A1312
Title: Probabilistic distance clustering for complex data structures
Authors: Francesco Palumbo - University of Naples Federico II (Italy) [presenting]
Cristina Tortora - San Jose State University (United States)
Abstract: Complex data arise when one or more sources of complexity coexist, such as high dimensionality, mixed variable types, and intrinsic structural features. In the data-driven era, the rapid growth of automatically recorded data has made traditional Clustering approaches increasingly inadequate, thereby motivating the development of new methods within the statistical learning framework. In this context, Probabilistic Distance Clustering (PDC) and its Factorial variant provide a flexible, geometry-based framework for Clustering several types of complex data. The method is based on the point classifiability criterion and can operate with any generic Distance or dissimilarity measure. Given a set of $n$ statistical units described by $p$ variables and a set of $G$ cluster centers, PDC searches for the best configuration of centers by minimizing the Joint Density Function: $JDF = \sum_{g=1}^{G} \sum_{i=1}^{n} p_{ig}^2 d(x_i, c_g)$, where $d(x_i, c_g)$ denotes the Distance or dissimilarity between observation $i$ and center $g$, and $p_{ig}$ is the probability of assigning observation $i$ to cluster $g$. This straightforward formulation makes PDC suitable not only for continuous data, but also for mixed-type, correlated, and compositional data, provided that an appropriate dissimilarity measure is used. Moreover, Factorial PDC extends the method to high-dimensional settings. The R package \texttt{FPDclustering} implements several variants of PDC.
