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I was thinking. Since any data can become linearly seprabale through kernel methods, meaning there is a dimension where this data is linearly seprable, so feed this processed data set into the perceptron algorithm and then it might get to 100 percent accuracy.

Am I correct?

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Yes and no.

Yes: Given a large enough perceptron (with enough layers and enough neurons), you can achieve 100% accuracy on the training set: i.e., you can construct a perceptron that perfectly fits everything in the training set.

No, not necessarily: Depending on the learning task, you might not be able to achieve 100% accuracy on the test set, no matter how large your perceptron is and no matter what your kernel is.

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The use of a nonlinear kernel never gives any guarantees to make any data set linearly separable in the higher dimensional feature space. Kernels are used to map the data from input space onto a higher dimensional space, in which a hyperplane will be better at separating the data (but no guarantee for linear separable higher dimensional mapped data). That is why we can not be sure that perceptron algorithm will work correctly on higher dimensional mapped dataset or not.

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