Multi-graph clustering via multi-modal topological manifold learning

Multi-view spectral clustering has drawn widespread interest in light of its sufficiency of exploring hidden structure details among samples. However, most existing approaches merely concentrate on constructing similarity graph by computing the geometric distance among any two samples using the Euclidean formula, which limits their ability to accurately measure the relationship with far apart but high similarity. Moreover, they implement integration step in the similarity graph construction stage in which the early fusion results in information loss. To solve these problems, we develop a novel multi-view clustering method, namely, Multi-graph Clustering via Multi-modal Topological Manifold Learning (MC_MTML). Specifically, the initial affinity graphs are firstly generated by employing K-Nearest Neighbor (KNN) algorithm. Then, learning similarity matrices by introducing the topological manifold learning mechanism. Finally, the common consensus representation of spectral embedding is derived from the similarity matrixes which can not merely incorporate the consensus structure knowledge from all view features but also reduce the information loss. An efficient alternate iterating algorithm is developed to resolve the resulting optimization issue. The experiments are conducted on a toy data set and five multi-view data sets. Extensive experimental results demonstrate the effectiveness of proposed MC_MTML algorithm comparing with eight state-of-the-art multi-view clustering methods.