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I have a question about classification of time series. Data has two features and I want to classify it into 5 classes. We have a stream of data and new data is generated every 5 seconds. Moreover in some classes we have inadequate data for training so we have classification problem with imbalanced data. I want to classify new data using machine learning methods according to the pattern shown in the figures. What methods do you suggest?

enter image description here

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Your datastream looks more like a regression problem for me. And in case you are trying to make a classification problem I suggest labelling the segments by hand, since it seems that you have a certain idea what the segments should represent.

Otherwise positive slope (green) and negative slope (pink) can be easily estimated and thus resemble a feature vector.

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