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Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under…

To do dimensionality reduction on the datasets with outliers, the $\ell_1$-norm principal component analysis (L1-PCA) as a typical robust alternative of the conventional PCA has enjoyed great popularity over the past years. In this work, we…

Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests.…

This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA (Candes et al. 2011) to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) (Kilmer and Martin…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

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…

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Fair principal component analysis (FPCA), a ubiquitous dimensionality reduction technique in signal processing and machine learning, aims to find a low-dimensional representation for a high-dimensional dataset in view of fairness. The FPCA…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

In this paper, we propose a non-convex formulation to recover the authentic structure from the corrupted real data. Typically, the specific structure is assumed to be low rank, which holds for a wide range of data, such as images and…

We present an efficient stochastic algorithm (RSG+) for canonical correlation analysis (CCA) using a reparametrization of the projection matrices. We show how this reparametrization (into structured matrices), simple in hindsight, directly…

Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…

Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale,…

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…