Group-Invariant Cross-Modal Subspace Learning

Cross-modal learning tries to find various types of heterogeneous data (e.g., image) from a given query (e.g., text). Most cross-modal algorithms heavily rely on semantic labels and benefit from a semantic-preserving aggregation of pairs of heterogeneous data. However, the semantic labels are not readily obtained in many real-world applications. This paper studies the aggregation of these pairs unsupervisedly. Apart from lower pairwise correspondences that force the data from one pair to be close to each other, we propose a novel concept, referred as groupwise correspondences, supposing that each paired heterogeneous data are from an identical latent group. We incorporate this groupwise correspondences into canonical correlation analysis (CCA) model, and seek a latent common subspace where data are naturally clustered into several latent groups. To simplify this nonconvex and nonsmooth problem, we introduce a nonnegative orthogonal variable to represent the soft group membership, then two coupled computationally efficient subproblems (a generalized ratio-trace problem and a non-negative problem) are alternatively minimized to guarantee the proposed algorithm converges locally. Experimental results on two benchmark datasets demonstrate that the proposed unsupervised algorithm even achieves comparable performance to some state-of-the-art supervised cross-modal algorithms.