  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.
