The problem of detecting atypical objects or outliers is one of the classical topics in (robust) statistics. Recently, it has been proposed to address this problem by means of one-class SVM classifiers. The method presented in this letter bridges the gap between kernelized one-class classification and gaussian density estimation in the induced feature space. Having established the exact relation between the two concepts, it is now possible to identify atypical objects by quantifying their deviations from the gaussian model. This model-based formalization of outliers overcomes the main conceptual shortcoming of most one-class approaches, which, in a strict sense, are unable to detect outliers, since the expected fraction of outliers has to be specified in advance. In order to overcome the inherent model selection problem of unsupervised kernel methods, a cross-validated likelihood criterion for selecting all free model parameters is applied. Experiments for detecting atypical objects in image databases effectively demonstrate the applicability of the proposed method in real-world scenarios.

Data clustering describes a set of frequently employed techniques in exploratory data analysis to extract “natural” group structure in data. Such groupings need to be validated to separate the signal in the data from spurious structure. In this context, finding an appropriate number of clusters is a particularly important model selection question. We introduce a measure of cluster stability to assess the validity of a cluster model. This stability measure quantifies the reproducibility of clustering solutions on a second sample, and it can be interpreted as a classification risk with regard to class labels produced by a clustering algorithm. The preferred number of clusters is determined by minimizing this classification risk as a function of the number of clusters. Convincing results are achieved on simulated as well as gene expression data sets. Comparisons to other methods demonstrate the competitive performance of our method and its suitability as a general validation tool for clustering solutions in real-world problems.