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My problem is different from the common time series data problem. What I need to do is check if future time series data is in accord with previous time series data I already consider to be correct.
In short, I need a one-class classifier applied to time series data, which have variable length (going from 110 to 125 points).
Does anyone know any lib that might help me with this task? I usually use Python+scikit-learn, but I'm open to use any other configuration.
Apart from the approach @Rolf Schorpion mentioned, there are others. For example, you could use a deep neural network, specifically, an auto-encoder (see here for a tutorial).
But there's an important catch to all purely "data-driven" approaches: if the figure of 30 time series you mention in the comments is a typical order of magnitude for your training set, the results will be more or less arbitrary. If you don't define "accordance" in any way, this is a classification problem with only positive training data which consists of 30 data points with more than 100 features each.
Unless your data is very, very special (e.g., all time series are identical), there is just too much freedom in the solution of this problem. Different algorithms (or different parameter sets for the same algorithm) will use this freedom in very different ways. So you will probably see very different solutions when you experiment with different methods.
So if you don't want to do more or less arbitrary experiments and choose from the solutions afterwards, you have to use a method in which you somehow define the meaning of "in accordance" in advance. You may try and use traditional time series techniques to find a common model that fits each of the time series well. You could then postulate that "accordance" is a good fit to this model.
Or you might just do some exploratory analysis of your data to decide upon a simple rule which could be used to detect accordance. There's lots of possibilities, and without further details on the application it's difficult to decide which one is appropriate. Delegating the decision of what's "in accordance" to some algorithm doesn't seem to be a good choice in this case, though.
Based on your description, a simple cross-correlation should do it. You are testing whether a series point in the future correlates with a series in the past which you consider correct. This measurement is given exactly by the cross-correlation between the future series and the past series -
The other good thing about cross correlation is you can adjust the length of your series accordingly, which gives a lot of flexibility.
Cross correlation itself might not be enough for your system, as it only provides a measure of difference, you can still build a model for the actual "classification" - since your output are binary, anything simple from a threshold detector (i.e. if xcor > value then 1 else 0) to a small neural network should both work fine.
It sounds like 'novelty detection' is what you might be looking for.
There is a scikit library for this. It generates a one-class model and predicts whether new observations fit into the one class or not.
For further reading, I would like to refer to this link: Novelty detection scikit-learn There you can also find an example using a SVM classifier.
As you (OP) further clarified, you've got equipment sensor data. Your first time-series was recorded when you knew the machine was in good operating condition. Later, you sample another time series, and you want to know if anything has changed. This is called anomaly detection.
You described the time-series as stochastic, meaning there is an element of randomness. There are several interesting methods you can use to find the probability that the two series were generated by the same process (nothing has changed). I'm afraid the answers I've read to your question so far would only work in special cases, and are perhaps too complicated for the job.
The general concept is that there is an underlying probability distribution (described by a 'probability density function' or PDF) which generates your time-series. When the machine gets out of order, that PDF changes. You test if the new distribution is different from the old one. You should use a completely general approach which does not assume a particular form of the PDF (Gaussian, Poisson, Beta, etc).
First, you can always construct and graph the empirical cumulative distribution function or ECDF for each time-series and compare them visually. This requires a qualitative judgement on what "different" looks like.
To make it quantitative, a test from classical statistics is a K-S test. It's a one-liner in R. The disadvantage of this test is, well, it's not Bayesian. :) There are other issues too. That being said, I use the K-S test all the time because it's so fast and easy.
There are many caveats here. You'll probably want to use the first-differences (changes) of sensor data instead of the values themselves. If you have more than a few sensors, you'll probably want to use dimensionality reduction such as principal component analysis (PCA) as well.
I much prefer a Bayesian A-B test. This requires you to construct models of the PDFs to which your data are applied. This generates a PDF which most likely explains your data. In fact, it generates a PDF for each parameter in your PDF. You look to see how much overlap you have in the parameters. Not enough overlap means an anomaly. To get started with Bayesian probability I recommend Python and PYMC and the Bayesian Hackers book.
