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The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data…

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…

Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…

Sparse matrix computation is crucial in various modern applications, including large-scale graph analytics, deep learning, and recommender systems. The performance of sparse kernels varies greatly depending on the structure of the input…

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by…

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…

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…

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…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

This article focuses on the robust principal component analysis (PCA) of high-dimensional data with elliptical distributions. We investigate the PCA of the sample spatial-sign covariance matrix in both nonsparse and sparse contexts,…

Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…

The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient…

Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our…

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, the…

Due to advances in sensors, growing large and complex medical image data have the ability to visualize the pathological change in the cellular or even the molecular level or anatomical changes in tissues and organs. As a consequence, the…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of…