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Hybrid hidden Markov models

  A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. In a typical Markov model is visible observer, so the probability of transitions . a single option. In HMM, we can monitor only variables that are affected by this condition. Each state has a probability distribution among all possible output values . Therefore, the sequence of characters generated HMM provides information about the sequence of states. We now turn directly to the classification of HMM. In a broad sense HMM can be classified into the following general classes [12]: Fig. 1. Basic Structure of HSMM Rys. 1. Podstawowa struktura ukrytych modeli semi-Markowa Fig. 2. The general scheme of classification of classical hidden Markov models Rys. 2. Ogolny schemat klasyfikacji klasycznych ukrytych modeli Markowa . hidden semi-Markov model; . classic HMM; . hybrid Markov model. Hidden semi-Markov model (HSMM) is a generalization of the HMM, which allows a more general distribution of residence time. The basic structure HSMM is shown in Figure 1. Arrows from S1 to 1 X1,..., Xd and from S2 to 1 1 2 Xd 1,..., Xd d + + indicate conditional dependence of observations on the hidden states. Hidden semi-Markov model consists of a pair of random processes with discrete time { } St and { }Xt . As "N"M"M the observed process { }Xt is associated with a hidden state semi-Markov process { } St with conditional distribution. Classic HMM divided in the following classification criteria by: . number of states (1); . number of levels (2); . temporal characteristics (3); . type of probability distribution that underlie the HMM (10); . parametric property (11); . type of topology (4); . homogeneity (5); . linearity (6); . dynamic properties (7); . structure of matrix transitions (8); . connectivity graph transitions (9). The general classification of classic HMM showed in Fig. [...]

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