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Archive for the ‘Applied math’ Category

The numerical estimate of matrix rank

Friday, January 27th, 2012, 14:25 Posted in Applied math, Chemometrics, Coding | No Comments »

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 ...

A numerically stable PLS algorithm

Friday, December 30th, 2011, 10:53 Posted in Applied math, Chemometrics, Coding | No Comments »

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 ...

Numerically good null spaces

Thursday, November 3rd, 2011, 10:42 Posted in Applied math, Chemometrics, Coding | No Comments »

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 ...

A fast Householder bidiagonalization algorithm

Wednesday, August 10th, 2011, 21:43 Posted in Applied math, Chemometrics, Coding | No Comments »

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. The Householder decomposition is a ...

PLS regression — NEW animation

Thursday, July 21st, 2011, 23:15 Posted in Animation, Applied math, Chemometrics, Video | No Comments »

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 ...

How about orthogonality? How about differences between PLS algorithms?

Wednesday, June 22nd, 2011, 21:51 Posted in Applied math, Better words, Chemometrics | No Comments »

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 ...

Nine algorithms

Monday, March 7th, 2011, 19:35 Posted in Applied math, Chemometrics, Coding | No Comments »

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 ...

Code for analytical separation videos

Wednesday, February 23rd, 2011, 01:31 Posted in Animation, Applied math, Chemistry, Coding | No Comments »

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 ...