Hidden Markov Models with Generalised Emission Distribution for the Analysis of High-Dimensional, Non-Euclidean Data
Georg Pfundstein · Open access LMU (Ludwid Maxmilian's Universitat Munchen) · 2011
Hidden Markov models (HMM) are tremendously popular for the analysis of sequential data, such as biological sequences, speech recognition as well as gesture recognition.However, since the method has got some limitations, that is mainly the restrictive emission distribution assumption in each hidden state, a generalised extension of the ordinary HMM is introduced.The method proposed in this work aims to overcome this limitation through adapting the multivariate Gaussian density so it can handle data obtained from non-Euclidean metric space.The generalised emission distribution is only dependent on the pairwise distances of all observations and no longer on a center of mass nor a variance term.We show that our method performs as good as the original HMM in many scenarios and even outperforms it in a certain non-Euclidean data situation.In addition we apply the method to ChIP-chip data in order to find out whether or not we can determine distinct gene classes that can be distinguished by different transcription state sequences.