CODEWITHSUNDEEP
time-seriesdistancehierarchical-clusteringdtw
paolof89
paolof89

Reputation: 1369

Time series distance metric

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 that my cluster algorithm extracts this three centroids [s1, s2, s3]: enter image description here

I want to put this new example [sx] in the most similar cluster:

enter image description here

The most similar centroids is the second one, so I need to find a distance function d that gives me d(sx, s2) < d(sx, s1) and d(sx, s2) < d(sx, s3)

edit

Here the results with metrics [cosine, euclidean, minkowski, dynamic type warping] enter image description here]3

edit 2

User Pietro P suggested to apply the distances on the cumulated version of the time series The solution works, here the plots and the metrics: enter image description here

Upvotes: 11

Views: 8877

Answers (4)

Granary_Oaf
Granary_Oaf

Reputation: 11

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.

Upvotes: 1

Dogan Askan
Dogan Askan

Reputation: 1238

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.

Upvotes: 2

pietroppeter
pietroppeter

Reputation: 1473

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.

Upvotes: 11

lorenzori
lorenzori

Reputation: 747

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>)

Upvotes: 1

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