Clustering with feature selection using alternating minimization. Application to computational biology

This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combina-torial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Frobenius norm criterion. We provide a new efficient algorithm named K-sparse which alternates k-means with projection-gradient minimization. The projection-gradient step is a method of splitting type, with exact projection on the ℓ 1 ball to promote sparsity. The convergence of the gradient-projection step is addressed, and a preliminary analysis of the alternating minimization is made. The Frobenius norm criterion converges as the number of iterates in Algorithm K-sparse goes to infinity. Experiments on Single Cell RNA sequencing datasets show that our method significantly improves the results of PCA k-means, spectral clustering, SIMLR, and Sparcl methods. The complexity of K-sparse is linear in the number of samples (cells), so that the method scales up to large datasets. Finally, we extend K-sparse to supervised classification.