7 – Optimizing Centers (Rubber Bands)

So now we know that these four points correspond to the present class center one that was randomly chosen. And these three points over here correspond to class center in the middle. That’s the assignment step. obviously that’s not good enough. Now we have to optimize. And what we are optimizing is, you are minimizing the total quadratic distance. Of our cluster center to the points. We’re now free to move our cluster center. I think of these little blue lines over here as rubber bands, and that we’re trying to find the state of minimum energy for the rubber bands, where the total quadratic error is minimized. And for the top one, I’m going to give you three positions. They’re all approximate, but pick the one that looks best in terms of minimization. And that’s a not a trivial question at all. So one could be right over here, one could be at and one could be right over here. Which one do you think best minimize, or is minimize of the three positions, the total quadratic length of these rubber bands?

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