Robust clustering method for the detection of outliers: using AIC to select the number of clusters

Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications, Studies in Theoretical and Applied Statistics, Springer, Berlin Heidelberg, (2013), 409-415
http://dx.doi.org/10.1007/978-3-642-34904-1_43

In Santos-Pereira and Pires (Computational Statistics, pp. 291–296. Physica, Heidelberg, 2002) we proposed a method to detect outliers in multivariate data based on clustering and robust estimators. To implement this method in practice it is necessary to choose a clustering method, a pair of location and scatter estimators, and the number of clusters, k. After several simulation experiments it was possible to give a number of guidelines regarding the first two choices. However, the choice of the number of clusters depends entirely on the structure of the particular data set under study. Our suggestion is to try several values of k (e.g., from 1 to a maximum reasonable k which depends on the number of observations and on the number of variables) and select k minimizing an adapted AIC. In this chapter we analyze this AIC-based criterion for choosing the number of clusters k (and also the clustering method and the location and scatter estimators) by applying it to several simulated data sets with and without outliers.