This was a great explanation. Many thanks. Please upload your other videos on PCA as well.
@brandomiranda6703
2 жыл бұрын
Fantastic lecture! thanks, this is really appreciated! :)
@wojciechkulma7748
3 жыл бұрын
Great explanation, many thanks!
@brandomiranda6703
2 жыл бұрын
Technical question (sorry for the spam). if (will ignore the tildes, all a,bs have them) a = M b but b = v1 (first V SVF from M = U Sig V^T), then how is a not equal to sqrt(lambda1) u1? My reasoning is simple a = M b = U Sig V v1 = sum_r sig_i u_i v^T_i v1 but v^T_i v1 = 0 for i!= 0 and 1 for i=1 so we get a is sig1 u1 where sig1=sqrt lambda_1? Btw, fantastic video! thanks in advance!
@maxturgeon89
2 жыл бұрын
Actually, this relates to your other question above about the constant C. Remember that we want a tilde to have norm 1. So what we have is that a tilde = c sig1 u1. If we add the norm 1 constraint, we'll see that c sig1 must equal 1. In other words, we have a tilde = u1, as expected.
@brandomiranda6703
2 жыл бұрын
What is the value of C? for \tilde a = C M \tilde b when they have to be colinear. To me it results that C=1 and \tilde b = EigenValue(M^TM) should be sufficient to get maximization to work. Is that right or what value of C did you get?
@abdolreza82
Жыл бұрын
If we standardize the data upfront on all sets, do we still need the correlation? I guess we will have correlations through the entire calculations.
@maxturgeon89
Жыл бұрын
If we standardize the data upfront, then the covariance and correlation matrices will be equal, and therefore both approaches become equivalent.
@abdolreza82
Жыл бұрын
Thanks@@maxturgeon89
@mohamedrefaat197
2 жыл бұрын
Great explanation! Will make other recordings from this course be available?
@maxturgeon89
2 жыл бұрын
There is no plan at the moment, unfortunately! Perhaps in the future I could record my PCA lectures, they would be a good companion to the CCA ones.
@kennethlewis1516
2 жыл бұрын
Thank you for this CCA video. While it is informative, right now, I need a video that literally walks me from the original data set of p and q columns of data to the final period of the interpretation. I need a real life example without all the theoretical notation. I am proficient at EXCEL matrix operations and I am proficient with SPSS. I don't know R well enough to use it. I hope you understand. Is there a way you can communicate with me? Thank you. Kenneth
@maxturgeon89
2 жыл бұрын
Thanks for the comment. These lectures were recorded for a course on Multivariate Analysis for graduate students in statistics, so it was definitely more on the theoretical side. But I like your suggestion of a video walking through a data analysis, I'll add it to my list of potential future videos. I don't know Excel or SPSS well enough to tell you how to perform CCA using these software. For R, the main function is "cancor", and it is available with base R (i.e. no need to install any package). There is also the package "vegan", which is a great package for multivariate analysis. It was developed by applied researchers (in this case, ecologists), so it is very much designed to be user-friendly. However, the terminology is sometimes slightly different than what statisticians use.
@brandomiranda6703
2 жыл бұрын
what is the shape of the square root of the variance matrices?
@maxturgeon89
2 жыл бұрын
The variance matrices are positive-definite (symmetric) matrices. Therefore, all their eigenvalues are real and positive. You can get the square root by taking the eigendecomposition Sigma = UDV^T, take the square root of the elements of D, and remultiply the matrices Sigma^{1/2} = UD^{1/2}V^T
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