The most commonly used function to calculate the matrix rank is probably the one in the MATLAB software package [1]. It is based on the calculation of singular values of the matrix A, and the number of singular values that are greater than some tolerance defines the rank. The algorithm is simple: r = svd(A); …
During 2011 year, I have tried many different ways of making a PLS algorithm (PLS1) as stable possible. The goal was to make it as numerically good as the SVD implemented in MATLAB. The pseudocode that solved the PLS1 case for one y‑varable is shown below and it includes the addition of null vectors to …
There are many methods to obtain null vectors to a given set of vectors. One of the numerically best methods is implemented in MATLAB, based on singular value decomposition, SVD. Null vectors can be used for many different things; one of them is to remove properties that are ore orthogonal to another, given property. Such …
Please note that this is not regarding the Lanczos or the PLS bidiagonalization algorithm. This is about the Householder bidiagonalization algorithm. The difference is huge. For example, there are no y‑variables in the Householder decomposition. It is a decomposition of X that results in a factorization with a bidiagonal matrix in the middle, similar to …
A fast Householder bidiagonalization algorithm Read More »
During the conference in Cape Town on Near Infrared Spectroscopy, NIR2011, I had a keynote in the chemometrics session. I presented a comparison of three different methods for making calibrations including the LOCAL concept by Shenk and Westerhaus, and followng that, I presented another comparison, on different PLS algorithms. As a link between these two …
When good predictive ability is the one and only goal, it is perhaps less important to think about orthogonality. The reason is simple: we decide to only think about the predicted values and we don’t care about looking at anything else in the models we have created. When talking about differences between different linear algorithms …
How about orthogonality? How about differences between PLS algorithms? Read More »
I got a request to send the code of the nine algorithms that were compared in “A comparison of nine PLS1 algorithms” and published in the Journal of Chemometrics 2009; 23: 518–529 and led to the Kowalski price 2010 for best theoretical paper. Then I thought it would be even better if they would be …
My old videos about analytical separation processes should be added to this site. The scripts are still good and easy to modify to simulate different scenario by changing a few parameters. When I first made them in 1996 and 1999, I saved them in mpeg1 formats. Nowadays, other formats are more popular, especially MP4 that …
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