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This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…

Numerical Analysis · Mathematics 2023-03-22 Maolin Che , Yimin Wei , Hong Yan

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

Machine Learning · Computer Science 2014-11-17 Anima Anandkumar , Rong Ge , Daniel Hsu , Sham M. Kakade , Matus Telgarsky

We introduce an online tensor decomposition based approach for two latent variable modeling problems namely, (1) community detection, in which we learn the latent communities that the social actors in social networks belong to, and (2)…

Machine Learning · Computer Science 2015-10-06 Furong Huang , U. N. Niranjan , Mohammad Umar Hakeem , Animashree Anandkumar

In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…

Statistics Theory · Mathematics 2020-01-09 Anru Zhang , Dong Xia

We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\mathcal{X}$, the algorithm provides a set of…

Numerical Analysis · Mathematics 2016-07-04 Arvind K. Saibaba

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Numerical Analysis · Mathematics 2014-11-04 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

Memory and network bandwidth are decisive bottlenecks when handling high-resolution multidimensional data sets in visualization applications, and they increasingly demand suitable data compression strategies. We introduce a novel lossy…

Graphics · Computer Science 2019-03-12 Rafael Ballester-Ripoll , Peter Lindstrom , Renato Pajarola

Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data…

Machine Learning · Computer Science 2022-05-20 Cagri Ozdemir , Randy C. Hoover , Kyle Caudle , Karen Braman

This paper presents an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component…

Numerical Analysis · Mathematics 2021-11-09 Olivier Coulaud , Alain Franc , Martina Iannacito

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-07-19 Venkatesan T Chakaravarthy , Jee W Choi , Douglas J Joseph , Xing Liu , Prakash Murali , Yogish Sabharwal , Dheeraj Sreedhar

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

Machine Learning · Computer Science 2025-11-03 Hiroki Hasegawa , Yukihiko Okada

High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…

Machine Learning · Statistics 2023-02-17 Kirandeep Kour , Sergey Dolgov , Peter Benner , Martin Stoll , Max Pfeffer

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

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Information Theory · Computer Science 2016-02-18 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling…

Computation and Language · Computer Science 2019-02-01 Lipeng Zhang , Peng Zhang , Xindian Ma , Shuqin Gu , Zhan Su , Dawei Song

Tensor decomposition methods are popular tools for analysis of multi-way datasets from social media, healthcare, spatio-temporal domains, and others. Widely adopted models such as Tucker and canonical polyadic decomposition (CPD) follow a…

Machine Learning · Computer Science 2023-09-19 Maxwell McNeil , Petko Bogdanov

Higher-order singular value decomposition (HOSVD) is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete…

Numerical Analysis · Mathematics 2016-08-11 Yangyang Xu

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…

Machine Learning · Computer Science 2022-06-23 Tian Tong , Cong Ma , Ashley Prater-Bennette , Erin Tripp , Yuejie Chi

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

Methodology · Statistics 2024-03-20 Yuefeng Si , Yingying Zhang , Yuxi Cai , Chunling Liu , Guodong Li

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

Emerging Technologies · Computer Science 2014-08-26 Andrzej Cichocki