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Old 05-27-2012, 09:32 AM
AqibEjaz AqibEjaz is offline
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Default HW 8, A case of data being hopelessly inseparable?

I post this question assuming my analysis has been correct. If not then just ignore this path of reasoning.

The data that has been provided for the HW 8 seems to be hopelessly inseparable, particularly for the one-vs-all classification case. Although the accuracy of classification, that I am sure everyone of us is getting, is quite spectacular, but actually it is a spectacle in disguise. Since our training data is heavily skewed, i.e. about 90% of training data comes from one class (say class 'All' in 7-vs-All, where y=-1) and 10 % from the other class (say class '7' in 7-vs-All, where y=1), even a final hypothesis as ridiculous as h(x)=-1 will have 90% accuracy. And this is exactly what I am getting for most of the one-vs-all classifications.

Now this brings me to my actual question and that is how do you approach such a problem where data is so hopelessly inseparable. Perhaps one should look for extracting other kinds of features from the original images. An official comment here would be appreciated.

Thanks.
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Old 05-27-2012, 10:31 AM
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yaser yaser is offline
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Default Re: HW 8, A case of data being hopelessly inseparable?

Quote:
Originally Posted by AqibEjaz View Post
Now this brings me to my actual question and that is how do you approach such a problem where data is so hopelessly inseparable.
With a finite resource of training examples, your best bet is often to accept that the data will not be perfectly separated, and find a compromise between a non-zero E_{\rm in} and a not-so-complex fit that would give good generalization.
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Old 05-27-2012, 01:01 PM
dudefromdayton dudefromdayton is offline
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Default Re: HW 8, A case of data being hopelessly inseparable?

Or leave the box entirely; that is, find or generate data that you can use. Real life is sometimes friendlier than homework in this respect. Few today would try to classify digits solely on an R^2 reduction of symmetry and intensity. So you'd add something else, and see if that data might be separable.
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