3. Training of the Hybrid Rbf-hmm System

Table 1: Phoneme recognition rates for diierent hybrid RBF-HMM systems; all values in %. In line two the results for a NN with one additional hidden layer of 100 sigmoidal units are depicted. The recognition rates for both training procedures are inferior to the net without hidden layer. This is mainly contributed to the relatively small hidden layer with 100 nodes, which acts like a bottleneck in computing the state probabilities. The information from 400 RBF a-posteriori probabilities is compressed in 100 hidden node scores and expanded to calculate the 169 state probabilities. The number of trainable parameters (weights) for this system is about 57,000 and for the baseline system without hidden layer about 68,000. The enhanced transformation capability from the hidden layer was of no additional use for this task. In a third experiment contextual information from the adjacent feature vectors is used for the calculation of state probabilities in the net. The output nodes refer to the a-posteriori probabilities of the RBF nodes from 3 frames. This expands the hidden layer to 1200 normalized scores and results in about 203,000 trainable parameters. Since the computing of the delta-loudness incorporates the processing of ve frames for every feature vector, the usage of the 3 frame contextual window results in acoustic information from 70ms in total. The phoneme recognition results for this RBF net are printed in line three of table 1. 62.5% of the phonemes in the test data are correctly classiied after the MSE optimization and 63.8% after the MCE-GPD training. The incorporation of contextual information in the estimation of a-posterioris leads to some improvements in performance. The minimum error (MCE) training in the second optimization phase is started after no more increase in recognition performance on the test data for the MSE training occurred. The optimization of the MCE objective function , which is more related to the classiier error rate than the MSE, leads to some additional improvements in performance. The best result (63.8%) for the RBF-HMM is achieved , exploiting contextual information. SCHMMs with the same number of prototypes and model structure were trained with MLE for comparison. The SCHMM phoneme recognition rate for the training data is 58.5% and 57.9% for the test data. The improvement of about 6% for the RBF-HMM is attributed to the discriminative structure based on Bayes probabilities, the discriminative learning techniques and the incorporation of contextual input. 5. CONCLUSIONS …