Non-negative durational HMM

Non-negative HMM (N-HMM) has been proposed in the literature as a combination of NMF (non-negative matrix factorisation) and HMM, to model a mixture of non-stationary signals using latent variables. The original formulation of N-HMM does not generalise to unseen data and hence limits its usage in automatic speech recognition (ASR). We propose modifications to the N-HMM formulation to generalise for unseen data and thereby making it suitable for ASR. The modified model is referred to as Non-negative durational HMM (NdHMM). We derive the EM algorithm for estimating the NdHMM parameters and show that the proposed model requires less number of parameters than conventional HMM.