A new Dirichlet process for mining dynamic patterns in functional data

This paper proposes a novel model for mining patterns including dynamic function clustering, segmentation, and forecasting values of dependent variables simultaneously. The proposed Dependent Dirichlet Process Piecewise Regression Mixture (DDPPRM) model is capable of handling dynamic nature of data by detecting evolving clusters at each time step. This evolution manifests dynamically in three states of clusters: newly created, existing, and transient states of clusters. The model is also able to generate clusters over time infinitely. It is capable of learning the optimal number of clusters rather than using the fixed, predefined clusters. However, other clustering methods such as Fuzzy C-Regression Model and Piecewise Regression Mixture technique support none of those capabilities. The proposed model is also capable of showing regime changes and segmenting functions in regression/time series problems. A two-step Gibbs sampling method is utilized for assigning data to clusters. Expectation-Maximization method is used for finding the optimal values of parameters of functions and probability distributions. The model is validated by using some numerical experiments and calculating three validity indexes as well as Mean Square Error of the model. The results indicate that the proposed method outperforms other clustering, segmentation, and forecasting models in literature.