Penalized Model-based Clustering of Complex Functional Data

Abstract

High dimensional data, large-scale data, imaging and manifold data are all fostering new frontiers of statistics. These type of data are commonly considered in Functional Data Analysis (FDA) where they are viewed as infinite-dimensional random vectors in a functional space. The rapid development of new technologies has generated a flow of complex data that have led to the development of new modeling strategies by scientists. In this paper, we basically deal with the problem of clustering a set of complex functional data into homogeneous groups. Working in a mixture model-based framework, we develop a flexible clustering technique achieving dimensionality reduction schemes through an L1 penalization. The proposed procedure results in an integrated modelling approach where shrinkage techniques are applied to enable sparse solutions in both the means and the covariance matrices of the mixture components, while preserving the underlying clustering structure. This leads to an entirely data-driven methodology suitable for simultaneous dimensionality reduction and clustering. The proposed methodology is evaluated through a Monte Carlo simulation study and an empirical analysis of real-world datasets showing different degrees of complexity.

Dynamic and Static Enhanced BIRCH for Functional Data Clustering

“…density estimation based on principal components analysis. This replaces the original probability density of the functions with a kernel density estimate constructed from the principal component scores [27][28][29][30][31][32][33][34][35][36][37]. For example, Wu et al [35] incorporated non-parametric curve features and developed a probabilistic model based on Bayesian criteria for functional data clustering.…”