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I saw there are some posts on stackexchange on the subject (example1, example2 and example3). However, in this paper, they use SGD as an online learning model. They state that

The incremental learning system comprises of deep and online machine learning models

As far as I understood, in the online model, the initial model is not available and we train a model to be our initial model using online learning. For example deep learning model with SGD. Besides, they state two types of incremental learning: class incremental learning (CIL) and data incremental learning (DIL).

They also state that

Note that the OL model is constructed using features generated from the LSTM model which can be 64, 128 or 256 in length depending on the number of hidden units present in the LSTM model.

So, online learning (OL) model is a separate model? If yes, I do not understand how SGD works in that way.

I, more or less, understood that the class incremental learning is different from online learning because it has new classes which is not the case in online learning. However, I do not understand the difference between online learning and data incremental learning. Maybe using a different loss (e.g. weighted loss) causes to have different learnings but I am not sure. Can anyone give me more explanation about it in the aspect of online, class incremental and data incremental learning?

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The differences between the terms online learning, incremental learning and sequential learning are not sharp, as pointed out already in the other questions linked in this question and the answers therein. Broadly, the term online learning is used when data samples become available sequentially over time, for example, through a data stream, while incremental learning covers the case when the whole dataset may be available completely at any single time point, but it is so large that it is impractical to train the model on the whole dataset directly. In both these two scenarios, the data blocks are used sequentially (hence sequential learning). In incremental learning, new data blocks may contain data on classes already encountered, or new classes. These two cases are denoted as data incremental learning and class incremental learning respectively.

Now, it is completely possible that the new data blocks are generated over time, and become sequentially available as in the problem of user authentication considered in the paper mentioned in the question. So, in such scenarios, methods of online learning need to be combined with data or class incremental learning methodology to get useful results, and this is what is achieved in that paper.

Finally, the terms online learning or incremental learning are used based on how the data blocks become available for analysis and the characteristics of the data contained in those blocks (e.g., whether a new class is present). The terms are not concerned with how the data blocks are analyzed. Stochastic gradient descend, long short-term memory networks as well as good old least squares are all methods to analyze the data. Essentially, the paper employs some suitable methods of analyzing the data, which become available sequentially over time, towards a solution of the particular problem of concern, which is analyzing user authentication behavior.

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