Clustering and outlier detection using isoperimetric number of trees

We propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in O ( n log n ) and with post-processing in almost O ( n log n ) (average case) and O ( n 2 ) (worst case) time where n is the size of the data-set. It is also shown that our generalized graph model, which also allows the use of potentials at vertices, can be used to extract an extra piece of information related to anomalous data patterns and outliers. In this regard, we propose an algorithm that extracts outliers in parallel to data clustering. We also provide a comparative performance analysis of our algorithms with other related ones and we show that they behave quite effectively on hard synthetic data-sets as well as real-world benchmarks.