Efficient Nonnegative Tensor Factorization via Saturating Coordinate Descent
With the advancements in computing technology and web-based applications, data is increasingly generated in multi-dimensional form. This data is usually sparse due to the presence of a large number of users and fewer user interactions. To deal with this, the Nonnegative Tensor Factorization (NTF) based methods have been widely used. However existing factorization algorithms are not suitable to process in all three conditions of size, density, and rank of the tensor. Consequently, their applicability becomes limited. In this paper, we propose a novel fast and efficient NTF algorithm using the element selection approach. We calculate the element importance using Lipschitz continuity and propose a saturation point based element selection method that chooses a set of elements column-wise for updating to solve the optimization problem. Empirical analysis reveals that the proposed algorithm is scalable in terms of tensor size, density, and rank in comparison to the relevant state-of-the-art algorithms.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Accelerating Block Coordinate Descent for Nonnegative Tensor Factorization
This paper is concerned with improving the empirical convergence speed of block-coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in-between block …
Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization
Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usually with much fewer columns than $A$, such that $A \approx HH^T$. SymN…
ClusteringSparse Nonnegative CANDECOMP/PARAFAC Decomposition in Block Coordinate Descent Framework: A Comparison Study
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, a…
Tensor DecompositionDID: Distributed Incremental Block Coordinate Descent for Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) has attracted much attention in the last decade as a dimension reduction method in many applications. Due to the explosion in the size of data, naturally the samples are collected a…
Dimensionality ReductionAccelerating Nonnegative Matrix Factorization Algorithms using Extrapolation
In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient me…