Multiview Spectral Clustering of High-Dimensional Observational Data

Abstract

The joint analysis of large-scale datasets is crucial when studying complex processes involving diverse sensing sources and multiple variables. This paper proposes a multiview nonlinear manifold learning framework to fuse or combine data from different types of measurements. Spectral clustering techniques are employed to obtain a low-dimensional system representation, where the physical data are projected onto a low-dimensional Euclidean space that preserves the intrinsic geometry of the data. The theoretical properties of various multiview diffusion maps are examined, and algorithms for the efficient computation of multiview kernel representations are outlined. Measures of similarity are also derived, and the results are compared with other state-of-the-art methods for model reduction. Finally, multiple datasets obtained from transient stability simulations of a large-scale power system model are utilized to evaluate the effectiveness of the developed algorithms, thereby illustrating their superiority over other state-of-the-art multiview clustering approaches.