2023/05/31 by Mohamed El Amine Seddik, Mastane Achab, Seddik, Mohamed El Amine +5
Mathematics · Medicine · Social Sciences · #Advanced Neuroimaging Techniques and Applications #FOS: Computer and information sciences #Human Mobility and Location-Based Analysis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2305.19992
openalex publication_date 2023/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a nested matrix-tensor model which extends the spiked rank-one tensor model of order three. This model is particularly motivated by a multi-view clustering problem in which multiple noisy observations of each data point are acquired, with potentially non-uniform variances along the views. In this case, data can be naturally represented by an order-three tensor where the views are stacked. Given such a tensor, we consider the estimation of the hidden clusters via performing a best rank-one tensor approximation. In order to study the theoretical performance of this approach, we characterize the behavior of this best rank-one approximation in terms of the alignments of the obtained component vectors with the hidden model parameter vectors, in the large-dimensional regime. In particular, we show that our theoretical results allow us to anticipate the exact accuracy of the proposed clustering approach. Furthermore, numerical experiments indicate that leveraging our tensor-based approach yields better accuracy compared to a naive unfolding-based algorithm which ignores the underlying low-rank tensor structure. Our analysis unveils unexpected and non-trivial phase transition phenomena depending on the model parameters, ``interpolating'' between the typical behavior observed for the spiked matrix and tensor models.