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 such unsupervised entropy-based losses for discriminative models. Recent self-labeling methods based on such losses represent the state of the art in deep clustering. First, we discuss a number of general properties of such entropy clustering methods, including their relation to K-means and unsupervised SVM-based techniques. Disproving some earlier published claims, we point out fundamental differences with K-means. On the other hand, we show similarity with SVM-based clustering allowing us to link explicit margin maximization to entropy clustering. Finally, we observe that the common form of cross-entropy is not robust to pseudo-label errors. Our new loss addresses the problem and leads to a new EM algorithm improving the state of the art on many standard benchmarks.