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Old 10-13-2012, 07:50 PM
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magdon magdon is offline
Join Date: Aug 2009
Location: Troy, NY, USA.
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Default Re: Problem 3.3 Typo

The hypothesis is not a line. The hypothesis is a region on the 2-dimensional space that is +1 and the complement of that region is -1. The boundary that separates the +1 from the -1 region is a line for linear classification. For nonlinear classification the boundary is something else. In either case you can identify the boundary by identifying the regions which are +1 and the regions which are -1.

For nonlinear boundary, there may be more than one x2 for a given x1 or even no x2 for a given x1. This is why the brute force approach is the simplest for identifying the boundary.

Originally Posted by rpistu View Post
Thanks. It seems like what you said is to plot the data that classified based on the hypothesis. However, the problem requires us to plot the original data and the final hypothesis. For linear classification, the hypothesis is a line, so it's easy to plot. But for nonliear classification, for example the 3rd order polynomial feature transform here, I think it really hard to find the corresponding x2 if given x1 for h(x1, x2): x->ᶲ3. I cannot imagine by using the brute force approach.
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