Pattern Recognition, 4th Edition

9.3. Markov Chain Models

One of the most widely used models describing the underlying class dependence is the Markov chain rule. If ωⁱ¹, ωⁱ², … is a sequence of classes, then the Markov model assumes that(9.3)The meaning of this is that the class dependence is limited only within two successive classes. This type of model is also called a first-order Markov model, to distinguish it from obvious generalizations (second, third, etc.). In other words, given that the observations x^k−1, x^k−2, …, x¹ belong to classes ω^ik−1, ω^ik−2, …, ωⁱ¹, respectively, the probability of the observation x^k, at stage k, belonging to class ω^ik depends only on the class ...