This paper introduces a new extension of outlier detection approaches and a new concept, class separation through variance. We show that accumulating information about the outlierness of points in multiple subspaces leads to a ranking in which classes with differing variance naturally tend to separate. Exploiting this leads to a highly effective and efficient unsupervised class separation approach, especially useful in the difficult case of heavily overlapping distributions. Unlike typical outlier detection algorithms, this method can be applied beyond the `rare classes' case with great success. Two novel algorithms that implement this approach are provided. Additionally, experiments show that the novel methods typically outperform other state-of-the-art outlier detection methods on high dimensional data such as Feature Bagging, SOE1, LOF, ORCA and Robust Mahalanobis Distance and competes even with the leading supervised classification methods.

Clustering is the problem of grouping data based on similarity and consists of maximizing the intra-group similarity while minimizing the inter-group similarity. The problem Of clustering data sets is also known as unsupervised classification, since no class labels are given. However, all existing clustering algorithms require some parameters to steer the clustering process, such as the famous k for the number of expected clusters, which constitutes a supervision of a sort. We present in this paper a new, efficient, fast and scalable clustering algorithm that clusters over a range of resolutions and finds a potential optimum clustering without requiring any parameter input. Our experiments show that our algorithm outperforms most existing clustering algorithms in quality and speed for large data sets.