Statistical Modeling of Univariate Multimodal Data
This method addresses the challenge of statistical modeling for univariate multimodal data, which is incremental as it builds on existing unimodal modeling techniques.
The authors tackled the problem of modeling univariate multimodal data by partitioning it into unimodal subsets using recursive splitting around density valleys, resulting in a hierarchical statistical model called the Unimodal Mixture Model (UDMM) that is non-parametric, hyperparameter-free, and automatically estimates the number of subsets.
Unimodality constitutes a key property indicating grouping behavior of the data around a single mode of its density. We propose a method that partitions univariate data into unimodal subsets through recursive splitting around valley points of the data density. For valley point detection, we introduce properties of critical points on the convex hull of the empirical cumulative density function (ecdf) plot that provide indications on the existence of density valleys. Next, we apply a unimodal data modeling approach that provides a statistical model for each obtained unimodal subset in the form of a Uniform Mixture Model (UMM). Consequently, a hierarchical statistical model of the initial dataset is obtained in the form of a mixture of UMMs, named as the Unimodal Mixture Model (UDMM). The proposed method is non-parametric, hyperparameter-free, automatically estimates the number of unimodal subsets and provides accurate statistical models as indicated by experimental results on clustering and density estimation tasks.