Efficient algorithms for mining outliers from large data sets

<jats:p> In this paper, we propose a novel formulation for distance-based <jats:italic>outliers</jats:italic> that is based on the distance of a point from its <jats:italic> k <jats:sup>th</jats:sup> </jats:italic> nearest neighbor. We rank each point on the basis of its distance to its <jats:italic> k <jats:sup>th</jats:sup> </jats:italic> nearest neighbor and declare the top <jats:italic>n</jats:italic> points in this ranking to be outliers. In addition to developing relatively straightforward solutions to finding such outliers based on the classical nested-loop join and index join algorithms, we develop a highly efficient <jats:italic>partition-based</jats:italic> algorithm for mining outliers. This algorithm first partitions the input data set into disjoint subsets, and then prunes entire partitions as soon as it is determined that they cannot contain outliers. This results in substantial savings in computation. We present the results of an extensive experimental study on real-life and synthetic data sets. The results from a real-life NBA database highlight and reveal several expected and unexpected aspects of the database. The results from a study on synthetic data sets demonstrate that the partition-based algorithm scales well with respect to both data set size and data set dimensionality. </jats:p>