A Generic Clustering-Based Algorithm for Approximating IOHMM Topology and Parameters

Abstract

In this paper, a novel generic clustering-based algorithm for approximating the topology and the parameters of discrete state space Input/Output Hidden Markov Models (IOHMMs) with continuous observation spaces is introduced. The algorithm can accommodate any continuous space clustering method, whether incremental or not; it can easily be extended to Input/Output Hidden Semi-Markov Models (IOHSMMs) as well as standard HMMs and HSMMs. In this paper, the proposed algorithm is implemented with the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN*) clustering algorithm. This algorithm brings numerous benefits such as the capability to learn the topology and the parameters of the model with more or less conservatism and the capability to define distributions from several frameworks of the uncertainty theory such as the probabilities, the possibilities or the imprecise probabilities. The algorithm is validated on synthetic and real-world datasets.

Keywords

• Hidden Markov Models
• topology
• parameters
• inference algorithms