Discriminative Entropy Clustering and its Relation to K-means and SVM

Maximization of mutual information between the model's input and output is formally related to "decisiveness" and "fairness" of the softmax predictions, motivating these unsupervised entropy-based criteria for clustering. First, in the context of linear softmax models, we discuss some general properties of entropy-based clustering. Disproving some earlier claims, we point out fundamental differences with K-means. On the other hand, we prove the margin maximizing property for decisiveness establishing a relation to SVM-based clustering. Second, we propose a new self-labeling formulation of entropy clustering for general softmax models. The pseudo-labels are introduced as auxiliary variables "splitting" the fairness and decisiveness. The derived self-labeling loss includes the reverse cross-entropy robust to pseudo-label errors and allows an efficient EM solver for pseudo-labels. Our algorithm improves the state of the art on several standard benchmarks for deep clustering.