Time series distance metric

Question

In order to clusterize a set of time series I\'m looking for a smart distance metric. I\'ve tried some well known metric but no one fits to my case.

ex: Let\'s assume t

Answer 1

nice question! using any standard distance of R^n (euclidean, manhattan or generically minkowski) over those time series cannot achieve the result you want, since those metrics are independent of the permutations of the coordinate of R^n (while time is strictly ordered and it is the phenomenon you want to capture).

A simple trick, that can do what you ask is using the cumulated version of the time series (sum values over time as time increases) and then apply a standard metric. Using the Manhattan metric, you would get as a distance between two time series the area between their cumulated versions.

Answer 2

Pietro P's answer is just a special case of applying a convolution to your time series.

If I gave the kernel:

[1,1,...,1,1,1,0,0,0,0,...0,0]

I would get a cumulative series .

Adding a convolution works because you're giving each data point information about it's neighbours - it's now order dependent.

It might be interesting to try with a guassian convolution or other kernels.

Answer 3

what about using standard Pearson correlation coefficient? then you can assign the new point to the cluster with the highest coefficient.

correlation = scipy.stats.pearsonr(<new time series>, <centroid>)

Answer 4

Another approach would be by utilizing DTW which is an algorithm to compute the similarity between two temporal sequences. Full disclosure; I coded a Python package for this purpose called trendypy, you can download via pip (pip install trendypy). Here is a demo on how to utilize the package. You're just just basically computing the total min distance for different combinations to set the cluster centers.