I would just like to know what are the differences between kernel classifier and linear classifier?
In what kind of problems the first is used and in what kind the second?
What could be the advantages of the one over the other?
Linear classifiers take lesser time to train and give you only linear decision boundaries. Kernel classifiers need more complicated training algorithms (often involving convex quadratic programming) and provide non-linear classification boundaries. If you know (from eyeball inspection, data analysis) that your data classes are linearly separable, you can use linear classifiers. Otherwise, kernel classifiers are a better option.