Orthogonal nonnegative matrix factorization problems for clustering: A new formulation and a competitive algorithm

Orthogonal Nonnegative Matrix Factorization (ONMF) with orthogonality constraints on a matrix has been found to provide better clustering results over existing clustering problems. Because of the orthogonality constraint, this optimization problem is difficult to solve. Many of the existing constrai...

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Veröffentlicht in:Annals of operations research Jg. 339; H. 3; S. 1481 - 1497
Hauptverfasser: Dehghanpour, Ja’far, Mahdavi-Amiri, Nezam
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.08.2024
Springer
Schlagworte:
Algorithms
Business and Management
Clustering (Computers)
Combinatorics
Data mining
Mathematical optimization
Operations Research/Decision Theory
Original Research
Theory of Computation
Iran
Isoperimetry problem
Clustering
Optimization problem with orthogonality constraints
Orthogonal Nonnegative Matrix Factorization
ISSN:0254-5330, 1572-9338
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Zusammenfassung:Orthogonal Nonnegative Matrix Factorization (ONMF) with orthogonality constraints on a matrix has been found to provide better clustering results over existing clustering problems. Because of the orthogonality constraint, this optimization problem is difficult to solve. Many of the existing constraint-preserving methods deal directly with the constraints using different techniques such as matrix decomposition or computing exponential matrices. Here, we propose an alternative formulation of the ONMF problem which converts the orthogonality constraints into non-convex constraints. To handle the non-convex constraints, a penalty function is applied. The penalized problem is a smooth nonlinear programming problem with quadratic (convex) constraints that can be solved by a proper optimization method. We first make use of an optimization method with two gradient projection steps and then apply a post-processing technique to construct a partition of the clustering problem. Comparative performance analysis of our proposed approach with other available clustering methods on randomly generated test problems and hard synthetic data-sets shows the outperformance of our approach, in terms of the obtained misclassification error rate and the Rand index.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-022-04642-2