Building off of sparse PCA (Zou et al, 2006), which uses element-wise 1 regularization to encourage zeros in the loadings matrix, the authors propose an estimation procedure that alternates between estimating the principal components and the sparse loadings matrix.…”

Section: Contrastive Dimension Reduction Methodsmentioning

confidence: 99%

Contrastive latent variable modeling with application to case-control sequencing experiments

Jones¹,

Townes²,

Li³

et al. 2021

Preprint

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High-throughput RNA-sequencing (RNA-seq) technologies are powerful tools for understanding cellular state. Often it is of interest to quantify and summarize changes in cell state that occur between experimental or biological conditions. Differential expression is typically assessed using univariate tests to measure gene-wise shifts in expression. However, these methods largely ignore changes in transcriptional correlation. Furthermore, there is a need to identify the low-dimensional structure of the gene expression shift to identify collections of genes that change between conditions. Here, we propose contrastive latent variable models designed for count data to create a richer portrait of differential expression in sequencing data. These models disentangle the sources of transcriptional variation in different conditions, in the context of an explicit model of variation at baseline. Moreover, we develop a model-based hypothesis testing framework that can test for global and gene subset-specific changes in expression. We test our model through extensive simulations and analyses with count-based gene expression data from perturbation and observational sequencing experiments. We find that our methods can effectively summarize and quantify complex transcriptional changes in case-control experimental sequencing data.

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“…We have data on the BMMCs before stemcell transplant and the BMMCs after stem-cell transplant. We preprocess the data sets as described by the authors in [4] 2 keeping the 1000 most variable genes measured across all 16856 cells (patient-035: 4501 cells and two healthy individuals; one of 1985 cells and the other of 2472 cells). The data from the two healthy patients are combined to create a background data matrix of dimension 4457 × 1000 and we use patient-035 data set as the target data matrix of dimension 4501 × 1000 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

A Generalized CUR decomposition for matrix pairs

Gidisu¹,

Hochstenbach²

2021

Preprint

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We propose a generalized CUR (GCUR) decomposition for matrix pairs (A, B). Given matrices A and B with the same number of columns, such a decomposition provides low-rank approximations of both matrices simultaneously, in terms of some of their rows and columns. We obtain the indices for selecting the subset of rows and columns of the original matrices using the discrete empirical interpolation method (DEIM) on the generalized singular vectors. When B is square and nonsingular, there are close connections between the GCUR of (A, B) and the DEIM-induced CUR of AB −1 . When B is the identity, the GCUR decomposition of A coincides with the DEIM-induced CUR decomposition of A. We also show similar connection between the GCUR of (A, B) and the CUR of AB + for a nonsquare but full-rank matrix B, where B + denotes the Moore-Penrose pseudoinverse of B. While a CUR decomposition acts on one data set, a GCUR factorization jointly decomposes two data sets. The algorithm may be suitable for applications where one is interested in extracting the most discriminative features from one data set relative to another data set. In numerical experiments, we demonstrate the advantages of the new method over the standard CUR approximation; for recovering data perturbed with colored noise and subgroup discovery.

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Exploring high-dimensional biological data with sparse contrastive principal component analysis

Cited by 31 publications

References 41 publications

Interactive Dimensionality Reduction for Comparative Analysis

Interactive Dimensionality Reduction for Comparative Analysis

Contrastive latent variable modeling with application to case-control sequencing experiments

A Generalized CUR decomposition for matrix pairs

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