## Maximum likelihood clustering with outliers.(English)Zbl 1032.62059

Jajuga, Krzysztof et al., Classification, clustering, and data analysis. Recent advances and applications. Papers presented at the eighth conference of the International Federation of Classification Societies (IFCS), Cracow, Poland, July 16-19, 2002. Berlin: Springer. Studies in Classification, Data Analysis, and Knowledge Organization. 247-255 (2002).
Summary: Suppose that we are given a list of $$n$$ $$\mathbb{R}^p$$-valued observations and a natural number $$r\leq n$$. Further, assume that $$r$$ of them arise from any one of $$g$$ normally distributed populations, whereas the other $$n-r$$ observations are assumed to be contaminations. We develop estimators which simultaneously detect $$n-r$$ outliers and partition the remaining $$r$$ observations in $$g$$ clusters. We analyze under which conditions these estimators are maximum likelihood estimators. Finally, we propose algorithms that approximate these estimators.
For the entire collection see [Zbl 1026.00018].

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects) 65C60 Computational problems in statistics (MSC2010)