Simplex-Structured Matrix Factorization: Sparsity-Based Identifiability and Provably Correct Algorithms

DOI10.1137/20M1354982OpenAlexW3157795203WikidataQ114615452 ScholiaQ114615452MaRDI QIDQ4999395

Nicolas Gillis, Maryam Abdolali

Publication date: 6 July 2021

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.11446

zbMATH Keywords

uniquenessidentifiabilitysparsitynonnegative matrix factorizationminimum volumesimplex-structured matrix factorization

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Factorization of matrices (15A23) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (4)

Partial Identifiability for Nonnegative Matrix Factorization ⋮ A survey on deep matrix factorizations ⋮ Smoothed separable nonnegative matrix factorization ⋮ Multiplicative Updates for NMF with $\beta$-Divergences under Disjoint Equality Constraints

Uses Software

• CPLEX
• LowRankModels
• Pyglrm

Cites Work

• Primal-dual methods for vertex and facet enumeration
• On handling indicator constraints in mixed integer programming
• Computing a Nonnegative Matrix Factorization---Provably
• Generalized Low Rank Models
• Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation
• Robust Near-Separable Nonnegative Matrix Factorization Using Linear Optimization
• Underdetermined Sparse Blind Source Separation of Nonnegative and Partially Overlapped Data
• Exact and Heuristic Algorithms for Semi-Nonnegative Matrix Factorization
• Lectures on Polytopes
• Non-Negative Matrix Factorization Revisited: Uniqueness and Algorithm for Symmetric Decomposition
• Blind Separation of Quasi-Stationary Sources: Exploiting Convex Geometry in Covariance Domain
• Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering
• A Fast Hyperplane-Based Minimum-Volume Enclosing Simplex Algorithm for Blind Hyperspectral Unmixing
• Maximum Volume Inscribed Ellipsoid: A New Simplex-Structured Matrix Factorization Framework via Facet Enumeration and Convex Optimization
• Identifiability of Complete Dictionary Learning
• Blind Audio Source Separation With Minimum-Volume Beta-Divergence NMF
• Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorization
• Computing a nonnegative matrix factorization -- provably

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