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-   -   Failed to find the bias term for Q14 (http://book.caltech.edu/bookforum/showthread.php?t=4338)

skwong 06-10-2013 04:01 AM

Failed to find the bias term for Q14
 
For Q15, I coded to find the K centers for the RBF. Then use pseudo-inverse to find the w_k. Then have difficulty to find the b. I think it should be calculated by picking any point, and substitute into the formula for x and y:

y - \sum_{k=1}^{K}w_k exp(-\gamma \|x - \mu_{k}\|^2)

But, when I try it for all 100 points, all calculated b are different. Am I mis-understand something ? Or simply my program bug ? I read through all posts in the forum but cannot figure out any hints.

Further, from "on the right track" post, I used the 4 points sample to test my code, I can find those centres and clusters and phi, but cannot match the weights.

Without proper b, I cannot carry on the simulation for the remaining quiz.

bargava 06-10-2013 04:15 AM

Re: Failed to find the bias term for Q15
 
b should be found along with the other weight vectors - using pseudo inverse.

This will be similar to how we did in linear regression. Add a column in the phi matrix with all 1's - and if you solve for w, you will get b.

yaser 06-10-2013 06:08 AM

Re: Failed to find the bias term for Q15
 
Quote:

Originally Posted by skwong (Post 11072)
For Q15, I coded to find the K centers for the RBF. Then use pseudo-inverse to find the w_k. Then have difficulty to find the b. I think it should be calculated by picking any point, and substitute into the formula for x and y:

y - \sum_{k=1}^{K}w_k exp(-\gamma \|x - \mu_{k}\|^2)

But, when I try it for all 100 points, all calculated b are different. Am I mis-understand something ? Or simply my program bug ? I read through all posts in the forum but cannot figure out any hints.

bargava is correct. This was discussed in a post that is buried in another thread:

http://book.caltech.edu/bookforum/sh...40&postcount=7

skwong 06-11-2013 08:03 PM

Re: Failed to find the bias term for Q15
 
Thank you very much bargava and professor. Now I understand what is going on. Many thanks !


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