# Learning From Data – A Short Course: Exercise 1.3

Page 8:

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 .

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

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

I think the above website lists the correct argument.

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