Fuzzy classification with distance-based depth prototypes: High-dimensional unsupervised and/or supervised problems

Abstract

Supervised and unsupervised classification is crucial in many areas where different types of data sets are common, such as biology, medicine, or industry, among others. A key consideration is that some units are more typical of the group they belong to than others. For this reason, fuzzy classification approaches are necessary. In this paper, a fuzzy supervised classification method, which is based on the construction of prototypes, is proposed. The method obtains the prototypes from an objective function that includes label information and a distance-based depth function. It works with any distance and it can deal with data sets of a wide nature variety. It can further be applied to data sets where the use of Euclidean distance is not suitable and to high-dimensional data (data sets in which the number of features p is larger than the number of observations n, often written as p>>n). In addition, the model can also cope with unsupervised classification, thus becoming an interesting alternative to other fuzzy clustering methods. With synthetic data sets along with high-dimensional real biomedical and industrial data sets, we demonstrate the good performance of the supervised and unsupervised fuzzy proposed procedures.