Year: 2022
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: KU Leuven
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G160199020, Structured Low-Rank matrix / tensor approximation: numerical optimization-based algorithms and applications, A unifying algorithmic framework for structured optimization, Learning to optimize nonconvex problems: provably and efficiently, G495187929, G5535625851, Deep Restricted Kernel Machines: Methods and Foundations, G6057626455, G6182351167, G6221759109, Risk-averse Control and Dynamic Optimization: Bridging the Gap Between Robust and Stochastic Control, G675632898, G7564167306, G8017291778, G8829997307
OpenAlex ID: W4288055561