Tensor-based Multi-view Spectral Clustering via Shared Latent Space

• URL: http://arxiv.org/abs/2207.11559v1
• Date: Sat, 23 Jul 2022 17:30:54 GMT
• Title: Tensor-based Multi-view Spectral Clustering via Shared Latent Space
• Authors: Qinghua Tao, Francesco Tonin, Panagiotis Patrinos, Johan A.K. Suykens
• Abstract summary: Multi-view Spectral Clustering (MvSC) attracts increasing attention due to diverse data sources. New method for MvSC is proposed via a shared latent space from the Restricted Kernel Machine framework.
• Score: 14.470859959783995
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Multi-view Spectral Clustering (MvSC) attracts increasing attention due to diverse data sources. However, most existing works are prohibited in out-of-sample predictions and overlook model interpretability and exploration of clustering results. In this paper, a new method for MvSC is proposed via a shared latent space from the Restricted Kernel Machine framework. Through the lens of conjugate feature duality, we cast the weighted kernel principal component analysis problem for MvSC and develop a modified weighted conjugate feature duality to formulate dual variables. In our method, the dual variables, playing the role of hidden features, are shared by all views to construct a common latent space, coupling the views by learning projections from view-specific spaces. Such single latent space promotes well-separated clusters and provides straightforward data exploration, facilitating visualization and interpretation. Our method requires only a single eigendecomposition, whose dimension is independent of the number of views. To boost higher-order correlations, tensor-based modelling is introduced without increasing computational complexity. Our method can be flexibly applied with out-of-sample extensions, enabling greatly improved efficiency for large-scale data with fixed-size kernel schemes. Numerical experiments verify that our method is effective regarding accuracy, efficiency, and interpretability, showing a sharp eigenvalue decay and distinct latent variable distributions.

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