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I am interested in clustering multivariate N time series of T'values' each(different lengths) using python. Each variable have many trends and values which are simultaneously numeric and nominal.

A sample $T_{i}$ in the dataset has the following format:

TimeStamp       | Sensor0 | Sensor1| Sensor2
2015-02-05 11:30|<Min     | On     | off
2015-02-05 11:31|<Min     | on     | off 
2015-02-05 11:32| Action2 | 10     | 0.0001  
2015-02-07 11:33| Action2 | 10     | 0.00012 
2015-02-07 11:34| Action2 | 10     | 0.00012 
2015-02-07 11:35| Action2 | 20     | 0.00015 

Another sample $T_{j}$ in the dataset has the following format:

TimeStamp       | Sensor0 | Sensor1| Sensor2
2015-10-05 11:30| Action2 | 11     | off
2015-10-05 11:31| Action1 | 11     | off 
2015-10-05 11:32| Action2 | NAN    | 0.0001  
2015-10-07 11:33| Action3 | NAN    | 0.00012 
2015-10-07 11:34| <Min    | 10     | 0.00012 
2015-10-07 11:35| <Min    | 15     | on 

For the missing values (not numeric), they were not collected by the sensors so my idea was to replace them by minimum values., given that all values are strictly positive. Otherwise, they would be considered as missing values. In which case the problem would be of finding a similiraty measure that can compare missing values (off,on..) and numeric values.

I am wondering if there is a similarity / distance measure already exist in the litterature to compare such multivariate timeseries, with hetergonuos lengths, and whether this kind of problem has already been formulated in the papers, books or else for R and python.

Thanks for your advice.

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  • $\begingroup$ Fit the time series to a model, and cluster the model parameters. $\endgroup$ – Emre Aug 16 '16 at 19:45
  • $\begingroup$ @ emre thank you for your response. I just can't seem to find a way of finding the right modeling framework for such context. So you have a specific method in mind? $\endgroup$ – user23440 Aug 16 '16 at 21:48
  • $\begingroup$ I'd use a neural network. $\endgroup$ – Emre Aug 16 '16 at 21:51
  • $\begingroup$ That's indeed a very good paper. I am a newbie to deep learning. It will be difficult for me to implement it in python. Do you know of good resources for a beginner(books moods github..)? $\endgroup$ – user23440 Aug 16 '16 at 22:24
  • $\begingroup$ Start here, then try these time series tutorials. $\endgroup$ – Emre Aug 16 '16 at 23:03
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Try this recent paper: Consistent Algorithms for Clustering Time Series.

Your question is very much a current research topic.

Here's an older but excellent paper which talks about the fundamentals: Generalized Feature Extraction for Structural Pattern Recognition in Time-series Data.

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  • $\begingroup$ @ Pete thank you for your response.this seems to me an interesting avenue to explore.I will get back to you when I finish reading $\endgroup$ – user23440 Aug 16 '16 at 21:49

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