Performance Gaps in Multi-view Clustering under the Nested Matrix-Tensor Model

Hugo Lebeau (1, 2) , Mohamed El Amine Seddik (3) , José Henrique de M Goulart (4)

1 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
2 GIPSA-GAIA - GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes
3 TII - Technology Innovation Institute
4 IRIT-SC - Signal et Communications

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rankone approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrixbased methods in handling structured tensor data.

Keywords: random tensors; multi-view clustering; random matrix theory; tensor unfolding

Domains: Statistics [stat]; Computer Science [cs]; Mathematics [math]

Hugo Lebeau, Mohamed El Amine Seddik, José Henrique de M Goulart. Performance Gaps in Multi-view Clustering under the Nested Matrix-Tensor Model. ICLR 2024 - 12th International Conference on Learning Representations (ICLR 2024), May 2024, Wien, Austria. pp.1-29. ⟨hal-04464877⟩