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I am studying perceptron for the first time. I came across the assumption from online resources that if the data is linearly separable with gamma margin then the perceptron algorithm will converge. Is this true? Also does this assumption mean that if there is a classifier corresponding to w* which separates both classes correctly and no data point lies on it then only the perceptron algorithm will converge?

If this is the case then I got an example where the dataset is linearly separable with gamma margin but the choice of initial weight vector lead to perceptron algorithm oscillate between two weight vectors and hence it doesn't converge.

Does the assumption that no data point should lie on the classifier applies to the final classifier w* or to each classifier we encounter in the perceptron after applying the update rule?

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