Similarity¶
DTW¶
If two time series are identical, but one is shifted slightly along the time axis, then Euclidean distance may consider them to be very different from each other. Created in 1978, Dynamic Time Wrapping (DTW) was introduced to overcome this limitation and give intuitive distance measurements between time series by ignoring both global and local shifts in the time dimension.
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FastDTW is a faster implementation of DTW.
import numpy as np
from scipy.spatial.distance import euclidean
from fastdtw import fastdtw
x = np.array([[1,1], [2,2], [3,3], [4,4], [5,5]])
y = np.array([[2,2], [3,3], [4,4]])
distance, path = fastdtw(x, y, dist=euclidean)
print(distance)
There are many variants of DTW. An example is to first normalize both signals before running DTW so that the distance will mostly be shape, rather than amplitude-related.
from scipy.stats import zscore
from fastdtw import fastdtw
sig1 = zscore(sig1)
sig2 = zscore(sig2)
distance, path = fastdtw(sig1, sig2, dist=euclidean)
Further Readings¶
- 1978 Dynamic programming algorithm optimization for spoken word recognition
- 2004 FastDTW: Toward Accurate Dynamic Time Warping in Linear Time and Space