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

arXiv: https://arxiv.org/abs/2402.10677 · HTML: https://mlsanity.com/paper/2402.10677/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 16 Feb 2024.

## Builds on (most cited first, 10 of 10)

- [A statistical model for tensor PCA](https://mlsanity.com/paper/1411.1076/) (2014)
- [Optimality of Spectral Clustering in the Gaussian Mixture Model](https://mlsanity.com/paper/1911.00538/) (2019)
- [Essential Tensor Learning for Multi-view Spectral Clustering](https://mlsanity.com/paper/1807.03602/) (2018)
- [SimpleMKKM: Simple Multiple Kernel K-means](https://mlsanity.com/paper/2005.04975/) (2020)
- [A Random Matrix Perspective on Random Tensors](https://mlsanity.com/paper/2108.00774/) (2021)
- [Long Random Matrices and Tensor Unfolding](https://mlsanity.com/paper/2110.10210/) (2021)
- [When Random Tensors meet Random Matrices](https://mlsanity.com/paper/2112.12348/) (2021)
- [A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation](https://mlsanity.com/paper/2402.03169/) (2024)
- [Projected Tensor Power Method for Hypergraph Community Recovery](https://mlsanity.com/paper/2307.00210/) (2023)
- [A Nested Matrix-Tensor Model for Noisy Multi-view Clustering](https://mlsanity.com/paper/2305.19992/) (2023)

## Abstract (arXiv)

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 rank-one 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 matrix-based methods in handling structured tensor data.