Robust clustering around regression lines with high density regions. (English) Zbl 1474.62217

Cerioli, Andrea; Perrotta, Domenico

Adv. Data Anal. Classif., ADAC 8, No. 1, 5-26 (2014).

Summary: Robust methods are needed to fit regression lines when outliers are present. In a clustering framework, outliers can be extreme observations, high leverage points, but also data points which lie among the groups. Outliers are also of paramount importance in the analysis of international trade data, which motivate our work, because they may provide information about anomalies like fraudulent transactions. In this paper we show that robust techniques can fail when a large proportion of non-contaminated observations fall in a small region, which is a likely occurrence in many international trade data sets. In such instances, the effect of a high-density region is so strong that it can override the benefits of trimming and other robust devices. We propose to solve the problem by sampling a much smaller subset of observations which preserves the cluster structure and retains the main outliers of the original data set. This goal is achieved by defining the retention probability of each point as an inverse function of the estimated density function for the whole data set. We motivate our proposal as a thinning operation on a point pattern generated by different components. We then apply robust clustering methods to the thinned data set for the purposes of classification and outlier detection. We show the advantages of our method both in empirical applications to international trade examples and through a simulation study.

MSC:

62H30	Classification and discrimination; cluster analysis (statistical aspects)
62H11	Directional data; spatial statistics
62G35	Nonparametric robustness
62G07	Density estimation
62G08	Nonparametric regression and quantile regression
62P20	Applications of statistics to economics
91B60	Trade models

Keywords:

anti-fraud; concentrated noise; international trade; orthogonal regression; outlier detection; robust clusterwise regression; TCLUST; thinning; trimming

Software:

spatstat; TCLUST

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