We began by discussing the different types of matrices (positive definite etc). Some lectures for this are here:
http://www.youtube.com/watch?v=26lLZZz0KGg (Symmetric Matrices and Positive Definiteness)
http://www.youtube.com/watch?v=0sCLv2EQPg8 (Complex Matrices; Fast Fourier Transform)
http://www.youtube.com/watch?v=ZW8NWVyt4rg (Positive Definite Matrices and Minima)
From Gilbert Strang's lecture on SVD, we identified the most important aspects to be the geometric picture(3:00-4:38) and the equations(7:40-17:00). Here is the lecture:
http://www.youtube.com/watch?v=c9271ZFGKrU
Ina would post the Matlab commands for SVD on the blog. We would all look at the ICA/ NCA papers on our own.
For next week, we decided to look at feature selection. A good paper for this is
http://www.cs.waikato.ac.nz/~mhall/HallHolmesTKDE.pdf
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Matlab code for svd is:
[U,S,V] = svd(X)
Some variations for return variables include:
s = svd(X)
[U,S,V] = svd(X,0)
[U,S,V] = svd(X,'econ')
where
s = svd(X) returns a vector of singular values.
[U,S,V] = svd(X) produces a diagonal matrix S of the same dimension as X, with nonnegative diagonal elements in decreasing order, and unitary matrices U and V so that X = U*S*V'.
[U,S,V] = svd(X,0) produces the "economy size" decomposition. If X is m-by-n with m > n, then svd computes only the first n columns of U and S is n-by-n.
[U,S,V] = svd(X,'econ') also produces the "economy size" decomposition. If X is m-by-n with m >= n, it is equivalent to svd(X,0). For m < n, only the first m columns of V are computed and S is m-by-m.
Ref: mathworks Help.
Try handout : http://www.math.udel.edu/~monk/Classes/m611/MATLAB-Handout-4.pdf
Also memory considerations/ discussions are present at :
1. http://mathforum.org/kb/message.jspa?messageID=6428150&tstart=0
2. http://mathforum.org/kb/message.jspa?messageID=6428215&tstart=0
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