Ensemble mapper

Abstract

Mapper is a popular topological data analysis method to analyse structure of complex high-dimensional data sets. As the Mapper algorithm can be applied to clustering and feature selection with visualization, it is used in various fields such as biology and chemistry. However, some resolution parameters have to be chosen by the user before applying the Mapper algorithm, and the results are sensitive to the selection. In this paper, we focus on the selection of two resolution parameters, the number of intervals and the overlapping percentage. We propose a new resolution parameter selection method in Mapper based on the ensemble technique. We generate multiple Mapper results under various parameter values and apply the fuzzy clustering ensemble method to combine the results. To evaluate Mapper algorithms including the proposed one, three real data sets are considered. The results demonstrate the superiority of the proposed ensemble Mapper method.