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This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…

Machine Learning · Computer Science 2017-08-03 Jonathan Q. Jiang , Michael K. Ng

Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…

Computation · Statistics 2025-10-01 Michele Gallo

There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…

Numerical Analysis · Mathematics 2023-04-18 Melven Röhrig-Zöllner , Jonas Thies , Achim Basermann

Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing…

Computer Vision and Pattern Recognition · Computer Science 2015-04-30 Yanfeng Sun , Junbin Gao , Xia Hong , Bamdev Mishra , Baocai Yin

Multi-view learning can cover all features of data samples more comprehensively, so multi-view learning has attracted widespread attention. Traditional subspace clustering methods, such as sparse subspace clustering (SSC) and low-ranking…

Machine Learning · Computer Science 2022-01-04 Jian-wei Liu , Hao-jie Xie , Run-kun Lu , Xiong-lin Luo

By representing documents as mixtures of topics, topic modeling has allowed the successful analysis of datasets across a wide spectrum of applications ranging from ecology to genetics. An important body of recent work has demonstrated the…

Statistics Theory · Mathematics 2025-01-03 Yating Liu , Claire Donnat

Multi-view clustering (MVC) is a popular technique for improving clustering performance using various data sources. However, existing methods primarily focus on acquiring consistent information while often neglecting the issue of redundancy…

Machine Learning · Computer Science 2023-09-26 Chenhang Cui , Yazhou Ren , Jingyu Pu , Jiawei Li , Xiaorong Pu , Tianyi Wu , Yutao Shi , Lifang He

Low-rank Multi-view Subspace Learning (LMvSL) has shown great potential in cross-view classification in recent years. Despite their empirical success, existing LMvSL based methods are incapable of well handling view discrepancy and…

Computer Vision and Pattern Recognition · Computer Science 2020-03-24 Jiamiao Xu , Fangzhao Wang , Qinmu Peng , Xinge You , Shuo Wang , Xiao-Yuan Jing , C. L. Philip Chen

This paper aims at developing a clustering approach with spectral images directly from the compressive measurements of coded aperture snapshot spectral imager (CASSI). Assuming that compressed measurements often lie approximately in low…

Image and Video Processing · Electrical Eng. & Systems 2020-09-30 Jianchen Zhu

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…

Machine Learning · Computer Science 2023-05-22 Wenjin Qin , Hailin Wang , Feng Zhang , Weijun Ma , Jianjun Wang , Tingwen Huang

During the last decades, we have witnessed a surge of interests of learning a low-dimensional space with discriminative information from one single view. Even though most of them can achieve satisfactory performance in some certain…

Machine Learning · Computer Science 2019-05-21 Lin Feng , Xiangzhu Meng , Huibing Wang

Concept Factorization (CF), as a novel paradigm of representation learning, has demonstrated superior performance in multi-view clustering tasks. It overcomes limitations such as the non-negativity constraint imposed by traditional matrix…

Machine Learning · Computer Science 2023-07-04 Qi Jiang , Guoxu Zhou , Qibin Zhao

Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the…

Machine Learning · Computer Science 2022-03-09 Eysan Mehrbani , Mohammad Hossein Kahaei , Seyed Aliasghar Beheshti

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low…

Optimization and Control · Mathematics 2013-10-08 Lei Yang , Zheng-Hai Huang , Yufan Li

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…

Numerical Analysis · Mathematics 2014-08-12 Ming Gu

Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of…

Computer Vision and Pattern Recognition · Computer Science 2023-08-15 Mahdi Molavi , Mansoor Rezghi , Tayyebeh Saeedi

Exploring the complementary information of multi-view data to improve clustering effects is a crucial issue in multi-view clustering. In this paper, we propose a novel model based on information theory termed Informative Multi-View…

Machine Learning · Computer Science 2023-05-31 Fu Lele , Zhang Lei , Wang Tong , Chen Chuan , Zhang Chuanfu , Zheng Zibin

A plethora of multi-view subspace clustering (MVSC) methods have been proposed over the past few years. Researchers manage to boost clustering accuracy from different points of view. However, many state-of-the-art MVSC algorithms, typically…

Machine Learning · Computer Science 2019-11-22 Zhao Kang , Wangtao Zhou , Zhitong Zhao , Junming Shao , Meng Han , Zenglin Xu

We study the problem of learning to rank from multiple information sources. Though multi-view learning and learning to rank have been studied extensively leading to a wide range of applications, multi-view learning to rank as a synergy of…

Machine Learning · Computer Science 2019-09-24 Guanqun Cao , Alexandros Iosifidis , Moncef Gabbouj , Vijay Raghavan , Raju Gottumukkala

This study investigates the problem of multi-view subspace clustering, the goal of which is to explore the underlying grouping structure of data collected from different fields or measurements. Since data do not always comply with the…

Machine Learning · Computer Science 2021-03-25 Qinghai Zheng , Jihua Zhu , Yuanyuan Ma , Zhongyu Li , Zhiqiang Tian
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