Given data where the class is categorical (finite and discrete), there are multiple ways to come up with a classifier. One could use multinomial logistic regression, or support vector clustering (implemented, for example, as SVC in scikit-learn). What is the fundamental difference between these two algorithms? When is one better than the other? Are they fundamentally trying to minimize a different type of error?

An entirely different approach is generative algorithms, and in particular naive Bayes. When is that appropriate as opposed to the discriminative alogirthms above?


Your question really requires more of an answer than can really fit in a space like this. Luckily there is a good book on the topic and an electronic copy can be downloaded for free. See The Elements of Statistical Learning.

The book has sections/chapters on each of the topics you ask about.

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