The answer of one sentence is that the SVM classifier performs binary classification and SVM regression performs regression .
Performing very different tasks, they are both characterized by the following points.
- use of cores
- lack of local minima
- sparse solutions
- power control obtained by action on the border
- number of supporting vectors, etc.
Loop loss is used to classify SVMs, and epsilon insensitivity is used for SVM regression.
SVM classification is more widely used and, in my opinion, better understood than SVM regression.
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