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Erschienen in:
Unsupervised Integration of Single-Cell Multi-omics Datasets with Disproportionate Cell-Type Representation Kapitel lesen Erstes Kapitel lesen

2022 | OriginalPaper | Buchkapitel

A Fast, Provably Accurate Approximation Algorithm for Sparse Principal Component Analysis Reveals Human Genetic Variation Across the World

verfasst von : Agniva Chowdhury, Aritra Bose, Samson Zhou, David P. Woodruff, Petros Drineas

Erschienen in: Research in Computational Molecular Biology

Verlag: Springer International Publishing

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Abstract

Principal component analysis (PCA) is a widely used dimensionality reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have been proposed, which are termed Sparse Principal Component Analysis (SPCA). In this paper, we present ThreSPCA, a provably accurate algorithm based on thresholding the Singular Value Decomposition for the SPCA problem, without imposing any restrictive assumptions on the input covariance matrix. Our thresholding algorithm is conceptually simple; much faster than current state-of-the-art; and performs well in practice. When applied to genotype data from the 1000 Genomes Project, ThreSPCA is faster than previous benchmarks, at least as accurate, and leads to a set of interpretable biomarkers, revealing genetic diversity across the world.

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Vorheriges Kapitel MetaCoAG: Binning Metagenomic Contigs via Composition, Coverage and Assembly Graphs
Nächstes Kapitel Gene Set Priorization Guided by Regulatory Networks with p-values through Kernel Mixed Model
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Fußnoten
1
Recall that the p-th power of the \(\ell _p\) norm of a vector \({\mathbf {x}} \in \mathbb {R}^n\) is defined as \(\Vert \mathbf {x}\Vert _p^p = \sum _{i=1}^n {\left| {\mathbf {x}} _i\right| } ^p\) for \(0<p<\infty \). For \(p=0\), \(\Vert x\Vert _0\) is a semi-norm denoting the number of non-zero entries of x.
 
2
Each column of \(\mathbf {R}\) has a single non-zero entry (set to one), corresponding to one of the |R| selected columns. Formally, \(\mathbf {R}_{i_t,t}=1\) for \(t=1,\ldots , |R|\); all other entries of \(\mathbf {R}\) are set to zero.
 
3
Results from L-PCA are qualitatively very similar to AL-PCA and we only report results for the latter.
 
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Metadaten
Titel
A Fast, Provably Accurate Approximation Algorithm for Sparse Principal Component Analysis Reveals Human Genetic Variation Across the World
verfasst von
Agniva Chowdhury
Aritra Bose
Samson Zhou
David P. Woodruff
Petros Drineas
Copyright-Jahr
2022
Buch
Research in Computational Molecular Biology

Print ISBN: 978-3-031-04748-0

Electronic ISBN: 978-3-031-04749-7

Copyright-Jahr: 2022

DOI
https://doi.org/10.1007/978-3-031-04749-7_6