Extended Tied-Mixture HMMs for Both Labeled and Unlabeled Time Series Data

Classifier design often faces a lack of sufficient labeled data because the class labels are identified by experienced analysts and therefore collecting labeled data often costs much. To mitigate this problem, several learning methods have been proposed to effectively use unlabeled data that can be inexpensively collected. In these methods, however, only static data have been considered; time series unlabeled data cannot be dealt with by these methods. Focusing on Hidden Markov Models (HMMs), in this paper we first present an extension of HMMs, named Extended Tied-Mixture HMMs (ETM-HMMs), in which both labeled and unlabeled time series data can be utilized simultaneously. We also formally derive a learning algorithm for the ETM-HMMs based on the maximum likelihood framework. Experimental results using synthetic and real time series data show that we can obtain a certainly better classification accuracy when unlabeled time series data are added to labeled training data than the case only labeled data are used.