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Cd-Hmm For Normal Sinus Rhythm
1
0 t
1
2
H (t ) 1
1 t 1 (2)
2
0 others ,
Fig. 1: Continuous wavelet transform of the raw time data series (left panel – premature ventricular
contraction, right panel – normal sinus rhythm).
Scales were finally chosen from an interval of . The signals were extracted as periods of 250
samples (f s =360 Hz) containing R-waves of each QRS complex. After transforming by CWT, the wavelet
coefficients were squared and normalized.
2.2 Continuous Density Hidden Markov Model (Cd-Hmm)
The Hidden Markov model is a finite state machine having a set of states Q, each of which is associated
with probability distribution, an output alphabet O, transition probabilities A, output probabilities B, and initial
state probabilities Π. The current state is not observable. Instead, each state produces an output with a certain
probability B. The CD-HMM stage is proceeded by the pre-processing step (CWT).
Continuous emission probability B = {b j (O t )}, where O = O 1 ,O 2 , . . . ,O T , the emission probability density
function of each state is defined by a finite multivariate Gaussian mixture:
M
b j (O t ) ∑d jm N (O t , jm , C jm ), 1 j N (3)
M1
where O t is the feature vector of the sequence being modelled, d jm is the mixture coefficient from the mth
mixture in state j and N is a Gaussian probability with mean vector µ jm and covariance matrix C jm for the mth
mixture component in state j. We will refer to these models as a continuous density HMM (CD-HMM).
The used CD-HMM had left-to-right topology. The number of states is possible to change. The first state
is designated as the initial state and the last state as the output state.
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