Does the perceptron algorithm allow w[0] to obtain non-integer values?

[carpdiem]

Since the perceptron algorithm updates each of the weights with y_n * x_n, then it updates w[0] with

w[0] <- w[0] + y_n * x_n[0]

and y_n is +/- 1, and we have defined x_n[0] = 1.

Then, it seems that w[0] may only ever attain values that differ from its initial value by an integer. For example, if we initialized w[0] = 0, then w[0] could never attain a value of 1/2.

This seems like an odd limitation to the perceptron algorithm. Am I interpreting it correctly that this limitation exists, and does this limitation have any other side effects?

[yaser]

Originally Posted by carpdiem

Since the perceptron algorithm updates each of the weights with y_n * x_n, then it updates w[0] with

w[0] <- w[0] + y_n * x_n[0]

and y_n is +/- 1, and we have defined x_n[0] = 1.

Then, it seems that w[0] may only ever attain values that differ from its initial value by an integer. For example, if we initialized w[0] = 0, then w[0] could never attain a value of 1/2.

This seems like an odd limitation to the perceptron algorithm. Am I interpreting it correctly that this limitation exists, and does this limitation have any other side effects?

You are right, but this is not really a limitation since scaling the weight vector up or down leads to an equivalent perceptron, so an integer value of is equivalent to a non-integer value in a properly scaled version.