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Define hyperplane $w*x+b=0$, the goal of PLA(Perceptron Learning Algorithm) is minimizing the distance of misclassified points to the decision boundary, i.e. $$-\frac{1}{||w||}\sum_{i\in M} y_i(w*x_i + b)$$ But actual algorithm is $$ \min_{w,b} -\sum_{i\in M} y_i(w*x_i + b)$$

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