Distributed and Robust Support Vector Machine

Abstract

In this paper, we consider the distributed version of Support Vector Machine (SVM) under the coordinator model, where all input data (i.e., points in [Formula: see text] space) of SVM are arbitrarily distributed among [Formula: see text] nodes in some network with a coordinator which can communicate with all nodes. We investigate two variants of this problem, with and without outliers. For distributed SVM without outliers, we prove a lower bound on the communication complexity and give a distributed [Formula: see text]-approximation algorithm to reach this lower bound, where [Formula: see text] is a user specified small constant. For distributed SVM with outliers, we present a [Formula: see text]-approximation algorithm to explicitly remove the influence of outliers. Our algorithm is based on a deterministic distributed top [Formula: see text] selection algorithm with communication complexity of [Formula: see text] in the coordinator model.