Category Archives: Chemometrics

I got an email from a prospective user of our software the other day that really set me back. Paraphrasing a bit here, it was “Are there any unique features of your PLS algorithm/diagnostics?” The problem with questions like this one is that I never know where to start. But here is what I wrote.

As for “unique features of your pls algorithm,” well, there are numerous ways to calculate a PLS model, but they all pretty much arrive at the same result (which is good). If you’d like to learn more about PLS algorithms and their accuracy, I suggest you have a look at a series of blog posts I did on the subject. See:

Accuracy of PLS Algorithms
Re-orthogonalization of PLS Algorithms
One Last Time on Accuracy of PLS Algorithms
Speed of PLS Algorithms

As to diagnostics, most of the packages use pretty much the same diagnostics, though sometimes they call them by different names. Usually there is a sample distance metric (e.g. T²) and some sort of residual (e.g. Q).

But maybe what you are really looking for is what makes our software unique, rather than our specific PLS algorithm. We have two major packages for chemometrics. The first is our MATLAB-based PLS_Toolbox, the second is our stand-alone product Solo, which is essentially the compiled version of PLS_Toolbox. The two packages provide identical interfaces and share the same model and data formats. The advantage of PLS_Toolbox is that, because it works within the MATLAB environment, it can be run from the command line and functions from it can be incorporated into other analyses. The advantage of Solo is that you don’t have to have MATLAB.

So right off the bat, a unique feature of our software is that there are completely compatible solutions for working with or without MATLAB. And both of these solutions are available on all platforms, including Windows, Mac OSX and Linux. That is unique.

PLS_Toolbox and Solo have the widest available array of analysis methods. This includes PLS and PCA of course, but also PCR, MLR, MCR, PARAFAC, N-PLS, PLS-DA, SIMCA, SVM, KNN, CLS, LWR, MPCA, Cluster Analysis and Batch Maturity. Plus they have a large number of auxiliary tools for Instrument Standardization, Data Transformation, Dynamic Modeling, Sample Selection, Trend Analysis, Correlation Spectroscopy and Design of Experiments. And numerous tools for variable selection including Genetic Algortihm, iPLS and Stepwise MLR. Plus diagnostic methods such as VIP and Selectivity Ratio. The collection of all of these analysis methods and auxiliary functions with one interface is unique.

PLS_Toolbox and Solo can be extended for use with Multivariate Images with MIA_Toolbox and Solo+MIA. The ability to apply such a wide array of multivariate analysis techniques to images is unique. There is also an add-on for the patented Extended Multiplicative Scatter Correction, EMSC_Toolbox. If not completely unique, this method for preprocessing data from highly scattering samples is not widely available.

For on-line application there is our Solo_Predictor and Model_Exporter. Solo_Predictor can be used with any model generated by PLS_Toolbox/Solo and can communicate via TCP/IP sockets, ActiveX, .NET, timed action or wait-for-file. Model_Exporter translates PLS_Toolbox/Solo models into mathematical formulas that can be compiled into other languages. Model_Exporter’s XML output can be parsed for execution in .NET (C#). Additional output formats include MATLAB .m file (compatible with older versions of MATLAB and OCTAVE, plus LabView, Symbion and Tcl). This wide array of on-line options is unique.

Beyond that, PLS_Toolbox and Solo are also extremely flexible tools and include the widest array of data preprocessing methods with user-specified ordering, ability to add user-specified method, and customizable favorites settings.

And finally, price. PLS_Toolbox is only $1395 for industrial users, $395 for academic. Solo is $2195/$695. The price/performance ratio of these products is most certainly unique.

If you have any questions about the specific functionality of our software, please write me.

BMW

Autumn is nearly here and with it comes the first semester of the school year. This morning I was greeted by a sign of fall: a slew of student account creation notifications, drifting into my email inbox like falling leaves.

At EVRI, we work with professors to make our software freely available to students enrolled in chemometrics courses. Students can get free 6-month demo licenses of our MATLAB-based PLS_Toolbox and MIA_Toolbox, or stand-alone Solo or Solo+MIA.

I traded emails this morning with Professor Anna de Juan of the Universitat de Barcelona. This will be the third year we’ve worked with Prof. de Juan on her chemometrics class. She wrote, “we had a very good experience the two semesters using PLS_Toolbox in the classroom. The students were happy and only a pair of them had problems of installation at home. It really made it easy that they could play with proposed data sets out of the classroom, at their own pace and exploring many possibilities.” de Juan noted her students typically use Solo at home because they generally don’t have personal copies of MATLAB.

Another advantage of Solo is that it is available for multiple platforms, including Windows, Linux and Mac OS X. I see lots of Apple laptops on college campuses. A search of the web reveals estimates ranging from 30-70% of college students using Macs. We see a substantial number of student downloads of our Solo for Mac, and expect that number to grow.

Interested in teaching Chemometrics? Drop me a line and we’ll be happy to work with you to provide software for your students.

BMW

Our Chief of Technology Development Jeremy M. Shaver received a very nice letter this morning from Balázs Vajna, who is a Ph.D. student at Budapest University of Technology and Economics. As you’ll see from the references below, he is a very productive young man! Here is his letter to Jeremy, highlighting how he used PLS_Toolbox in his work:

I would like to thank you for all your help with the Eigenvector products. With your help, I was able to successfully carry out detailed investigations using chemical imaging and chemometric evaluation in such a way that I could publish these results in relevant international journals. I would like to draw your attention to the following publications where (only) PLS_Toolbox was used for chemometric evaluation:

1. B. Vajna, I. Farkas, A. Farkas, H. Pataki, Zs. Nagy, J. Madarász, Gy. Marosi, “Characterization of drug-cyclodextrin formulations using Raman mapping and multivariate curve resolution,” Journal of Pharmaceutical and Biomedical Analysis, 56, 38-44, 2011.
2. B. Vajna, H. Pataki, Zs. Nagy, I. Farkas, Gy. Marosi, “Characterization of melt extruded and conventional Isoptin formulations using Raman chemical imaging and chemometrics,” International Journal of Pharmaceutics, 419, 107-113, 2011.

These may be considered as showcases of using PLS_Toolbox in Raman chemical imaging, and – which is maybe even more interesting in the light of your collaboration with Horiba Jobin Yvon – the joint use of PLS_Toolbox and LabSpec. The following studies have also been published where MCR-ALS and SMMA (Purity) were carried out with PLS_Toolbox and were tested along with other curve resolution techniques.

3. B. Vajna, G. Patyi, Zs. Nagy, A. Farkas, Gy. Marosi, “Comparison of chemometric methods in the analysis of pharmaceuticals with hyperspectral Raman imaging,” Journal of Raman Spectroscopy, 42(11), 1977-1986, 2011.
4. B. Vajna, A. Farkas, H. Pataki, Zs. Zsigmond, T. Igricz, Gy. Marosi, “Testing the performance of pure spectrum resolution from Raman hyperspectral images of differently manufactured pharmaceutical tablets,” Analytica Chimica Acta, in press.
5. B. Vajna, B. Bodzay, A. Toldy, I. Farkas, T. Igricz, G. Marosi, “Analysis of car shredder polymer waste with Raman mapping and chemometrics,” Express Polymer Letters, 6(2), 107-119, 2012.

I just wanted to let you know that these publications exist, all using PLS_Toolbox in the evaluaton of Raman images, and that I am very grateful for your help throughout. I hope you will find them interesting.

Best regards,

Balázs
—
Balázs Vajna
PhD student
Department of Organic Chemistry and Technology
Budapest University of Technology and Economics
8 Budafoki str., H-1111 Budapest, Hungary

Thanks, Balázs, your letter just made our day! We’re glad you found our tools useful!

BMW

In the first and second installments of this series, we considered aspects of using an existing PCA model to replace missing variables. In this third part, we’ll move on to using PLS models.

Although it was shown previously that PCA can be used to perfectly impute missing values in rank deficient, noise free data, it’s not hard to guess that PCA might be suboptimal with regards to imputing missing elements in real, noisy data. The goal of PCA, after all, is to estimate the data subspace, not predict particular elements. Prediction is typically the goal of regression methods, such as Partial Least Squares. In fact, regression models can be used to construct estimates of any and all variables in a data set based on the remaining variables. In our 1989 AIChE paper we proposed comparing those estimates to actual values for the purpose of fault detection. Later this became known as regression adjusted variables, as in Hawkins, 1991.

There is a little known function in PLS_Toolbox, (since the first version in 1989 or 90), plsrsgn, that can be used to develop collections of PLS models, where each variable in a data set is predicted by the remaining variables. The regression vectors are mapped into a matrix that generates the residuals between the actual and predicted values in much the same way as the I–PP‘ matrix from PCA.

We can compare the results of using these collections of PLS models to using the PCA done previously. Here we created the coeff matrix using (a conservative) 3 LVs in each of the PLS submodels. Each sub model could of course be optimized individually, but for illustration purposes this will be adequate. The reconstruction error of the PLS models is compared with PCA in the figure shown at left, where the error for the collection of PLS models is shown in red, superimposed over the reconstruction via the PCA model error, in blue. The PLS models’ error is lower for each variable, in some cases, substantially, e.g. variables 3-5.

The second figure, at left, shows the estimate of variable 5 for both the PLS (green) and PCA (red) methods compared to the measured values (blue). It is clear that the PLS model tracks the actual value much better.

Because the estimation error is smaller, collections of PLS models can be much more sensitive to process faults than PCA models, particularly individual sensor faults.

It is also possible to replace missing variables based on these collections of PLS models in (nearly) exactly the same manner as in PCA. The difference is that, unlike in PCA, the matrix which generates the residuals is not symmetric, so the R₁₂ term (see part one) does not equal R₂₁‘. The solution is to calculate b using their average, thus

b = 0.5(R₁₂ + R₂₁‘)R₁₁^-1

Curiously, unlike the PCA case, the residuals on the replaced variables will not be zero except in the unlikely case that R₁₂ = R₂₁‘.

In the case of an existing single PLS model, it is of course possible to use this methodology to estimate the values of missing variables based on the PLS loadings. (Or, if you insist, on the PLS weights. Given that residuals based on weights are larger than residuals based on loadings, I’d expect better luck reconstructing from the loadings but I offer that here without proof.)

In the next installment of this series, we will consider the more challenging problem of building models on incomplete data records.

BMW

B.M. Wise, N.L. Ricker, and D.J. Veltkamp, “Upset and Sensor Failure Detection in Multivariate Pocesses,” AIChE Annual Meeting, 1989.

D.M. Hawkins, “Multivariate Quality Control Based on Regression Adjusted Variables,” Technometrics, Vol. 33, No. 1, 1991.