Cluster weighted models with multivariate skewed distributions for functional data

We propose a clustering method, funWeightClustSkew, based on mixtures of functional linear regression models and three skewed multivariate distributions: the variance-gamma distribution, the skew-t distribution, and the normal-inverse Gaussian distribution. Our approach follows the framework of the functional high dimensional data clustering (funHDDC) method, and we extend to functional data the cluster weighted models based on skewed distributions used for finite dimensional multivariate data. We consider several parsimonious models, and to estimate the parameters we construct an expectation maximization (EM) algorithm. We illustrate the performance of funWeightClustSkew for simulated data and for the Air Quality dataset.

Cluster weighted models for functional data

We propose a method, funWeightClust, based on a family of parsimonious models for clustering heterogeneous functional linear regression data. These models extend cluster weighted models to functional data, and they allow for multivariate functional responses and predictors. The proposed methodology follows the approach used by the the functional high dimensional data clustering (funHDDC) method. We construct an expectation maximization (EM) algorithm for parameter estimation. Using simulated and benchmark data we show that funWeightClust outperforms funHDDC and several two-steps clustering methods. We also use funWeightClust to analyze traffic patterns in Edmonton, Canada.