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Old 09-29-2012, 07:00 AM
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magdon magdon is offline
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Default Re: Exercise 2.4b

Class means \pm1. (Note: there is no PLA or algorithm here; the VC dimension has only to do with the hypothesis set.)

At this point you have established that some input vector x^* is linearly dependent on the others. If you assign the class (\pm1) of the other vectors appropriately, you should be able to show that the linear dependence dictates that the class of x^* must be (say) +1. This means you cannot implement -1 with the other points having those appropriately chosen classifications, and hence this data set cannot be shattered.

This argument will apply to any data set of d+2 points, and so you cannot shatter any set of d+2 points.

Originally Posted by rozele View Post
The final part of the hint in this question says:
"Now, if you choose the class of these other vectors carefully, then the classification of the dependent vector will be dictated."
The other vectors refers to the set of linearly independent vectors that make up the d+2th vector. What do you mean by class? Do you mean class of vector, (e.g., unit vector), or class based on the PLA algorithm (i.e., +1 or -1)?
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