Multi-feature Spectral Clustering with Minimax Optimization

In this paper, we propose a novel formulation for multi-feature clustering using minimax optimization. To find a consensus clustering result that is agreeable to all feature modalities, our objective is to find a universal feature embedding, which not only fits each individual feature modality well, but also unifies different feature modalities by minimizing their pairwise disagreements. The loss function consists of both (1) unary embedding cost for each modality, and (2) pairwise disagreement cost for each pair of modalities, with weighting parameters automatically selected to maximize the loss. By performing minimax optimization, we can minimize the loss for the worst case with maximum disagreements, thus can better reconcile different feature modalities. To solve the minimax optimization, an iterative solution is proposed to update the universal embedding, individual embedding, and fusion weights, separately. Our minimax optimization has only one global parameter. The superior results on various multi-feature clustering tasks validate the effectiveness of our approach when compared with the state-of-the-art methods.