Let us first consider the case of
isolated word recognition, which is simpler
than connected speech recognition. For isolated
word recognition, a single HMM can be built for each word w
within a preset vocabulary. This is illustrated in
Figure 5, with one left-to-right
model (with skips) for each word. With these models
one can compute
for
each word w within the vocabulary,
when an acoustic sequence
is given.
When an a priori distribution P(w) on the words
is also given, the most likely word
given
the acoustic sequence can be obtained by picking
the model which maximizes both the acoustic
probability and the prior:
The computational cost for recognition is simply the number of words times the cost of computating the acoustic probability for a word (forward computation, equation 5). The recognition time can however be significantly reduced by using search techniques mentioned in the previous section.
Figure 6: Example of hierarchical organization of speech knowledge
in the topology of an HMM. Each level can be represented
by a different weighted transducer or acceptor.
Arcs represent transitions
and nodes represent HMM states at a certain level
(or groups of states at a lower level). Low-level
models (e.g. phoneme models) are shared in many
places in the overall HMM.