@Ayoub: Question, if they are applied on enrollement data, then we only have i-vector classes equal to number of enrollement data, so for new user what we do??
@Hamid, Waiting for the response for the comment.....?
It depends on what you're doing. Speaker recognition is a broad term and in practice, you're generally doing either verification (checking if two recordings correspond to the same speaker) or identification (trying to recognize the identity of the speaker persent in the test segment by comparing it to a set of known speaker models).
In these two contexts, "enrollement data" generally means "known speakers" and "test data" means "suspected/unknown speakers". Enrollement data are some kind of "reference" to which you compare your test recordings (either for verification or identification) and "can" be used to train a scoring model, eventhough in general, a different set is used for this matter, which is called "training set".
For example, In the NIST SRE 2010 (speaker recognition evaluation), enrollement and test data (reference speakers and unknown/suspected speakers) are a subset of the NIST 2010 database, while the training data (used to train the UBM, the T matrix AND the PLDA model) belong to a completely different dataset (eg. NIST SRE 2004, 2005, 2006 / Switchboard II Phases 2 and 3 / Switchboard Cellular Parts 1 and 2 / Fisher English Parts 1 and 2/ ..). You can check the "Experiments and results" section of this paper for example [1].
Now what happens if you add a new speaker ? It depends.
1 - If you are adding a new speaker class to your training data (a set of i-vectors corresponding to one particular speaker), you'll have to re-train your scoring model in order to take this new class into account (retrain your PLDA or re-compute your WCCN matrix, ..) and then use the new model to compare your enrollement/test segments. Generally, this does not happen because you're supposed to use as much training data as possible from the start and stick with the same model for all you experiments (otherwise you'll have to redo all your experiments everytime you add new data in order to have comparable results (scores coming from the same model)).
2 - If you're adding new enrollement data (new reference speakers), then nothing changes. The scoring model is supposed to perform as a black box that provides scores for any new test/enrollement utterances. Once it is trained, it is used the same way for any test/enrollement data.
The important thing to understand is that the expression "speaker class" can have different interpretations when used to talk about enrollement and train data. The former refers to a "reference speaker" that will be compared to in the scoring phase (you can compare a test segment to one or many enrollement sessions [2]) while the latter refers to the speaker classes used to train the scoring model. It's like training a PCA or a regression model, the dataset used to train the model is generally independent from the one you're testing on, but if needed, you can transform your training data using the same model.
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References :
[1] Bousquet, Pierre-Michel, et al. "Variance-spectra based normalization for i-vector standard and probabilistic linear discriminant analysis." Odyssey. 2012.
[2] Liu, Gang, et al. "An investigation on back-end for speaker recognition in multi-session enrollment." Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on. IEEE, 2013.