MultiView Diffusion Maps

In this paper, a reduced dimensionality representation is learned from multiple views of the processed data. These multiple views can be obtained, for example, when the same underlying process is observed using several different modalities, or measured with different instrumentation. The goal is to effectively utilize the availability of such multiple views for various purposes such as non-linear embedding, manifold learning, spectral clustering, anomaly detection and non-linear system identification. The proposed method, which is called multi-view, exploits the intrinsic relation within each view as well as the mutual relations between views. This is achieved by defining a cross-view model in which an implied random walk process is restrained to hop between objects in the different views. This multi-view method is robust to scaling and it is insensitive to small structural changes in the data. Within this framework, new diffusion distances are defined to analyze the spectra of the implied kernels. The applicability of the multi-view approach is demonstrated for clustering, classification and manifold learning using both artificial and real data.