Exploiting Correlation Consensus: Towards Subspace Clustering for Multi-modal Data

Often, a data object described by many features can be decomposed as multi-modalities, which always provide complementary information to each other. In this paper, we study subspace clustering for multi-modal data by effectively exploiting data correlation consensus across modalities, while keeping individual modalities well encapsulated. Our technique can yield a more ideal data similarity matrix, which encodes strong data correlations for the cross-modal data objects in the same subspace. To these ends, we propose a novel angular based regularizer coupled with our objective function, which is aided by trace lasso and minimized to yield sparse representation vectors encoding data correlations in multiple modalities. As a result, the sparse code vectors of the same cross-modal data have small angular difference so as to achieve the data correlation consensus simultaneously. This can generate a compatible data similarity matrix for multi-modal data. The final subspace clustering result is obtained by applying spectral clustering on such data similarity matrix.