English
Related papers

Related papers: Dictionary-based Tensor Canonical Polyadic Decompo…

200 papers

Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades…

Computer Vision and Pattern Recognition · Computer Science 2015-12-22 Xiaoxia Sun , Nasser M. Nasrabadi , Trac D. Tran

The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the…

Numerical Analysis · Computer Science 2020-03-16 N. Benjamin Erichson , Krithika Manohar , Steven L. Brunton , J. Nathan Kutz

The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…

Logic · Mathematics 2013-04-30 Edward Grefenstette

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

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse…

Numerical Analysis · Mathematics 2020-12-04 Jeremy M. Myers , Daniel M. Dunlavy , Keita Teranishi , D. S. Hollman

Recently, coupled tensor decomposition has been widely used in data fusion of a hyperspectral image (HSI) and a multispectral image (MSI) for hyperspectral super-resolution (HSR). However, exsiting works often ignore the inherent…

Signal Processing · Electrical Eng. & Systems 2025-01-28 Xi-Yuan Liu , Xiao-Feng Gong , Lei Wang , Wei Feng , Qiu-Hua Lin

In this letter, we propose a novel computationally efficient coupled dictionary learning method that enforces pairwise correlation between the atoms of dictionaries learned to represent the underlying feature spaces of two different…

Machine Learning · Computer Science 2021-09-29 F. G. Veshki , S. A. Vorobyov

Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and…

Methodology · Statistics 2025-05-30 Runshi Tang , Julien Chhor , Olga Klopp , Anru R. Zhang

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…

Machine Learning · Computer Science 2023-09-21 Taehyung Kwon , Jihoon Ko , Jinhong Jung , Kijung Shin

Distributional models are derived from co-occurrences in a corpus, where only a small proportion of all possible plausible co-occurrences will be observed. This results in a very sparse vector space, requiring a mechanism for inferring…

Computation and Language · Computer Science 2016-08-25 Thomas Kober , Julie Weeds , Jeremy Reffin , David Weir

The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…

Optimization and Control · Mathematics 2025-11-11 Zequn Zheng , Hongchao Zhang , Guangming Zhou

We present an algorithm, Decision-Directed Data Decomposition (D4), which decomposes a dataset into two components. The first contains most of the useful information for a specified supervised learning task. The second orthogonal component…

Machine Learning · Computer Science 2020-03-12 Brent D. Davis , Ethan Jackson , Daniel J. Lizotte

The low-rank canonical polyadic tensor decomposition is useful in data analysis and can be computed by solving a sequence of overdetermined least squares subproblems. Motivated by consideration of sparse tensors, we propose sketching each…

Numerical Analysis · Mathematics 2022-01-05 Brett W. Larsen , 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

Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order…

Computer Vision and Pattern Recognition · Computer Science 2017-07-04 Fujiao Ju , Yanfeng Sun , Junbin Gao , Yongli Hu , Baocai Yin

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

In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of…

Machine Learning · Computer Science 2020-12-08 Cristian Rusu

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

We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…

Signal Processing · Electrical Eng. & Systems 2020-12-01 Gilles Monnoyer de Galland , Luc Vandendorpe , Laurent Jacques

This article provides next step towards solving speed bottleneck of any system that intensively uses convolutions operations (e.g. CNN). Method described in the article is applied on deformable part models (DPM) algorithm. Method described…

Computer Vision and Pattern Recognition · Computer Science 2017-07-12 D. V. Parkhomenko , I. L. Mazurenko