ROBUST AND CONSISTENT CLUSTERING RECOVERY VIA SDP APPROACHES

Clustering plays an important role in exploratory analysis by identifying patterns from a group of objects. Recently, similarity-based clustering has attracted much attention due to its ability to partition modern datasets with high dimensional, heterogeneous features. Furthermore, a variety of methods have been proposed to obtain the similarity metric between objects. In this paper, we focus on the following problem: given the (noisy) similarity information on a data set that may contain outliers, find the underlying clustering structure without prior knowledge on the number of clusters $K$. We propose a semidefinite programming (SDP) approach to solve the problem and give conditions that guarantee exact recovery on a Gaussian similarity matrix model with vanishing probability of error. We show that under certain necessary conditions, the SDP algorithm is consistent with high probability. Experimental results on synthetic data demonstrate the effectiveness of our approach.