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Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey

Farid Saberi-Movahed, Kamal Berahman, Razieh Sheikhpour, Yuefeng Li, Shirui Pan

TL;DR

This survey addresses the need for a comprehensive overview of Nonnegative Matrix Factorization (NMF) in dimensionality reduction, detailing its roles in both feature extraction and feature selection. It provides a structured taxonomy that groups feature-extraction NMF variants into four categories (Varieties, Regularized, Generalized, Robust) and feature-selection NMF perspectives into six (Standard, convex, graph-based, dual-graph, sparsity, orthogonality), along with a thorough review of methods such as SNMF, ONMF, NMTF, PNMF, and their regularized, semi-supervised, tensor-based, and deep extensions. The paper also outlines future directions including semi-supervised NMF, hypergraph-based NMF, sparse $L_{2,0}$-norm NMF, nonnegative tensor factorization in feature selection, deep NMF for selection, adaptive learning, and non-Frobenius loss functions. Its contributions lie in consolidating diverse NMF approaches for DR, clarifying their applicability, and highlighting promising research avenues to guide future work. The practical impact is to aid researchers in selecting and developing NMF-based dimensionality-reduction techniques tuned to data geometry, supervision level, and computational considerations.

Abstract

Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular and powerful method for dimensionality reduction. Despite its extensive use, there remains a need for a comprehensive analysis of NMF in the context of dimensionality reduction. To address this gap, this paper presents a comprehensive survey of NMF, focusing on its applications in both feature extraction and feature selection. We introduce a classification of dimensionality reduction, enhancing understanding of the underlying concepts. Subsequently, we delve into a thorough summary of diverse NMF approaches used for feature extraction and selection. Furthermore, we discuss the latest research trends and potential future directions of NMF in dimensionality reduction, aiming to highlight areas that need further exploration and development.

Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey

TL;DR

This survey addresses the need for a comprehensive overview of Nonnegative Matrix Factorization (NMF) in dimensionality reduction, detailing its roles in both feature extraction and feature selection. It provides a structured taxonomy that groups feature-extraction NMF variants into four categories (Varieties, Regularized, Generalized, Robust) and feature-selection NMF perspectives into six (Standard, convex, graph-based, dual-graph, sparsity, orthogonality), along with a thorough review of methods such as SNMF, ONMF, NMTF, PNMF, and their regularized, semi-supervised, tensor-based, and deep extensions. The paper also outlines future directions including semi-supervised NMF, hypergraph-based NMF, sparse -norm NMF, nonnegative tensor factorization in feature selection, deep NMF for selection, adaptive learning, and non-Frobenius loss functions. Its contributions lie in consolidating diverse NMF approaches for DR, clarifying their applicability, and highlighting promising research avenues to guide future work. The practical impact is to aid researchers in selecting and developing NMF-based dimensionality-reduction techniques tuned to data geometry, supervision level, and computational considerations.

Abstract

Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular and powerful method for dimensionality reduction. Despite its extensive use, there remains a need for a comprehensive analysis of NMF in the context of dimensionality reduction. To address this gap, this paper presents a comprehensive survey of NMF, focusing on its applications in both feature extraction and feature selection. We introduce a classification of dimensionality reduction, enhancing understanding of the underlying concepts. Subsequently, we delve into a thorough summary of diverse NMF approaches used for feature extraction and selection. Furthermore, we discuss the latest research trends and potential future directions of NMF in dimensionality reduction, aiming to highlight areas that need further exploration and development.
Paper Structure (45 sections, 46 equations, 2 figures, 4 tables)

This paper contains 45 sections, 46 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Dimensionality Reduction
  3. Feature Extraction
  4. Linear Feature Extraction Methods
  5. Matrix Factorization-based Feature Extraction Methods
  6. Discriminative-based Feature Extraction Methods
  7. Nonlinear Feature Extraction Methods
  8. Manifold-based Feature Extraction Methods
  9. Deep Learning-based Methods for Feature Extraction
  10. Feature Selection
  11. Filter Feature Selection Methods
  12. Univariate Filter Feature Selection Methods
  13. Multivariate Filter Feature Selection Methods
  14. Wrapper Feature Selection Methods
  15. Deterministic Wrapper Feature Selection Methods
  16. ...and 30 more sections

Figures (2)

  • Figure 1: Categorizing dimensionality reduction techniques: a clear division into feature extraction and feature selection approaches
  • Figure 2: Classifying current NMF approaches for feature extraction into four groups: Variants of NMF, Regularized NMF, Generalized NMF, and Robust NMF.