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The weight update rule in (1.3) has the nice interpretation that it moves in the direction of classifying correctly.

(a) Show that . [Hint: x(t) is misclassified by .]

Because is misclassified by so:

• : . Hence: .
• : . Hence: .

So: .

(b) Show that . [Hint: Use (1.3).]

My solution for (b) is wrong. Please see: http://problemania.org/wiki/index.php?title=%E3%80%8ALearning_from_Data_-_A_Short_Course%E3%80%8B_Exercise_1.3:_Iterative_perceptron_learning_algorithm (thanks Coleman). is misclassified by so . correcly classifies so (the argument is much alike above).

Hence: .

(c) As far as classifying is concerned, argue that the move from to is a move “in the right direction”.

Check the slide 13 of Lecture 01. Remind yourself the formula: where is the angle between and .

## 4 comments on “Learning From Data – A Short Course: Exercise 1.3”

1. Coleman says:

I think your argument for (b) is wrong. In details, “w(t + 1) is correctly classified” cannot be guaranteed.

1. Vy Nguyen says:

Thank you. You are correct. I misinterpreted the learning algorithm.