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;'''Q: Section 4 asks for the plots for the 12 largest eigenvalues. How can these be determined once the SVD is calculated from Z? | ;'''Q: Section 4 asks for the plots for the 12 largest eigenvalues. How can these be determined once the SVD is calculated from Z? | ||
:A - The SVD of Z is given by [U S V]=svd(Z,0). After this is computed, then U is a pXn matrix, and each column of U is an eigenvector | :A - The SVD of Z is given by [U S V]=svd(Z,0). After this is computed, then U is a pXn matrix, and each column of U is an eigenvector | ||
| − | :of the estimated covariance matrix. Furthermore, the singular values S are the square-root of the eigenvalues. | + | :of the estimated covariance matrix. Furthermore, the singular values S are the square-root of the associated eigenvalues. |
:So assuming that the singular values are ordered from largest to smallest, then U(*,1:12) represents the first 12 eigenvectors. | :So assuming that the singular values are ordered from largest to smallest, then U(*,1:12) represents the first 12 eigenvectors. | ||
:You can compute the first 12 projection coefficients for a vector X by computing Y = (U(*,1:12))' X . | :You can compute the first 12 projection coefficients for a vector X by computing Y = (U(*,1:12))' X . | ||
Revision as of 12:31, 22 February 2013
Discussion for Lab 5
Additional Information
Before jumping into the lab, I would get familiar with basic concepts in Bayes Methods
- http://en.wikipedia.org/wiki/Bayesian_inference
- http://en.wikipedia.org/wiki/Eigen_decomposition
- http://en.wikipedia.org/wiki/Principle_components_analysis
Some concepts on what you are actually doing in lab
For data acceleration, consider reading advance software development in the below link
Q&A Section
- Q: How do you calculate the theoretical R for section 2.2? I've calculated the Rhat 2x2 matrix, however I'm not sure how to calculate the theoretical one.
- A - The theoretical values are the known values of the covariance you used to generate the samples in Section 2.1.
- More specifically, they are the values of Rx given in equation (14) of section 2.1.
- Q: I don't understand what is to be produced in section 4 for the projection coefficients. It is an image or a regular plot? The paragraph describing that procedure is not too clear for me.
- A - The section has been re-written to be clearer.
- Q: Do the answers to Section 4 have to match with those provided in the pdf file Examples posted under course notes. Is the training data the same? For me, out of the 12 eigen images 9-10 match but a couple don't. Also, the projection coefficient variation is somewhat different.
- Q: Section 4 asks for the plots for the 12 largest eigenvalues. How can these be determined once the SVD is calculated from Z?
- A - The SVD of Z is given by [U S V]=svd(Z,0). After this is computed, then U is a pXn matrix, and each column of U is an eigenvector
- of the estimated covariance matrix. Furthermore, the singular values S are the square-root of the associated eigenvalues.
- So assuming that the singular values are ordered from largest to smallest, then U(*,1:12) represents the first 12 eigenvectors.
- You can compute the first 12 projection coefficients for a vector X by computing Y = (U(*,1:12))' X .
