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?
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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?
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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.

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