MATLAB Implementation of Continuous Hidden Markov Models (HMM)

This MATLAB implementation provides a complete framework for Continuous Hidden Markov Models (HMMs). Hidden Markov Models are probabilistic models used for time series data modeling, where the underlying states are hidden (unobservable), but observed data depends on these states. In continuous HMMs, observations are continuous variables typically modeled using Gaussian Mixture Models (GMMs).

The program includes essential components for continuous HMM implementation: data preparation, model training, and prediction. During data preparation, the code handles dataset partitioning into training and testing sets using MATLAB's built-in functions like cvpartition or custom data splitting routines. The model training phase employs the Expectation-Maximization (EM) algorithm to estimate HMM parameters - including transition probabilities, initial state distributions, and GMM parameters (means, covariances, and mixture weights). The implementation utilizes MATLAB's statistical and optimization toolboxes for efficient parameter estimation.

For prediction, the code implements the Viterbi algorithm to decode the most likely state sequence for test data. The Viterbi implementation includes dynamic programming optimization with logarithmic probabilities to prevent numerical underflow. Key functions in the implementation include:

- hmmtrain() for parameter estimation via EM algorithm
- gmdistribution() for Gaussian mixture modeling
- Custom Viterbi decoder with state path backtracking
- Data normalization and feature scaling routines

This continuous HMM implementation is applicable across various domains including speech recognition (for acoustic modeling), natural language processing (for sequence labeling), bioinformatics (for gene finding), and financial time series analysis.