HSM: Hierarchical spectral merger algorithm

In CarolinaEuan/HMClust: HMClust

Hierarchical spectral merger algorithm

Description

Compute the hierarchical spectral merger clustering algorithm for a set of time series X.

Usage

HSM(X,S=NULL,w=NULL, freq = 1, Merger = 1, par.spectrum = c(100, 1/(2 * dt), 512))

Arguments

X	Matrix of time series, the series should be located by column.
S	Optional. Matrix of spectrum as input.
w	Optional. Vector of Frequencies, required if matrix of spectrum is given as input.
freq	Sampling Frequency. Default value is 1.
Merger	If Merger==1 (default), the algorithm will estimate the new spectral density with the concatenated signals in order to get a better estimation of the original spectral density. If Merger==2 the algorithm will estimate the new spectral density with the mean spectrum using all time series in the cluster.
par.spectrum	Parameters for the estimation method: par.spectrum[1]=Bandwidth value, par.spectrum[2]= maximun evaluated frequency, par.spectrum[3]= length of the grid of the frequencies values.

Details

Let X_1,X_2,...,X_N be the signal for each channel with length T and sampling frequency F_s. The procedure starts with N clusters, one for each individual channel.

1) Estimate the spectral density for each cluster using the smoothed periodogram and compute the TVD between their spectra.

2) Find the two clusters that have lower TVD, save this value as a characteristic.

3) Merge the signals in the two closest clusters and replace the two clusters by this new one.

4) Repeat steps 1-3 there is only one cluster left.

Value

A HSM object with the following variables:

Diss.Matrix = Initial dissimilarity matrix.

min.value = trayectory of the minimum value.

Groups = list with the groupping structure at each step.

Author(s)

Carolina Euan.

References

Euan, C., Ombao, H. and Ortega, J. (2016) "The Hierarchical Spectral Merger algo- rithm: A New Time Series Clustering Procedure".

See Also

cutk

Examples

set.seed(9347)
#Series
TT<-1000
ww<-c(2,6,10,21,40);k<-6;ng<-3
# Original Groups (1,3,5) and (2,4,6)
e1<-c(0,1,0,1,0);e2<-c(0,1,1,0,0);A<-rbind(e1,e2)
ZZ<-matrix(NA,ncol=ng*5,nrow=TT)
for(index in 1:(ng*5))ZZ[,index]<-Sim.Ar(TT,ww[1+index%%5],1.01,100)
X<-cbind(t(A%*%t(ZZ[,1:5])),t(A%*%t(ZZ[,6:10])),t(A%*%t(ZZ[,11:15])))
#Algorithm
Fs<-100
Clust1<-HSM(X,freq=Fs)
cutk(Clust1,2)

CarolinaEuan/HMClust documentation built on Feb. 18, 2024, 10 p.m.