I got from my collaborator Jay Gu the following recent paper: A Single-Pass Algorithm for Efficiently Recovering Sparse Cluster Centers of High-dimensional Data from ICML 2014. Basically it is K-means with L1 constraint on the cluster center. The results are sparse cluster centers, which may sense for example when clustering text documents together.
A second relevant paper I got from my collaborator Yao Wu is
Web-Scale K-Means Clustering by Scully from Google Pittsburgh. The paper uses mini batch to speed up computation and achieve sparsity using project gradient ascent.