Pattern Recognition, 4th Edition

Discrete Observation HMM Models

We will assume that the training observation string x^k, k = 1, 2, …, N, consists of quantized vectors. In practice, this is achieved via vector quantization techniques, to be discussed later in Chapter 14. Hence, each observation vector can take one only out of L possible distinct values in the l-dimensional space. Thus, observations can be described as integers r, r = 1, 2, …, L. The steps for each of the two methods, that is, any path and best path, are as following:

Baum-Welch Reestimation

The “output” quantity in the any path procedure is p(X|S). Thus, estimating the parameters of the model S so that p(X|S) is a maximum is nothing but a maximum likelihood parameter estimation procedure. Before going into ...