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We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

Methodology · Statistics 2013-10-17 Lin Zhang , Abhra Sarkar , Bani K. Mallick

Registration is an essential tool in image analysis. Deep learning based alternatives have recently become popular, achieving competitive performance at a faster speed. However, many contemporary techniques are limited to volumetric…

Image and Video Processing · Electrical Eng. & Systems 2021-09-29 Balder Croquet , Daan Christiaens , Seth M. Weinberg , Michael Bronstein , Dirk Vandermeulen , Peter Claes

The CANDECOMP/PARAFAC (or Canonical polyadic, CP) decomposition of tensors has numerous applications in various fields, such as chemometrics, signal processing, machine learning, etc. Tensor CP decomposition assumes the knowledge of the…

Numerical Analysis · Mathematics 2025-01-08 Zihao Wang , Minru Bai , Liang Chen , Xueying Zhao

In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity…

Computational Complexity · Computer Science 2021-04-13 Petr Tichavsky

Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…

Machine Learning · Computer Science 2016-12-21 Bo Yang , Xiao Fu , Nicholas D. Sidiropoulos

In biomedical research and other fields, it is now common to generate high content data that are both multi-source and multi-way. Multi-source data are collected from different high-throughput technologies while multi-way data are collected…

Machine Learning · Statistics 2025-02-28 Zhiyu Kang , Raghavendra B. Rao , Eric F. Lock

Disentanglement aims to recover meaningful latent ground-truth factors from the observed distribution solely, and is formalized through the theory of identifiability. The identifiability of independent latent factors is proven to be…

Machine Learning · Computer Science 2024-03-14 Vitória Barin-Pacela , Kartik Ahuja , Simon Lacoste-Julien , Pascal Vincent

Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive…

Numerical Analysis · Mathematics 2013-09-16 Eric C. Chi , Tamara G. Kolda

Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model. The considered problem is well-motivated in many applications, e.g., hyperspectral image and video…

Signal Processing · Electrical Eng. & Systems 2020-08-26 Shahana Ibrahim , Xiao Fu , Xingguo Li

The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision,…

Numerical Analysis · Mathematics 2015-03-17 Evrim Acar , Tamara G. Kolda , Daniel M. Dunlavy , Morten Morup

Tensors have broad applications in neuroimaging, data mining, digital marketing, etc. CANDECOMP/PARAFAC (CP) tensor decomposition can effectively reduce the number of parameters to gain dimensionality-reduction and thus plays a key role in…

Statistics Theory · Mathematics 2023-11-23 Qiushi Bu , Hua Liang , Xinyu Zhang , Jiahui Zou

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity…

Machine Learning · Computer Science 2015-05-20 Volodymyr Kuleshov , Arun Tejasvi Chaganty , Percy Liang

Candecomp / PARAFAC (CP) decomposition, a generalization of the matrix singular value decomposition to higher-dimensional tensors, is a popular tool for analyzing multidimensional sparse data. On tensors with billions of nonzero entries,…

Numerical Analysis · Mathematics 2024-04-30 Vivek Bharadwaj , Osman Asif Malik , Riley Murray , Aydin Buluç , James Demmel

Coupled tensor decompositions (CTDs) perform data fusion by linking factors from different datasets. Although many CTDs have been already proposed, current works do not address important challenges of data fusion, where: 1) the datasets are…

Machine Learning · Computer Science 2024-12-13 Ricardo Augusto Borsoi , Konstantin Usevich , David Brie , Tülay Adali

The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…

Numerical Analysis · Computer Science 2018-09-05 Anh-Huy Phan , Andrzej Cichocki , Ivan Oseledets , Salman Ahmadi Asl , Giuseppe Calvi , Danilo Mandic

In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…

Methodology · Statistics 2025-06-03 Yuxi Cai , Lan Li , Yize Wang , Guodong Li

This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…

Numerical Analysis · Mathematics 2024-07-26 Ramin Goudarzi Karim , Dipak Dulal , Carmeliza Navasca

Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…

Machine Learning · Computer Science 2015-06-22 Furong Huang , Animashree Anandkumar

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…

Machine Learning · Computer Science 2019-05-28 Vatsal Sharan , Kai Sheng Tai , Peter Bailis , Gregory Valiant

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…

Methodology · Statistics 2023-04-11 Chanwoo Lee , Miaoyan Wang