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What is the best multi class classification method with (potentially) endless training input?
The classificator should get trained while a user interacts with the system.
At this time it gets ~ 30 training sets / second for a potentially endless time (probably 30 minutes - 1 hour).
The training must be continuus: When a user cannot be classified with a minimal certainty, the user should be treated as new and the classificator gets trained for a new class.
Which method/library (C#) is suitable for that problem? I will not be able to save all the training data (if all sets will be kept).

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Naive Bayes, LDA and QDA, Decision Trees, Random Forests, Nearest Neighbors etc can be used.

Hashing can be used to handle endless inputs.

I am not good at C, but you can use hashing to include new user in one of the existing user. This will induce Exploit-Explore dilemma.( Thompson sampling and multi-arm bandit for your further study). This way you can have online/real time learning/prediction.

Another classification in batch data is to be performed so that new variables can have exact separate class.

So solution can be a combination of online+Batch learning for your problem.

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