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

TL;DR

This paper introduces a tensor-based multi-view spectral clustering method that learns a shared latent space for better interpretability, efficiency, and out-of-sample prediction, suitable for large-scale data.

Contribution

It proposes a novel tensor-based approach using a shared latent space via the Restricted Kernel Machine framework, enabling efficient, interpretable multi-view clustering with out-of-sample extension.

Findings

Effective in accuracy and efficiency

Promotes well-separated, interpretable clusters

Requires only a single eigendecomposition

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.