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Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with tensor data. Precisely, the goal of MDA is to find mode-specific projections that optimally separate tensor data from…

Numerical Analysis · Mathematics 2022-03-03 F. Dufrenois , A. El Ichi , K. Jbilou

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Machine Learning · Computer Science 2020-11-26 Talal Ahmed , Haroon Raja , Waheed U. Bajwa

Modern empirical analysis often relies on high-dimensional panel datasets with non-negligible cross-sectional and time-series correlations. Factor models are natural for capturing such dependencies. A tensor factor model describes the…

Econometrics · Economics 2025-03-10 Andrii Babii , Eric Ghysels , Junsu Pan

This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case…

Optimization and Control · Mathematics 2013-11-19 Bo Jiang , Shiqian Ma , Shuzhong Zhang

This paper proposes a probabilistic neural network developed on the basis of time-series discriminant component analysis (TSDCA) that can be used to classify high-dimensional time-series patterns. TSDCA involves the compression of…

Machine Learning · Computer Science 2019-11-15 Hideaki Hayashi , Taro Shibanoki , Keisuke Shima , Yuichi Kurita , Toshio Tsuji

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

Machine Learning · Computer Science 2025-07-04 Junjing Zheng , Xinyu Zhang , Weidong Jiang , Xiangfeng Qiu , Mingjian Ren

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Machine Learning · Computer Science 2020-07-09 Koji Maruhashi , Heewon Park , Rui Yamaguchi , Satoru Miyano

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…

Machine Learning · Statistics 2012-02-14 Genevera I. Allen

Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…

Signal Processing · Electrical Eng. & Systems 2019-11-15 Giuseppe G. Calvi , Bruno Scalzo Dees , Danilo P. Mandic

Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…

Machine Learning · Statistics 2025-12-18 Bo Shen , Yutong Zhang , Zhenyu , Kong

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

Machine Learning · Statistics 2023-02-23 Harry Dong , Tian Tong , Cong Ma , Yuejie Chi

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…

Statistics Theory · Mathematics 2011-04-29 Hung Hung , Pei-Shien Wu , I-Ping Tu , Su-Yun Huang

In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any estimates achieving some attainable error rate, we develop the…

Statistics Theory · Mathematics 2021-11-01 Dong Xia , Anru R. Zhang , Yuchen Zhou

Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…

Computation · Statistics 2022-03-04 Summer Atkins , Gudmundur Einarsson , Brendan Ames , Line Clemmensen

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…

Machine Learning · Statistics 2022-09-05 Michael Weylandt , George Michailidis

We propose a compressive classification framework for settings where the data dimensionality is significantly higher than the sample size. The proposed method, referred to as compressive regularized discriminant analysis (CRDA) is based on…

Machine Learning · Statistics 2020-11-13 Muhammad Naveed Tabassum , Esa Ollila

Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…

Machine Learning · Computer Science 2025-07-09 Wenjin Qin , Hailin Wang , Jingyao Hou , Jianjun Wang

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

Statistics Theory · Mathematics 2023-02-16 Christina Auer , Thomas Paireder , Oliver Ploder , Oliver Lang , Mario Huemer

In probabilistic principal component analysis (PPCA), an observed vector is modeled as a linear transformation of a low-dimensional Gaussian factor plus isotropic noise. We generalize PPCA to tensors by constraining the loading operator to…

Statistics Theory · Mathematics 2025-10-23 Yaoming Zhen , Piotr Zwiernik

Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches…

Numerical Analysis · Mathematics 2026-01-15 Chao Wang , Huiwen Zheng , Raymond Chan , Youwei Wen