Tensor-based multi-view spectral clustering via shared latent space

Abstract

Multi-view Spectral Clustering (MvSC) partitions data into clusters according to multiple views for higher performance. However, most existing works overlook model interpretability and involve iterative and alternating updates on parameters with expensive computations, where out-of-sample predictions are also commonly prohibitive. In this paper, we construct a novel weighted conjugate feature duality for formulating the MvSC problem cast as a weighted principal components analysis. In this new method, a common latent space is derived with shared dual variables, which achieves the couplings by learning projections from different views into the latent space. To boost higher-order correlations, the tensor-based modelling is introduced. Our method leads to a closed-form solution in the dual through a single eigendecomposition thanks to the primal–dual representation, leading to easy algorithmic setups in practice. Our novel conjugate duality and the conceived shared latent space greatly boost the efficiency in model representation and computation: element-wise operations of kernels are involved in the dual instead of the explicit tensor computation in the primal and the size of our eigendecomposition is independent of the number of views. Besides, we can effectively incorporate the visualization of the clusters in a single latent space, which is particularly useful with many data views. For predicting unseen data under generic applications, our method can be flexibly applied with out-of-sample extensions, which can also be utilized for further efficiency in large-scale cases with fixed-size kernel schemes. Numerical experiments verify our superiority in accuracy, efficiency, and diverse data explorations.