Deep Fuzzy Clustering Network With Matrix Norm Regularization

Recently, deep clustering networks, which able to learn latent embedding and clustering assignment simultaneously, attract lots of attention. Among the deep clustering networks, the suitable regularization term is not only beneficial to training of neural network, but also enhancing clustering performance. In the paper, we propose a deep fuzzy clustering network with mixed matrix norm regularization (DFCNR). Specifically, DFCNR uses the weighted intra-class variance as clustering loss,
$\ell _{1,2}$
norm and the Frobenius norm of soft assignment matrix as regularization term, where the minimization of
$\ell _{1,2}$
norm aims to achieve balanced assignment, and maximization of Frobenius norm aims to achieve discriminative assignment. Moreover, by solving the quadratic convex constraint optimization problem about soft assignment, we derive the activation function of clustering layer. Extensive experiments conducted on several datasets illustrate the superiority of the proposed approach in comparison with current methods.