We present a unified approach for simultaneously clustering and discovering outliers in data. Our approach is formalized as a generalization of the k-means problem. We prove that the problem is NP-hard and then present a practical polynomial time algorithm, which is guaranteed to converge to a local optimum. Furthermore we extend our approach to all distance measures that can be expressed in the form of a Bregman divergence. Experiments on synthetic and real datasets demonstrate the effectiveness of our approach and the utility of carrying out both clustering and outlier detection in a concurrent manner. In particular on the famous KDD cup network-intrusion dataset, we were able to increase the precision of the outlier detection task by nearly 100% compared to the classical nearest-neighbor approach.
Chawla et al. REF improved their previous method to guaranteed to converge to a local optimum and proposed a new approach to measure data distance presenting in the form of a Bregman divergence.
k-means--: A Unified Approach to Clustering and Outlier Detection
SDM
Computer Science