# Perceptron learning for non-linearly separable data

It is well known that perceptron learning will never converge for non-linearly separable data. This means that you cannot fit a hyperplane in any dimensions that would separate the two classes. Is it possible to do basis transformation to learn more complex decision boundaries for the apparently non-linearly separable data using perceptron classifier?

• By basis transformation, do you mean transforming your features, e.g. $(x,y)$ to $(x,y,x^2,y^2)$? – gunes Apr 3 at 9:28
• Yes. Can I use this transformation and make the data linearly separable in some higher dimension and then apply perceptron? – bandit_king28 Apr 3 at 9:30

## 1 Answer

Not restricted to Perceptron algorithm, the idea behind all transformations is in general making your data more separable, so that the applied algorithm will work fine. Using different kernels (e.g. polynomial, RBF, ...) in SVM carries the same purpose. So, you can do basis transformations in the hope of separating your data; however choice of underlying transformation is crucial and highly depends on your data. An quite related question has been asked lately for logistic regression, with an example of such situation.