MPMSVC: Multiple Parametric-Margin Support Vector Clustering

In this work, we propose an unsupervised multiple parametric-margin support vector clustering (MPMSVC) for noisy clustering tasks. The main idea of MPMSVC is to find a parametric-margin center hyperplane for each cluster in a manner that gathers the within-cluster instances around the corresponding center hyperplane, and keeps the between-cluster instances far away. Specifically, our MPMSVC owns the following attractive merits: i) The primal of MPMSVC is enhanced in the least squares sense, which enjoys an effective learning procedure. ii) The utilization of the linear
$L_{1}$
-norm loss makes MPMSVC be more robust to noisy clustering tasks. iii) An efficient iterative algorithm is presented to optimize the non-smooth problem in MPMSVC, which only involves a set of linear equations. Also, the convergence of the proposed algorithm is guaranteed theoretically. iv) The nonlinear extension is further derived via kernel technique to deal with more complex clustering tasks. Finally, the feasibility and effectiveness of MPMSVC is validated by extensive experiments on both synthetic and real-world datasets.