Classifying time-series similarity - what variable should I train on?

I have ~10,000 time series, each with 65 time points. I'm interested in classifying each pair of time series as "similar" or "not similar". Here's an example of two similar (left) and not similar time series (right): I know a priori whether some pairs should be "similar" or not, so I have class labels and can train a classifier. The inputs I'm using for the classifier are i) correlation coefficient between the two time series and ii) Euclidean distance.

My question is, what other statistics measure similarity of time series like this and could be used as input for the classifier? Dynamic time warping? I'm interested in calculating a number of measures for input into the classifier. I'd be really grateful if anyone can suggest others.

Edit: Here are more examples of "similar" (top) and "not similar" pairs (bottom). Edit2: Responding to Eamonn's answer, this is the histogram of Euclidean distance for the Similar (magenta) and Non-Similar class (cyan). Euclidean distance is informative, but it's not enough to perfectly classify the pairs. hard to say from just two examples.

is the amplitude important? If so, try the area under the curves as a feature.

if not, you need to z-normalize the data.

This paper lists many many possible time series features http://arxiv.org/pdf/1401.3531.pdf

I could help you more, if you showed many more examples.

eamonn keogh

• Thanks a lot. I added more examples. The time series are well-modelled with a Gaussian mixture model, so I will also try using features based on the Gaussian parameters. – R Greg Stacey Feb 1 '16 at 18:09
• This paper (yours) is also very relevant when dealing with time-series cs.ucr.edu/~eamonn/SIGKDD_trillion.pdf – Vladislavs Dovgalecs Feb 5 '16 at 0:49

Based on the examples you show, simple Euclidean distance will get you 100% accuracy. This appears to be VERY easy.

• Sorry, my bad. I only showed clean examples (TP and TN, as picked out by the classifier). I added another figure showing how the two classes are separated by Euclidean distance. You can see that a Euclidean distance threshold is not enough to perfectly classify. Same goes for all other metrics I tried. – R Greg Stacey Feb 4 '16 at 23:38