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A parametric version of probabilistic distance clustering. (English) Zbl 1436.62281
Greselin, Francesca (ed.) et al., Statistical learning of complex data. Selected papers of the 11th scientific meeting of the Classification and Data Analysis Group of the Italian Statistical Society (CLADAG 2017), Milan, Italy, September 13–15, 2017. Cham: Springer. Stud. Classification Data Anal. Knowl. Organ., 33-43 (2019).
Summary: Probabilistic distance (PD) clustering method grounds on the basic assumption that the product between the probability of the unit belonging to a cluster and the distance between the unit and the cluster center is constant, for each statistical unit. This constant is a measure of the classificability of the point, and the sum of the constant over units is referred to as the joint distance function (JDF). The parameters that minimize the JDF maximize the classificability of the units. The goal of this paper is to introduce a new distance measure based on a probability density function, specifically, we use the multivariate Gaussian and Student-\(t\) distributions. We show using two simulated data sets that the use of a distance based on these two density functions improves the performance of PD clustering.
For the entire collection see [Zbl 1427.62004].
MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62F03 Parametric hypothesis testing
62H10 Multivariate distribution of statistics
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