HiddenMarkovModel: HiddenMarkovModel

In Mthrun/TSAT: Time Series Analysis Tools (TSAT)

HiddenMarkovModel

Description

HiddenMarkovModel using Rhmm package.

Procedure:

1. Selection of the number of states (Knowledge Discovery)

2. the Baum-Welch algorithm (generalized EM) determines the transition matrix P and the output probability

3. Veterbi algorithm: Determination of the probable sequence of states for a given observation, i.e. clustering is reproduced as output

Usage

HiddenMarkovModel(Data,ClusterNo,DistributionName='NORMAL',

Iterations=500,PriorClassification,PlotIt=TRUE,Silent=TRUE)

Arguments

Data	[1:n,1:d] d-dimensional data of n cases
ClusterNo	number of states, k
DistributionName	Normal==gaussian distributions
Iterations	number of maximal iteration steps
PriorClassification	Optional, to be compared with HMM
PlotIt	Optional, Plots the distributions of HMMmodell
Silent	Optional, additional outputs during the process of the function, e.g. summary(HMMmodell)

Details

"Hidden", since only time series given, but no actual states. States cannot be observed The output in a state is probalistic. The output in one state is therefore probalistic, since neither the transition probability nor the states are known. The number must be specified using a cluster procedure or from expert knowledge. The states should have semantics.

Value

List of

HMMmodell	please see HMMFit
HMM_means	[1:k] means of distributions, please see distributionSet
HMM_SDs	[1:k] standard deviations of distributions, please see distributionSet
HMM_weights	[1:k] weights of distributions
Uebergangsmatrix	Transition matrix, please see HMMSet
VitPath	please see viterbi
HMMcls	[1:n] classification defining which datapoint (case) belongs to which case
XTable	if PriorClassification given, compares to HMMcls
Accuracy	if PriorClassification given, compares to HMMcls

Author(s)

Michael Thrun

References

Bilmes, Jeff A.: A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models http://ssli.ee.washington.edu/people/bilmes/mypapers/em.ps.gz, 1997.

See Also

Baum-Welch-Algorithmus (generalisierter EM): HMMFit

Viterbi-Algorithmus: viterbi,HMMFit

Examples

requireNamespace('Rhmm')
data(n1d_3s)
Data=as.matrix(obs_n1d_3s[[1]])
model=HiddenMarkovModel(Data,3,PlotIt = T,Silent = T)

TagNR=1:nrow(Data)
plot(TagNR,Data[,1],col=model$HMMcls,main='HMM states with Viterbi',pch=20)
legend("topright", inset = c(-0.2, 0), legend = sort(unique(model$HMMcls)), 
            fill =  sort(unique(model$HMMcls)))

Mthrun/TSAT documentation built on Feb. 5, 2024, 11:15 p.m.