A novel HMM distance measure with state alignment

In this paper, we introduce a novel distance measure that conforms to the definition of a semi-distance, for quantifying the similarity between Hidden Markov Models (HMMs). This distance measure is not only easier to implement, but also accounts for state alignment before distance calculation, ensuring correctness and accuracy. Our proposed distance measure presents a significant advancement in HMM comparison, offering a more practical and accurate solution compared to existing measures. Numerical examples that demonstrate the utility of the proposed distance measure are given for HMMs with continuous state probability densities. In real-world data experiments, we employ HMM to represent the evolution of financial time series or music. Subsequently, leveraging the proposed distance measure, we conduct HMM-based unsupervised clustering, demonstrating promising results. Our approach proves effective in capturing the inherent difference in dynamics of financial time series, showcasing the practicality and success of the proposed distance measure.