Sparse Nonnegative CANDECOMP/PARAFAC Decomposition in Block Coordinate Descent Framework: A Comparison Study

12/27/2018
by   Deqing Wang, et al.
14

Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, an optimization method for NCP that can impose sparsity efficiently is required. In this paper, we construct NCP with sparse regularization (sparse NCP) by l1-norm. Several popular optimization methods in block coordinate descent framework are employed to solve the sparse NCP, all of which are deeply analyzed with mathematical solutions. We compare these methods by experiments on synthetic and real tensor data, both of which contain third-order and fourth-order cases. After comparison, the methods that have fast computation and high effectiveness to impose sparsity will be concluded. In addition, we proposed an accelerated method to compute the objective function and relative error of sparse NCP, which has significantly improved the computation of tensor decomposition especially for higher-order tensor.

READ FULL TEXT

page 3

page 4

page 6

page 7

page 9

page 10

page 12

page 15

01/13/2020

Accelerating Block Coordinate Descent for Nonnegative Tensor Factorization

This paper is concerned with improving the empirical convergence speed o...
08/17/2022

Sparse Nonnegative Tucker Decomposition and Completion under Noisy Observations

Tensor decomposition is a powerful tool for extracting physically meanin...
05/29/2017

Learning the Sparse and Low Rank PARAFAC Decomposition via the Elastic Net

In this article, we derive a Bayesian model to learning the sparse and l...
12/05/2020

Approximation Algorithms for Sparse Best Rank-1 Approximation to Higher-Order Tensors

Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity...
04/17/2014

Efficient Nonnegative Tucker Decompositions: Algorithms and Uniqueness

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extrac...
12/02/2013

Efficient coordinate-descent for orthogonal matrices through Givens rotations

Optimizing over the set of orthogonal matrices is a central component in...
10/27/2021

Nonnegative Tucker Decomposition with Beta-divergence for Music Structure Analysis of audio signals

Nonnegative Tucker Decomposition (NTD), a tensor decomposition model, ha...