March 2010
Intermediate to advanced
150 pages
7h 13m
English
book
Introduction to Pattern Recognition: A Matlab Approach
by Sergios Theodoridis, Aggelos Pikrakis, Konstantinos Koutroumbas, Dionisis Cavouras
Content preview from Introduction to Pattern Recognition: A Matlab Approach
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148 CHAPTER 6 Hidden Markov Models
In summary, an HMM is described by the foll owing set of parameters:
• The number of states, k.
• The probability densities, p(x|j), j = 1, ...,k. For discrete variables, where x = r, r = 1, ...,L,the
observation probability matrix that is defined as
B =
⎡
⎢
⎣
P(x = 1|1) P(x = 1|2) ... P(x = 1|k)
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P(x = L|1) p(x = L|2) ... P(x = L|k)
⎤
⎥
⎦
• The state transition matrix, A,
A =
⎡
⎢
⎣
P(1|1) p(2|1) ... p(k|1)
.
.
.
.
.
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P(1|k) P(2|k) ... P(k|k)
⎤
⎥
⎦
• The vector π of the initial probabilities,
π =
⎡
⎢
⎢
⎢
⎣
P(1)
P(2)
.
.
.
P(k)
⎤
⎥
⎥
⎥
⎦
6.3 RECOGNITION AND TRAINING
During recognition, we assume that we have more than one HMM, each one d
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