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Sparse principal component analysis (SPCA) methods have proven to efficiently analyze high-dimensional data. Among them, threshold-based SPCA (TSPCA) is computationally more cost-effective than regularized SPCA, based on L1 penalties. We…
Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…
Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral…
Sparse principal component analysis (sPCA) enhances the interpretability of principal components (PCs) by imposing sparsity constraints on loading vectors (LVs). However, when used as a precursor to independent component analysis (ICA) for…
Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…
Principal components computed via PCA (principal component analysis) are traditionally used to reduce dimensionality in genomic data or to correct for population stratification. In this paper, we explore the penalized eigenvalue problem…
The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…
Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most…
Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…
Sparse principal component analysis (SPCA) is widely used for dimensionality reduction and feature extraction in high-dimensional data analysis. Despite many methodological and theoretical developments in the past two decades, the…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…
Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…
Sparse principal component analysis (PCA), an important variant of PCA, attempts to find sparse loading vectors when conducting dimension reduction. This paper considers the nonsmooth Riemannian optimization problem associated with the…