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how do I determine whether to use linear, square, or other types of SVM models?

under which criteria should an SVM model be applied in the first place?

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By Default, SVM in Sklearn uses RBF Kernel. You have to try out all the 3 kernels, with different Gamma and C.

SVM treats outliers better and add a penalty on every outlier it detects.

You should understand your data well or vizualize well to know what kernel fits well. SVM literally adds a new dimension to the data to create a hyperplane.

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There is no rule of thumb for choosing best kernel. You should try simpler methods first (linear SVM) and go for more complex ones (RBF Kernel) if you don't get good results.

As @Syenix said, you should try different SVM parameters, which can be done by the grid search method.

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