English
Related papers

Related papers: Tensor Completion with BMD Factor Nuclear Norm Min…

200 papers

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…

Numerical Analysis · Computer Science 2015-07-07 Yangyang Xu , Ruru Hao , Wotao Yin , Zhixun Su

In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does…

Numerical Analysis · Computer Science 2017-09-26 Anh-Huy Phan , Petr Tichavský , Andrzej Cichocki

This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…

Optimization and Control · Mathematics 2022-03-04 Dinesh Krishnamoorthy , Vyacheslav Kungurtsev

Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…

Data Structures and Algorithms · Computer Science 2015-04-23 Rong Ge , Tengyu Ma

In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…

Optimization and Control · Mathematics 2024-09-02 Andrea Raith , Richard Lusby , Ali Akbar Sohrabi Yousefkhan

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

Numerical Analysis · Mathematics 2021-07-07 Zehan Chao , Longxiu Huang , Deanna Needell

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

Numerical Analysis · Mathematics 2019-08-14 Stefan Klus , Patrick Gelß , Sebastian Peitz , Christof Schütte

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

Machine Learning · Statistics 2020-09-22 Miaoyan Wang , Lexin Li

Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be…

Machine Learning · Computer Science 2020-03-17 Huyan Huang , Yipeng Liu , Ce Zhu

This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…

Machine Learning · Computer Science 2023-06-06 Chengyu Zhou , Xiaolei Fang

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

Numerical Analysis · Mathematics 2019-05-24 Omri Azencot , Wotao Yin , Andrea Bertozzi

In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric…

Algebraic Geometry · Mathematics 2022-06-22 Rima Khouja , Pierre-Alexandre Mattei , Bernard Mourrain

In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…

Numerical Analysis · Computer Science 2018-03-23 Longhao Yuan , Qibin Zhao , Jianting Cao

In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…

Optimization and Control · Mathematics 2020-06-05 Vando A. Adona , Max L. N. Gonçalves

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…

Methodology · Statistics 2018-11-28 Anru Zhang

Nonnegative Tucker decomposition (NTD), a tensor decomposition model, has received increased interest in the recent years because of its ability to blindly extract meaningful patterns, in particular in Music Information Retrieval.…

This paper considers the completion problem for a tensor (also referred to as a multidimensional array) from limited sampling. Our greedy method is based on extending the low-rank approximation pursuit (LRAP) method for matrix completions…

Numerical Analysis · Mathematics 2020-04-21 An-Bao Xu

Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…

Machine Learning · Computer Science 2020-11-10 Huyan Huang , Yipeng Liu , Ce Zhu

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

Computer Vision and Pattern Recognition · Computer Science 2021-09-22 Chang Nie , Huan Wang , Zhihui Lai

Modern 3D image recovery problems require powerful optimization frameworks to handle high dimensionality while providing reliable numerical solutions in a reasonable time. In this perspective, asynchronous parallel optimization algorithms…

Optimization and Control · Mathematics 2020-06-26 Mathieu Chalvidal , Emilie Chouzenoux