Unifying dynamic programming methods

Dynamic programming has come to be widely used and accepted in automatic speech recognition. However, two different but similar applications have often been described more in terms of their differences than their similarities. On the one hand, dynamic programming is used to find the best nonlinear dynamic time warping to align two instances of a word. On the other hand, dynamic programming may be used to find the best state sequence for a hidden Markov process. Not only are these procedures essentially equivalent, but significant generalization comes from an explicit unification. Dynamic programming may be used not only to align two instances of a word, but also to align an instance of a word with an arbitrary finite state model for the word, or even to align two arbitray models. Multiple instances of a word may contribute to a single model, and multiple passes on a finite set of training data can be used to further refine word models.