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Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented…

CP decomposition (CPD) is prevalent in chemometrics, signal processing, data mining and many more fields. While many algorithms have been proposed to compute the CPD, alternating least squares (ALS) remains one of the most widely used…

Singular Value Decomposition (SVD) and its close relative, Principal Component Analysis (PCA), are well-known linear matrix decomposition techniques that are widely used in applications such as dimension reduction and clustering. However,…

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

We consider the problem of synthetic aperture radar (SAR) imaging and motion estimation of complex scenes. By complex we mean scenes with multiple targets, stationary and in motion. We use the usual setup with one moving antenna emitting…

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…

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The widely used alternating least squares (ALS) method, which solves a sequence of over-determined least squares subproblems, is costly for large and sparse…

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…

Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

We propose a new supervised dimensionality reduction technique called Supervised Linear Centroid-Encoder (SLCE), a linear counterpart of the nonlinear Centroid-Encoder (CE) \citep{ghosh2022supervised}. SLCE works by mapping the samples of a…

Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA…

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…

We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…

We present a cost-reduced approach for the distinguishable cluster approximation to coupled cluster with singles, doubles and iterative triples (DC-CCSDT) based on a tensor decomposition of the triples amplitudes. The triples amplitudes and…

Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…

Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a…