# Clustering time series with wavelets in R

Can discrete wavelet trasform be used for feature extraction from time series in order to cluster them? Any R code how to do this will be appreciated.

You might find this useful:

# EXAMPLE OF BIAS CORRECTION:
install.packages("biwavelet")
require(biwavelet)
# Generate a synthetic time series ’s’ with the same power at three distinct periods
t1=sin(seq(from=0, to=2*5*pi, length=1000))
t2=sin(seq(from=0, to=2*15*pi, length=1000))
t3=sin(seq(from=0, to=2*40*pi, length=1000))
s=t1+t2+t3
# Compare non-corrected vs. corrected wavelet spectrum
wt1=wt(cbind(1:1000, s))
par(mfrow=c(1,2))
plot(wt1, type="power.corr.norm", main="Bias-corrected")
plot(wt1, type="power.norm", main="Not-corrected")
# Compare non-corrected vs. corrected cross-wavelet spectrum
x1=xwt(cbind(1:1000, s), cbind(1:1000, s))
par(mfrow=c(1,2))
plot(x1, type="power.corr.norm", main="Bias-corrected")
plot(x1, type="power.norm", main="Not-corrected")
t1=cbind(1:100, rnorm(100))
t2=cbind(1:100, rnorm(100))
# Continuous wavelet transform
wt.t1=wt(t1)
# Plot power
# Make room to the right for the color bar
par(oma=c(0, 0, 0, 1), mar=c(5, 4, 4, 5) + 0.1)
plot(wt.t1, plot.cb=TRUE, plot.phase=FALSE)
# Cross-wavelet
xwt.t1t2=xwt(t1, t2)
# Plot cross wavelet power and phase difference (arrows)
plot(xwt.t1t2, plot.cb=TRUE)
# Wavelet coherence; nrands should be large (>= 1000)
wtc.t1t2=wtc(t1, t2, nrands=10)
# Plot wavelet coherence and phase difference (arrows)
# Make room to the right for the color bar
par(oma=c(0, 0, 0, 1), mar=c(5, 4, 4, 5) + 0.1)
plot(wtc.t1t2, plot.cb=TRUE)
# Perform wavelet clustering of three time series
t1=cbind(1:100, sin(seq(from=0, to=10*2*pi, length.out=100)))
t2=cbind(1:100, sin(seq(from=0, to=10*2*pi, length.out=100)+0.1*pi))
t3=cbind(1:100, rnorm(100))
# Compute wavelet spectra
wt.t1=wt(t1)
wt.t2=wt(t2)
wt.t3=wt(t3)
# Store all wavelet spectra into array
w.arr=array(NA, dim=c(3, NROW(wt.t1$wave), NCOL(wt.t1$wave)))
w.arr[1, , ]=wt.t1$wave w.arr[2, , ]=wt.t2$wave
w.arr[3, , ]=wt.t3$wave # Compute dissimilarity and distance matrices w.arr.dis=wclust(w.arr) plot(hclust(w.arr.dis$dist.mat, method="ward"), sub="", main="",
ylab="Dissimilarity", hang=-1)


and the output looks like:

I found it here.

Yes it can.

Any kind of feature extraction is a good idea for clustering. Go ahead, and try some of them.

If you can define a good distance function on your wavelet transformed data, then most distance based clustering algorithms should work for you.

• Ok, but how to extract relevant features? Are all wavelet coefficients relevant? Or only some of them? – Miroslav Sabo Oct 9 '12 at 17:16
• Depends on your data and domain. Sometimes they are, sometimes they aren't. Try different things. – Has QUIT--Anony-Mousse Oct 9 '12 at 19:08