what is bias means?
 

I am confused with the bias.
In wikipedia, w0 is called threshold, so I think it may be any value.
But in this lecture, we make this tuple (1, x0, y0). When in perception process, all changes performed on w0 is +1 or -1, it can't reach the degree of 0.1 or more precious.
Where am I wrong?

Re: what is bias means?
 

This may be a case of notational confusion, as the lectures follow the book notation, not wikipedia. The tuple in the lecture was which is the input vector , and by definition. The weight vector is and all 3 coordinates can assume different values, with being the threshold (also referred to as bias) coordinate.

Re: what is bias means?
 

Thanks dear prof first!
Assume we start at init hypothesis =(0, 0, 0), init target function is =(0.5, 2, 5)
As , equals 0 or 1, = (1, 0.5, 3) etc
When in iteration, , as and can only be 0 or 1, so the hypothesis function's threshold may be quite different from the target function, right?

Re: what is bias means?
 

In your case, the target function is equivalently , , so it can still be implemented with the PLA model even with integer . But of course, learning is not for replicating the target function, but for approximating it. In practice the learned hypothesis is somewhat different from the target function more often than not. Hope this helps.

Re: what is bias means?
 

Problem 1.3 proves that PLA converges (to give the correct sign for each training data point) and in steps of size x as you point out (and of size +/-1 for the 0 component). As w grows in magnitude the fractional accuracy will improve, and after it has converged, normalizing w[1:] to a unit vector gives the direction vector of the separating plane and w[0] will be its' offset from the origin.