k-meansNet: When k-means Meets Differentiable Programming

In this paper, we study two challenging problems. The first one is how to implement \textit{k}-means in the neural network, which enjoys efficient training based on the stochastic algorithm. The second one is how to enhance the interpretability of network design for clustering. To solve the problems, we propose a neural network which is a novel formulation of the vanilla $k$-means objective. Our contribution is in twofold. From the view of neural networks, the proposed \textit{k}-meansNet is with explicit interpretability in neural processing. We could understand not only why the network structure is presented like itself but also why it could perform data clustering. Such an interpretable neural network remarkably differs from the existing works that usually employ visualization technique to explain the result of the neural network. From the view of \textit{k}-means, three highly desired properties are achieved, i.e. robustness to initialization, the capability of handling new coming data, and provable convergence. Extensive experimental studies show that our method achieves promising performance comparing with 12 clustering methods on some challenging datasets.