Category Archives: Chemometrics
Jun 16, 2022
There are a number of measures that are used to evaluate the performance of machine learning/chemometric models for calibration, i.e. for predicting a continuous value. Most of these come down to reducing the model error, the difference between the reference values and the values predicted (estimated) by the model, to some single measure of “goodness.” The most ubiquitous measure is the correlation coefficient R2. Many people have produced examples of how data sets can be very different and still produce the same R2 (see for example What is R2 All About?). Those arguments are important but well known and I’m not going to reproduce them here. My main beef with R2 is that it is not in the units that I care about; it is in fact dimensionless. Models used in the chemical domain typically predict values like concentration (moles per liter or weight percent) or some other property value like tensile strength (kilo-newtons per mm2) so it is convenient to have the model error expressed in these terms. That’s why the chemometrics community tends to rely on the measures like root mean square error of calibration (RMSEC). This measure is in the units of the property being predicted.
We also want to know about “goodness” in a number of different circumstances. The first is when the model is being applied to the same data that was used to derive it. This is the error of calibration and we often refer to the calibration R2 or alternately the RMSEC. The second situation is when we are performing cross validation (CV) where the majority of the calibration data set is used to develop the model and then the model is tested on the left out part, generally repeating this procedure until all samples (observations) have been left out once. The results are then aggregated to produce the cross-validation equivalent of R2, which is Q2, or the cross validation equivalent of RMSEC, which is RMSECV. Finally, we’d like to know how models perform on totally independent test sets. For that we use the prediction Q2 and the RMSEP.
Besides the fact that R2 is not in the same units as the value being predicted, it has a non-linear relationship with it. In the plot below the RMSEC is plotted versus R2 for a synthetic example.
Overfit is another performance measure of interest. The amount of overfit is the difference between the error of calibration (R2 or RMSEC) and prediction, typically in cross-validation (Q2 or RMSECV). Generally, model error is lower in calibration than in cross validation (or prediction, but that is subject to corruption by prediction test set selection). So a somewhat common plot to make is R2-Q2 versus Q2. (I first saw these in work by David Broadhurst.) An example of such a plot is shown in Figure 2 on the left for a simple PLS model where each point is using a different number of LVs. The problem with this plot is that neither axis is physically meaningful. We know that the best models should somehow be in the lower right corner, but how much difference is significant? And how does it relate to the accuracy with which we need to predict?
I propose here an alternative, which is to plot the ratio of RMSECV/RMSEC versus RMSECV, which is shown in Figure 2 on the right. Now the best model would be in the lower left corner, where the amount of overfit is small along with the prediction error in cross-validation.
Lately I’ve been working with Gray Classical Least Squares (CLS) models, where Generalized Least Squares (GLS) weighting filters are used with CLS to improve performance. Without going into details here (for more info see this presentation) the model can be tuned with a single parameter, g, which governs the aggressiveness of the GLS filter. A data set of NIR spectra of a styrene-butadiene co-polymer system is used as an example (data from Dupont thanks to Chuck Miller). The goal of the model is to predict the weight percent of each of the 4 polymer blocks. The R2-Q2 versus Q2 plot for the four reference concentrations are shown in the left panel of Figure 3 while the corresponding RMSECV/RMSEC versus RMSECV curves are shown the right. The g parameter is varied from 0.1 (least filtering) to 0.0001 (most filtering).
As in figure 2 approximately the same information is presented in each plot but the RMSECV/RMSEC plot is more easily interpreted. For instance, the R2-Q2 plot would lead one to believe that the predictions for 1-2-butadiene were quite a bit better than for styrene as their Cross-validation Q2 is substantially better. However, the RMSECV/RMSEC plot shows that the models perform similarly with an RMSECV around 0.8 weight percent. The difference in Q2 for these models is a consequence of the distribution of the reference values and is not indicative of a difference in model quality. The RMSECV/RMSEC shows that the models are somewhat prone to overfitting as this ratio goes to rather high values for aggressive GLS filters. The is less obvious in the R2-Q2 plot as it is not obvious what this difference really relates to in terms of amount of overfitting. And a given change in R2-Q2 is more significant in models with high Q2 than with lower Q2. The R2-Q2 plot would lead one to believe that the 1-2-butadiene model was not overfit much even at g = 0.0001, whereas the styrene model is. In fact, their RMSECV/RMSEC ratio is over 5 for both these models at the g = 0.00001 point, which is terribly overfit.
The RMSECV/RMSEC plot can be further improved if the reference error in the property being predicted is known. In general it is not possible for the apparent model performance to be better than this. Even if the model is predicting the divine omniscient only God knows true answer, the apparent error will still be limited by the error in the reference values. Occasionally models do appear to predict better than the reference error but this is generally a matter of luck. (And yes, it is possible for models to predict better than the reference error, but that is a demonstration for another time.) So it would be useful to add the (root mean square or standard deviation) reference error, if known, as a vertical line.
Based upon the results I’ve seen to date, I highly recommend the RMSECV/RMSEC plot over the R2-Q2 plot for assessing model performance. Model fit and cross-validation metrics are in units of the properties being predicted, and the plots are more linear with respect to changes in these metrics. This plot is easily made for PLS models in PLS_Toolbox and Solo, of course!
Feb 23, 2022
The term chemometrics was coined by Svante Wold in a grant application he submitted in 1971 while at the University of Umeå. Supposedly, he thought that creating a new term, (in Swedish it is ‘kemometri’), would increase the likelihood of his application being funded. In 1974, while on a visit to the University of Washington, Svante and Bruce Kowalski founded the International Chemometrics Society over dinner at the Casa Lupita Mexican restaurant. I’d guess that margaritas were involved. (Fun fact: I lived just a block from Casa Lupita in the late 70s and 80s.)
Chemometrics is a good word. The “chemo” part of course refers to chemistry and “metrics” indicates that it is a measurement science: a metric is a meaningful measurement taken over a period of time that communicates vital information about a process or activity, leading to fact-based decisions. Chemometrics is therefore measurement science in the area of chemical applications. Many other fields have their metrics: econometrics, psychometrics, biometrics. Chemical data is also generated in many other fields including biology, biochemistry, medicine and chemical engineering.
So chemometrics is defined as the chemical discipline that uses mathematical, statistical, and other methods employing formal logic to design or select optimal measurement procedures and experiments, and to provide maximum relevant chemical information by analyzing chemical data.
In spite of being a nearly perfect word to capture what we do here at Eigenvector, there are two significant problems encountered when using the term Chemometrics: 1) In spite of the existence of the field for nearly five decades and two dedicated journals (Journal of Chemometrics and Chemometrics and Intelligent Laboratory Systems), the term is not widely known. I still run into graduates of chemistry programs who have never heard the term, and of course it is even less well known in the related disciplines, and less yet in the general population. 2) Many that are familiar with the term think it refers to a collection of primarily projection methods, (e.g. Principal Components Analysis (PCA), Partial Least Squares Regression (PLS)), and therefore other Machine Learning (ML) methods (e.g. Artificial Neural Networks (ANN), Support Vector Machines (SVM)) are not chemometrics regardless of where they are applied. Problem number 2 is exacerbated by the current Artificial Intelligence (AI) buzz and the proclivity of managers and executives towards things that are new and shiny: “We have to start using AI!”
This wouldn’t matter much if choosing the right terms wasn’t so critical to being found. Search engines pretty much deliver what was asked for. So you have to be sure you are using terms that are actually being searched on. So what to use?
A common definition of artificial intelligence is the theory and development of computer systems able to perform tasks that normally require human intelligence. This is a rather low bar. Many of the models we develop make better predictions than humans could to begin with. But AI is generally associated with problems such as visual perception and speech recognition, things that humans are particularly adept at. These AI applications generally require very complex deep neural networks etc. And so while you could say we do AI this feels like too much hyperbole, and certainly there are other arguments against using this term loosely.
Machine learning is the use and development of computer systems that are able to learn and adapt without following explicit instructions, by using algorithms and statistical models to analyze and draw inferences from patterns in data. Most researchers (apparently) view ML as a subset of AI. Do a search on “artificial intelligence machine learning images” and you’ll find many Venn diagrams illustrating this. I tend to see it as the other way around: AI is the subset of ML that uses complex models to address problems like visual perception. I’ve always had a problem with the term “learning” as it anthropomorphizes data models: they don’t learn, they are parameterized! (If these models really do learn I’m forced to conclude that I’m just a machine made out of meat.) In any case, models from Principal Components Regression (PCR) through XGBoost are commonly considered ML models, so certainly the term machine learning applies to our software.
Process analytics is a much less used term and particular to chemical process data modeling and analysis. There are however conferences and research centers that use this term in their name, e.g. IFPAC, APACT and CPACT. Cheminformatics sounds relevant to what we do but in fact the term refers to the use of physical chemistry theory with computer and information science techniques in order to predict the properties and interactions of chemicals.
Data science is defined as the field that uses scientific methods, processes, algorithms and systems to extract knowledge and insights from data. Certainly this is what we do at Eigenvector, but of course primarily in chemistry/chemical engineering where we have a great deal of specific domain knowledge such as the fundamentals of spectroscopy, chemical processes, etc. Thus the term chemical data science describes us pretty well.
So you will find that we will use the terms Machine Learning and Chemical Data Science a lot in the future though we certainly will continue to do Chemometrics!
Jan 28, 2021
The development of a machine learning model is typically a fairly involved process, and the software for doing this commensurately complex. Whether it be a Partial Least Squares (PLS) regression model, Artificial Neural Network (ANN) or Support Vector Machine (SVM), there are a lot of calculations to be made to parameterize the model. These include everything from calculation of projections, matrix inverses and decompositions, computing fit and cross-validation statistics, optimization, you name it, it’s in there. Lots of loops and logic and checking convergence criteria, etc.
On the other hand, the application of these models, once developed, is typically quite straight forward. Most models can be applied to new data using a fairly simple recipe involving matrix multiplications, scalings, projections, activation functions, etc. There are exceptions, such as preprocessing methods like iterative Weighted Least Squares (WLS) baselining and models like Locally Weighted Regression (LWR) where you really don’t have a model per se, you have a data set and a procedure. (More on WLS and LWR in a minute!) But in the vast majority of cases effective models can be developed using methods whose predictions can be reduced to simple formulas.
Enter Model_Exporter. When you create any of the models shown at right (key to acronyms below) in PLS_Toolbox or Solo, Model_Exporter can take that model and create a numerical recipe for applying it to new data, including the supported preprocess steps. This recipe can be output in a number of formats, including MATLAB .m, Python .py or XML. And using our freely available Model_Interpreter, the XML file can be incorporated into Java, Microsoft .NET, or generic C# environments.
So what does all this mean?
- Total model transportability. Models can be built into any framework you need them in, from process control systems to hand-held analytical instruments.
- Minimal footprint. Exported model also have a very small footprint and minimal computing overhead. This means that they can be made to run with minimal memory and computing power.
- Order of magnitude faster execution. Lightweight recipe produces predictions much faster than the original model.
- Complete transparency. There’s no guessing as to exactly how the model gets from measurements to predictions, it’s all there.
- Simplified model validation. Don’t validate the code that makes the model, validate the model!
This is why our customers in many industries, from analytical instrument developers to the chemical process industries, are getting their models online using Model_Exporter. It is creating a revolution in how online models are generated and executed.
And what about those cases like WLS and LWR noted above? We’re working to create add-ons so exported models can utilize these functions too. Look for them, along with some additional model types, in the next release.
Is it for everybody? Well not quite. There are still times where you need a full featured prediction engine like our Solo_Predictor that has built in communication protocols (e.g. socket connections), scripting ability, and can run absolutely any model you can make in PLS_Toolbox or Solo (like hierarchical and even XGBoost). But we’re seeing more and more instances of companies utilizing the advantages of Model_Exporter.
Join the Model_Exporter revolution for the compact, efficient and seamless application of your machine learning models!
Models Supported: Principal Components Analysis (PCA), Multiple Linear Regression (MLR), Principal Components Regression (PCR), Partial Least Squares Regression (PLS), Classical Least Squares (CLS), Artificial Neural Networks (ANN), Support Vector Machine Regression (SVM), Partial Least Squares Discriminant Analysis (PLS-DA), Support Vector Machine Discriminant Analysis (SVM-DA), Artificial Neural Network Discriminant Coming Soon: Analysis (ANN-DA), Locally Weighted Regression (LWR), Logistic Regression Discriminant Analysis (LREG-DA).
Preprocessing Methods Supported: General scaling and centering options including Mean and Median Centering, Autoscaling, Pareto and Poisson Scaling, Multiplicative Scatter Correction (MSC), Savitsky-Golay Smoothing and Derivatives, External Parameter Orthogonalization (EPO), Generalized Least Squares Weighting (GLSW), Extended Least Squares, Standard Normal Variate (SNV), 1-, 2-, infinity and n-norm Normalization, Fixed point spectral baselining. Coming Soon: Iterative Weighted Least Squares Baselining (WLS) and Whittaker Baslining.
Apr 15, 2020
I just finished reading “Bad Blood: Secrets and Lies in a Silicon Valley Startup” by John Carreyrou. It is the story of Theranos and its founder Elizabeth Holmes. Our Bob Roginski sent it to me after I mentioned that I’d seen the HBO documentary “The Inventor: Out for Blood in Silicon Valley.” I highly recommend the book over the much shorter documentary.
I’ve followed this story a bit since first hearing of Theranos and their claims to be able to run hundreds of blood tests simultaneously on just a few drops of blood. Based on my experience this seemed more than unlikely. At Eigenvector we’ve worked on quite a few medical device development projects. This includes projects involving atherosclerotic plaques, cervical cancer, muscle tissue oxygenation, burn wound healing, limb ischemia, non-invasive glucose monitoring, non-invasive blood alcohol estimation and numerous other projects involving blood and urine tests. So we’ve developed an appreciation of how hard it is to develop new analytical techniques on biological samples. Beyond that, we’ve also learned a lot about the error in the reference methods we were trying to match. Even under ideal conditions, with standard laboratory equipment and large sample volumes, results are far from perfect.
So when the whole thing was blown wide open by Carreyrou’s reports in the Wall Street Journal I wasn’t surprised. I read several of the follow up articles as well. But as one reviewer of the book said, “No matter how bad you think the Theranos story was, you’ll learn that the reality was actually far worse.” I’ll say. Honestly it took me a while to get into the book, in fact, I put it down for a month because it just made me so mad.
We’ve had a few consulting clients over the years that were, let’s say, overly enthusiastic. To varying degrees some of them have been unrealistic about the robustness of their technology and have failed to address problems that could potentially impact accuracy. (I’m happy to report that none of our current consulting clients fall into this category.) In some instances things we saw as potential show stoppers were simply declared non-problems. In other cases people abused the data including cherry picking and grossly overfit and non-validated models. (My favorite line was when one client’s lawyer told me I didn’t know how to use my own software.) We have had falling outs with some of these folks when our analysis didn’t support their contentions.
But none of the people we’ve dealt with approached the level of overselling their technology to the degree that Holmes took it. As I see it there are two reasons for this. The first is that Holmes is a sociopath. Carreyrou said he would leave it to others to make that assessment but it seems obvious to me. Maybe she didn’t start out that way, but it’s clear that very early on she started believing her own bullshit. Defending that belief became all that mattered. And she teamed with Ramesh “Sunny” Balwani who was if anything worse. They ran an organization that was based on secrecy, lies and intimidation. And they made sure that nobody on their board had the scientific background to question the feasibility of what they were claiming they’d do.
But the second reason they got as far as they did was because they were exceedingly well connected. The book identifies these connections but doesn’t really discuss them in terms of being enablers of the scam that ensued. It started with Elizabeth’s parents connections to people around Stanford, and Elizabeth’s ChemE professor at Stanford, Channing Robertson. These lead to funding and legal help. From there Holmes just played leapfrog with these connections ending at former secretary of State George Shultz, (who I learned actually lives on the Stanford campus) and his circle including Henry Kissinger, James Mattis and high profile lawyer David Boies. (Boies led the Justice Department’s anti-trust suit against Microsoft, and was Al Gore’s lawyer in he 2000 election.) Famous for his scorched earth tactics, Boies and his firm kept the lid on things at Theranos by threatening lawsuits against potential whistleblowers and further intimidating them by hiring private eyes to surveil them. Having no firmer grasp of the science and engineering realities of what Theranos was attempting than the board members, Boies’ firm did this in exchange for stock options.
It’s second point here that really bothers me. There will always be people like Holmes that are willing to ignore the damage that they may do to others while pursuing wealth or fame and fortune. But this behavior was enabled by well-heeled and well-connected people that failed completely on their due diligence obligations from financial, scientific and most importantly, medical ethics perspectives. Somehow they completely forgot Carl Sagan’s adage “extraordinary claims require extraordinary evidence.” It’s hard to imagine that this could have ever gotten so far out of hand had Holmes attended a state university and had unconnected parents. Investors to whom you are not connected and who are not so wealthy as to be able to afford to lose a lot of money have a much higher standard of proof.
In our consulting capacity at Eigenvector we always try to be optimistic about what’s possible, and we do our best to help clients achieve success. But we never pull our punches with regards to the limitations of the technology we’re working with and the models we develop based on the data it produces. Theranos produced millions of inaccurate blood tests that were eventually vacated. While it doesn’t appear that anybody actually died because of these inaccurate tests, they certainly caused a lot of anxiety, lost time and expense among the customers. It’s our pledge that we will always do our due diligence, and expect those around us to do the same, so that Eigenvector will never be part of a fiasco like this.
Feb 4, 2020
I’ve just returned from Conference Chimiométrie 2020, the annual French language chemometrics conference, now in its 21st edition. The conference was held in Liège and unfortunately there wasn’t much time to explore the city. I can tell you they have a magnificent train station, Gare de Liège is pictured at right.
The vibrant French chemometrics community always produces a great conference with good attendance, well over 120 at this event, and food and other aspects were as enjoyable as ever thanks to the local organizing committee and conference chair Professor Eric Ziemons.
Age Smilde got the conference off to a good start with “Common and Distinct Components in Data Fusion.” In it he described a number of different model forms, all related to ANOVA Simultaneous Components Analysis (ASCA), for determining if the components in different blocks of data are unique or shared. What struck me most about this talk and many of the ones that followed is that there are a lot of different models out there. As Age says, “Think about the structure of your data!” The choice of model structure is critical to answering the questions posed to the data. And it is only with solid domain knowledge that appropriate modeling choices are made.
In addition to a significant number of papers on multi-block methods, Chimiométrie included quite a few papers in the domain of metabolomics, machine learning, Bayesian methods, and a large number of papers on hyper spectral image analysis (see the Programme du Congrès). All in all, a very well rounded affair!
I was pleased to see a good number of posters that utilized our PLS_Toolbox and in some instances MIA_Toolbox software very well! The titles are given below with links to the posters. We’re always happy to help researchers achieve an end result or provide a benchmark towards the development of new methods!
Development of plant phenotyping tools for potato resistance against Phytophthora infestans by François Stevens et. al.
Quantitative resolution of emulsifiers in an agrochemical formulation by S. Mukherjee et. al.
Partial Least Squares (PLS) versus Support Vector Machine (SVM) and Artificial Neural Network (ANN). Which model is the best performer in predicting monosaccharide content of pharmaceutical proteins based on their FT-IR spectrum? by Sabrina Hamla et. al.
Thanks again to the conference organizers. À l’année prochaine!
Jan 29, 2020
A colleague wrote to me recently and asked if Eigenvector was considering rebranding itself as a Data Science company. My knee-jerk response was “isn’t that what we’ve been for the last 25 years?” But I know exactly what she meant: few people have heard of Chemometrics but everybody has heard about Data Science. She went on to say “I am spending increasing amounts of time calming over-excited people about the latest, new Machine Learning (ML) and Artificial Intelligence (AI) company that can do something slightly different and better…” I’m not surprised. I know it’s partly because Facebook and LinkedIn have determined that I have an interest in data science, but my feeds are loaded with ads for AI and ML courses and data services. I’m sure many managers subscribe to the Wall Street Journal’s “Artificial Intelligence Daily” and, like the Stampeders on Chilkoot Pass pictured below, don’t want to miss out on the promised riches.
Oh boy. Déjà vu. In the late 80s and 90s during the first Artificial Neural Network (ANN) wave there were a slew of companies making similar promises about the value they could extract from data, particularly historical/happenstance process data that was “free.” One slogan from the time was “Turn your data into Gold.” It was the new alchemy. There were successful applications but there were many more failures. The hype eventually faded. One of biggest lessons learned: Garbage In, Garbage Out.
I attended The MathWorks Expo in San Jose this fall. In his keynote address, “Beyond the ‘I’ in AI,” Michael Agostini stated that 80-90% of the current AI initiatives are failing. The main reason: lack of domain knowledge. He used as an example the monitoring of powdered milk plants in New Zealand. The moral of the story: you can’t just throw your data into a ML algorithm and expect to get out anything very useful. Perhaps tellingly, he showed plots from Principal Components Analysis (PCA) that helped the process engineers involved diagnose the problem, leading to a solution.
Another issue involves what sort of data is even appropriate for AI/ML applications. In the early stages of the development of new analytical methods, for instance, it is common to start with tens or hundreds of samples. It’s important to learn from these samples so you can plan for additional data collection: that whole experimental design thing. And in the next stage you might get to where you have hundreds to thousands of samples. The AI/ML approach is of limited usefulness In this domain. First off it is hard to learn much about the data using these approaches. And maintaining parsimony is challenging. Model validation is paramount.
The old adage “try simple things first” is still true. Try linear models. Use your domain knowledge to select sample sets and variables, and to select data preprocessing methods that remove extraneous variance from the problems. Think about what unplanned perturbations might be affecting your data. Plan on collecting additional data to resolve modeling issues. The opposite of this approach is what we call the “throw the data over the wall” model where people doing the data modeling are separate from the people who own the data and the problem associated with it. Our experience is that this doesn’t work very well.
There are no silver bullets. In 30 years of doing this I have yet to find an application where one and only one method worked far and away better than other similar approaches. Realize that 98% of the time the problem is the data.
So is Eigenvector going to rebrand itself as a Data Science company? We certainly want people to know that we are well versed in the application of modern ML methods. We have included many of these tools in our software for decades, and we know how to work with these methods to obtain the best results possible. But we prefer to stay grounded in the areas where we have domain expertise. This includes problems in spectroscopy, analytical chemistry, chemical process monitoring and control. We all have backgrounds in chemical engineering, chemistry, physics, etc. Plus collectively over 100 man-years experience developing solutions that work with real data. We know a tremendous amount about what goes wrong in data modeling and what approaches can be used to fix it. That’s where the gold is actually found.
Jan 1, 2020
Eigenvector Research, Inc. was founded on January 1, 1995 by myself and Neal B. Gallagher, so we’re now 25 years old. On this occasion I feel that I should write something though I’m at a bit of loss with regards to coming up with a significantly profound message. In the paragraphs below I’ve written a bit of history (likely overly long).
We started Eigenvector with each of us buying a Power Mac 8100 with keyboard, mouse and monitor. These were about $4k, plus another $1700 to upgrade the 8Mb RAM it came with to 32Mb. Liz Callanan at The MathWorks gave us our first MATLAB licenses-thanks! PLS_Toolbox was in version 1.4 and still being marketed under Eigenvector Technologies. Our founding principle was and still is:
Life is too short to drink bad beer, do boring work or live in a crappy place.
That’s a bit tongue-in-cheek but it’s basically true. We certainly started Eigenvector to keep ourselves in interesting work. For me that meant continuing with chemometrics, data analysis in chemistry. New data sets are like Christmas presents, you never know what you’ll find inside. For Neal I think it meant anything you could do that let you use math on a daily basis. Having both grown up in rural environments and being outdoor enthusiasts location was important. And the bit about beer is just, well, duh!
As software developers we found it both interesting and challenging to make tools that allowed users (and ourselves!) to build successful models for calibration, classification, MSPC etc. As consultants we found a steady stream of projects which required both use of existing chemometric methods and adaptation of new ones. As we became more experienced we learned a great deal about what can make models go bad: instrument drift, differences between instruments, variable and unforeseen background interferents, etc. and often found ourselves as the sanity check to overly optimistic instrument and method developers. Determining what conclusions are supportable given the available data remains an important function for us.
Our original plan included only software and consulting projects but we soon found out that there was a market for training. (This seems obvious in retrospect.) We started teaching in-house courses when Pat Wiegand asked us to do one at Union Carbide in 1996. A string of those followed and soon we were doing workshops at conferences. And then another of our principles kicked in:
Let’s do something, even if it’s wrong.
Entrepreneurs know this one well. You can never be sure that any investment you make in time or dollars is actually going to work. You just have to try it and see. So we branched out into doing courses at open sites with the first at Illinois Institute of Technology (IIT) in 1998, thanks for the help Ali Çinar! Open courses at other sites followed. Eigenvector University debuted at the Washington Athletic Club in Seattle in 2006. We’re planning the 15th Annual EigenU for this spring. The 10th Annual EigenU Europe will be in France in October and our third Basic Chemometrics PLUS in Tokyo in February. I’ve long ago lost count of the number of courses we’ve presented but it has to be well north of 200.
Our first technical staff member, Jeremy M. Shaver, joined us in 2001 and guided our software development for over 14 years. Our collaborations with Rasmus Bro started the next year in 2002 and continue today. Initially focused on multi-way methods, Rasmus has had a major impact on our software from numerical underpinnings to usability. Our Chemometrics without Equations collaboration with Donald Dahlberg started in 2002 and has been taught at EAS for 18 consecutive years now.
We’ve had tremendously good fortune to work with talented and dedicated scientists and engineers. This includes our current technical staff (in order of seniority) R. Scott Koch, Robert T. “Bob” Roginski, Donal O’Sullivan, Manny Palacios and Lyle Lawrence. We wouldn’t trade you EigenGuys for anybody! Also past staff members of note including Charles E. “Chuck” Miller, Randy Bishop and Willem Windig.
So what’s next? The short answer: more of the same! It’s both a blessing and a curse that the list of additions and improvements that we’d like to make to our software is never ending. We’ll work on that while we continue to provide the outstanding level of support our users have come to expect. Our training efforts will continue with our live courses but we also plan more training via webinar and in other venues. And of course we’re still doing consulting work and look forward to new and interesting projects in 2020.
In closing, we’d like to thank all the great people that we’ve worked with these 25 years. This includes our staff members past and present, our consulting clients, academic colleagues, technology partners, short course students and especially the many thousands of users of our PLS_Toolbox software, its Solo derivatives and add-ons. We’ve had a blast and we look forward to continuing to serve our clients in the new decade!
Happy New Year!
Aug 21, 2019
I attended Metabolomics 2019 and was pleased to find a rapidly expanding discipline populated with very enthusiastic researchers. Applications ranged from developing plants with increased levels of nutrients to understanding cancer metabolism.
Metabolomics experiments, however, produce extremely large and complex data sets. Consequently, the ultimate success of any experiment in metabolomics hinges on the software used to analyze the data. It was not surprising to find that multivariate analysis methods were front and center in many of the presentations and posters.
At the conference I saw some nice examples using our software, but of course not as many as I would have liked. So when I got home I put together this table comparing our PLS_Toolbox and Solo software with SIMCA, R and Python for use with metabolomics data sets.
Compare Software for Metabolomics
|Available for Windows, |
Mac and Linux?
|Comes with User Support?||Yes||Yes||Yes||No|
|Point-and-click GUIs for |
all important analyses?
|Command Line available?||Yes||No||No||Yes, use is mandatory|
|Source Code available |
|Includes PCA, PLS, O-PLS?||Yes||Yes||Yes||Add-ons available|
|Includes ASCA, MLSCA?||Yes||Yes||No||Add-ons available|
|Includes SVMs, ANNs |
|Includes PARAFAC, |
|Includes Curve Resolution Methods?||Yes||Yes||No||Add-ons available|
|Extensible?||Yes||No||Yes, through Python||Yes|
calibration transfer tools?
|Easy to install?||Yes||Yes||Yes||No|
So it’s easy to see that PLS_Toolbox is in the sweet spot with regards to metabolomics software. Yes, it requires MATLAB, but MATLAB has over 3 millions users and is licensed by over 5000 universities world wide. And if you don’t care to use a command line Solo includes all the tools in PLS_Toolbox and doesn’t require MATLAB. Plus, Solo and PLS_Toolbox share the same model and data formats. So you can have people in your organization that use only GUIs work seamlessly with people who prefer access to the command line.
So the bottom line here is:
- If you are just getting started with metabolomics data PLS_Toolbox and Solo are easy to install, include all the analysis tools you’ll need in easy to use GUIs, are transparent and are relatively inexpensive.
- If you are using SIMCA, you should try out PLS_Toolbox because it includes many methods that SIMCA doesn’t have, the source code is available, its more easily extensible, works on all platforms, and it will save you money.
- If you are using R or Python, you should consider PLS_Toolbox because it is fully supported by our staff, has all the important tools in one place, sophisticated GUIs, and is easy to install.
Feb 16, 2019
Chimiométrie 2019 was held in Montpellier, January 30 to February 1. Now in its 20th year the conference attracted over 150 participants. The conference is mostly in French, (which I have been trying to learn for many years now), but also with talks in English. The Scientific and Organizing Committee Presidents were Ludovic Duponchel and J.M. Roger, respectively.
Eigenvector was proud to sponsor this event, and it was fun to have a display table and a chance to talk with some of our software users in France. As usual, I was on the lookout for talks and posters using PLS_Toolbox. I especially enjoyed the talk presented by Alice Croguennoc, Some aspects of SVM Regression: an example for spectroscopic quantitative predictions. The talk provided a nice intro to Support Vectors and good examples of what the various parameters in the method do. Alice used our implementation of SVMs, which adds our preprocessing, cross-validation and point-and-click graphics to the publicly available LIBSVM package. Ms. Croguennoc demonstrated some very nice calibrations on a non-linear spectroscopic problem.
I also found three very nice posters which utilized PLS_Toolbox:
Chemometric methods applied to FT-ICR/MS data: comprehensive study of aromatic sulfur compounds in gas oils by J. Guillemant, M. Lacoue-Nègre, F. Albrieux, L. Duponchel, L.P de Oliveira and J.F Joly.
Chemometric tools associated to FTIR and GC-MS for the discrimination and the classification of diesel fuels by suppliers by I. Barra, M. Kharbach, Y. Cherrah and A. Bouklouze.
Preliminary appreciation biodegradation of formate and fluorinated ethers by means of Raman spectroscopy coupled with chemometrics by M. Marchetti, M. Offroy, P. Bourson, C. Jobard, P. Branchu, J.F. Durmont, G. Casteran and B. Saintot.
By all accounts the conference was a great success, with many good talks and posters covering a wide range of chemometric topics, a great history of the field by Professor Steven D. Brown, and a delicious and fun Gala dinner at the fabulous Chez Parguel, shown at left. The evening included dancing, and also a song, La Place De la Conférence Chimiométrie, (sung to the tune of Patrick Bruel’s Place des Grands Hommes), written by Sylvie Roussel in celebration of the conference’s 20th year and sung with great gusto by the conferees. Also, the lecture hall on the SupAgro campus was very comfortable!
Congratulations to the conference committees for a great edition of this French tradition, with special thanks to Cécile Fontange and Sylvie Roussel of Ondalys for their organizational efforts. À l’année prochaine!
Jan 10, 2019
I logged in to LinkedIn this morning and found a discussion about Python that had a lot of references to PLS_Toolbox in it. The thread was started by one of our long time users, Erik Skibsted who wrote:
“MATLAB and PLS_Toolbox has always been my preferred tools for data science, but now I have started to play a little with Python (and finalised my first on-line course on Data Camp). At Novo Nordisk we have also seen a lot of small data science initiatives last year where people are using Python and I expect that a lot more of my colleagues will start coding small and big data science projects in 2019. It is pretty impressive what you can do now with this open source software and different libraries. And I believe Python will be very important in the journey towards a general use of machine learning and AI in our company.”
This post prompted well over 20 responses. As creator of PLS_Toolbox I thought I should jump in on the discussion!
In his response, Matej Horvat noted that Python and other open source initiatives were great “if you have the required coding skills.” This a key phrase. PLS_Toolbox doesn’t require any coding skills _at all_. You can use it entirely in point-and-click mode and still get to 90% of what it has to offer. (This makes it the equivalent of using our stand-alone product Solo.) When you are working with PLS_Toolbox interfaces it looks like the first figure below.
Of course if you are a coder you can take advantage of the ability to also use it in command line mode and build it into your own scripts and functions, just like you would do with other MATLAB toolboxes. The caveat is that you can’t redistribute it without an additional license from us. (We do sell these of course, contact me if you are interested.) When you are working with Python, (or developing MATLAB scripts incorporating PLS_Toolbox functions for that matter), it looks like the second figure.
Like Python, PLS_Toolbox is “open source” in the sense that you can actually see the code. We’re not hiding anything proprietary in it. You can find out exactly how it works. You can also modify if you wish, just don’t ask for help once you do that!
Unlike typical open source projects, with PLS_Toolbox you also get user support. If something doesn’t work we’re there to fix it. Our helpdesk has a great reputation for prompt responses that are actually helpful. That’s because the help comes from the people that actually developed the software.
Another reason to use PLS_Toolbox is that we have implemented a very wide array of methods and put them into the same framework so that they can be evaluated in a consistent way. For instance, we have PLS-DA, SVM-C, and now XGBoost all in the same interface that use the exact same preprocessing and are all cross-validated and validated in the same exact way so that they can be compared directly.
If you want to be able to freely distribute the models you generate with PLS_Toolbox we have have a tool for that: Model_Exporter. Model_Exporter allows users to export the majority of our models as code that you can compile into other languages, including direct export of Python code. You can then run the models anywhere you like, such as for making online predictions in a control system or with handheld spectrometers such as ThermoFisher’s Truscan. Another route to online predictions is using our stand-alone Solo_Predictor which can run any PLS_Toolbox/Solo model and communicates using a number of popular protocols.
PLS_Toolbox is just one piece of the complete chemometrics solutions we provide. We offer training at our renowned Eigenvector University and many other venues such as the upcoming course in Tokyo, EigenU Online, and an extensive array of help videos. And if that isn’t enough we also offer consulting services to help you develop and implement new instruments and applications.
So before you spend a lot of valuable time developing applications in Python, make sure you’re not just recreating tools that already exist at Eigenvector!
May 29, 2018
The 13th Annual Eigenvector University was held April 29-May 4 in Seattle. It was a busy, vibrant week with 40 students with a wide variety of backgrounds attending along with 10 instructors. Users of our PLS_Toolbox and Solo chemometrics packages showed some of their recent results at the Wednesday evening poster session, which has become an EigenU tradition. Now combined with our PowerUser Tips & Tricks session, it makes for a full evening of scientific and technical exchange fueled by hors d’oeuvres and adult beverages.
This year’s best poster, (as judged by the EVRI staff), was “Nondestructive Analysis of Historic Photographs” by Arthur McClelland, Elena Bulat, Melissa Banta, Erin Murphy, and Brenda Bernier. The poster described how Specular Reflection FTIR was used with Principal Components Analysis (PCA) to discriminate between coatings applied to prints in the Harvard class albums from 1853-1864.
For his efforts Arthur took home a pair of Bose Soundsport Wireless Headphones. Arthur is shown above accepting his prize from Eigenvector President Barry M. Wise and Vice-president Neal B. Gallagher. Congratulations Arthur!
The runner up poster was “Analytical Approach to Investigate Salt Disproportionation in Tablet Matrices by Stimulated Raman Scattering Microscopy” by Benjamin Figueroa, Tai Nguyen, Yongchao Su, Wei Xu, Tim Rhodes, Matt Lamm, and Dan Fu. The poster demonstrates how the the conversion of Active Pharmaceutical Ingredient (API) from its active salt form to its inactive free base form can be quantified in Raman images of tablets. Benjamin received a Bose Soundlink Bluetooth Speaker for his contribution. Kudos Benjamin!
We were also pleased to have several other very interesting poster submissions, as shown below:
Candace D. Harris, Xianglei Mao, Jiaojin Song, Jonathan Woodward, Lewis Johnson, and Ashley C. Stowe, “Multivariate Limit of Detection Interval for PLS Calibration Models via Laser Induced Breakdown Spectroscopy on U-235 and U-238 Enriched Glasses.”
Po Ki Tse, Amanda Lines, Sam Bryan, and Jenifer Shafer, “Chemometric Analysis to Predict the Formation of Interfacial Solids.”
Yulan Hernandez, Lesly Lagos and Betty C. Galarreta, “Selective and Efficient Mycotoxin Detection with Nanoaptasensors using SERS and Multivariate Analysis.”
Devanand Luthria and James Harnly, “Applications of Spectral Fingerprinting and Multivariate Analysis in Agricultural Sciences.”
Thanks to all EigenU 2018 poster presenters for a fun and informative evening!
Nov 22, 2017
Integration of Eigenvector’s multivariate analysis software with Metrohm’s Vis-NIR analyzers will give users access to advanced calibration and classification methods.
Metrohm’s spectroscopy software Vision Air 2.0 supports prediction models created in EVRI’s PLS_Toolbox and Solo software and offers convenient export and import functionality to enable measurement execution and sample analysis in Metrohm’s Vision Air software. Customers will benefit from data transfer between PLS_Toolbox/Solo and Vision Air and will enjoy a seamless experience when managing models and using Metrohm’s NIR laboratory instruments. Metrohm has integrated Eigenvector’s prediction engine, Solo_Predictor, so that users can apply any model created in PLS_Toolbox/Solo.
Data scientists, researchers and process engineers in a wide variety of industries that already use or would like to use Eigenvector software will find this solution appealing. PLS_Toolbox and Solo’s intuitive interface and advanced visualization tools make calibration, classification and validation model building a straightforward process. A wide array of model types, preprocessing methods and the ability to create more complex model forms, such as hierarchical models with conditional branches, make Eigenvector software the preferred solution for many.
“This a win-win for users of Metrohm NIR instruments and users of Eigenvector chemometrics software” says Eigenvector President Dr. Barry M. Wise. “Thousands of users of EVRI software will be able to make models for use on Metrohm NIR instruments in their preferred environment. And users of Metrohm NIR instruments will have access to more advanced data modeling techniques.”
Researchers benefit from Metrohm’s Vis-NIR Instrument and Vision Air software through instruments covering the visible and NIR wavelength range, intuitive operation, state-of-the art user management with strict SOPs and global networking capabilities. Combining the solutions will create an integrated experience that will save time, improve product development process and provide better control of product quality.
Key Advantages PLS_Toolbox/Solo:
- Integration of Solo_Predictor allows users to run any model developed in PLS_Toolbox/Solo
- Allows users to make calibration and classification models in PLS_Toolbox and Solo’s user-friendly modeling environment
- Supports standard model types (PCA, PLS, PLS-DA, etc.) with wide array of data preprocessing methods
- Advanced models (SVMs, ANNs, etc.) and hierarchical models also supported
Key Advantages Vision Air:
- Intuitive workflow due to appealing and smart software concept with specific working interfaces for routine users, and lab managers
- Database approach for secure data handling and easy data management
- Powerful network option with global networking possibility and one-click instruments maintenance
- Full CFR Part 11 compliance
Aug 3, 2017
Hello EigenFriends and EigenFans,
The ICNIRS conference was held June 11-15 in Copenhagen, Denmark, where close to 500 colleagues gathered for the largest forum on Near-Infared Spectroscopy in the world. The conference featured several keynote lectures, classes taught by EVRI associate Professor Rasmus Bro, and also held several poster sessions where over 20 conference attendees displayed their research using EVRI software! We’d like to feature some of the posters and authors below: thanks for using our software, everyone!
- Y. Allouche, J.A. Fernandez Perna, V. Baeten, & A. Jimenez. “On-line Near Infrared Spectroscopy and Chemometrics for Characterization of Olive Oils at the Exit of a Decanter Centrifuge”
- C. Y. Bastidas, C. von Plessing, J. Troncoso, & R. del Pilar Castillo. “Quantification of an Antibiotic in Salmon Feed Pellets with NIR Spectroscopy and Multivariate Calibration”
- B. Carrasco, D. Vincke, V. Baeten, & J.A. Fernandez Perna. “Application of Near Infrared Spectroscopy and Chemometrics for the Characterization of Complex Mixtures of Food Additives”
- M. Chaudhry, G. Colelli, & M. Amodio.“Potential of Hyperspectral Imaging to Predict Quality and Shelf-Life of Fresh Rocket Leaves to be Used for Fresh-Cut Processing”
- S.Duthen, D. Kleiber, J. Dayde, C. Raynaud, & C. Levasseur-Garcia. “Determination of the Moisture Content of Gelatin Sample”
- D. Eylenbosch, J. A. Fernandez Pierna, V. Baeten, & B. Bodson. “Comparison of PLS and SVM Discriminant Analysis for NIR Hyperspectral Data of Wheat Roots in Soil”
- L. Franca, S. Grassi, M. F. Pimentel, & J. M. Amigo. “Handcraft Beer Monitoring Using NIR Handheld Equipment”
- R. Gasbarrone, S. Serranti & G. Bonifazi. “An Investigation on Non-ferrous Metals Particles Separability from Electronic Scraps using Hyperspectral Imaging and Micro-XRF Analysis”
- S. Montagneir, J. Lallemand, P. Herbert, J. Guilment, & S. Roussel. “Discriminant Strategies for Polymer Identification during Continuous On-line Processes by Near Infrared Spectroscopy”
- R. Palmieri, S. Serranti, G. Bonifazi, & F. Maffei. “Monitoring of Microplastics from Marine Environment Adopting HyperSpectral Imaging”
- J. F. Q. Pereira, C. S. Silva, M. J. Vieira, M. F. Pimentel, A. Braz, & R. S. Honorato. “Evaluation and Identification of Blood Stains in Crime Scenes with Ultra-portable NIR Spectrometer”
- Y. Pu, D. Sun, C. Riccioli, M. Buccheri, M. Grassi, T. M. P. Cattaneo, & A. Gowen. “Calibration Transfer from MicroNIR Spectrometer to Hyperspectral Imaging: A Case Study on Predicting Soluble Solids Content of Bananito Fruit (Musa acuminata)”
- M. M. Reis, I. Kaur, G. Weralupitiya, C. Wang, & M. G. Reis. “Near InfraRed Spectroscopy Applied to Non-invasive Assessment of Physical-chemical Attributes of Dairy Powders”
- R. Rios-Reina, D. L. Garcia-Gonzalez, R. M. Collejon, & J. M. Amigo. “Application of Near-Infrared (NIR) Spectroscopy and Chemometrics to Classify and Authentify Wine Vinegars from Different Protected Designation of Origin”
- J. Sun, A. McGlone, R. Kunnememeyer, N. Tomer, & M. Punter. “Which Optical Geometry is Best to Detect Vascular Browning in Apples?”
Feb 4, 2016
Last month I had the pleasure of attending Chimiométrie XVII. This installment ran from January 17-20 in the beautiful city of Namur, BELGIUM. The conference was largely in French but with many talks and posters in English. (My French is just good enough that I can get the gist of most of the French talks if the speakers put enough text on their slides!) There were many good talks and posters demonstrating a lot of chemometric activity in the French speaking world.
I was pleased to see evidence of EVRI software in many presentations and posters. I particularly enjoyed “An NIRS Prediction Engine for Discrimination of Animal Feed Ingredients” by Aitziber Miguel Oyarbide working with the folks at AUNIR. This presentation was done with Prezi which I find quite refreshing. I also enjoyed posters about standardization in milk analysis, determination of post mortem interval, evaluation of pesticide coating on cereal seeds, and sorting of archeological material. All of these researchers used PLS_Toolbox, MIA_Toolbox or Solo to good effect.
EVRI was also proud to sponsor the poster contest which was won by Juan Antonio Fernández Pierna et al. with “Chemometrics and Vibrational Spectroscopy for the Detection of Melamine Levels in Milk.” For his efforts Juan received licenses for PLS_Toolbox and MIA_Toolbox. Congratulations! We wish him continued success in his chemometric endeavors!
Finally I’d like to thank the organizing committee, headed by Pierre Dardenne of Le Centre wallon de Recherches agronomiques. The scientific content was excellent and, oh my, the food was fantastic! I’m already looking forward to the next one!
Sep 30, 2015
On October 1, 1985 I walked into Bruce Kowalski’s chemometrics class and my world changed forever. It was my first day of chemical engineering graduate school at the University of Washington. My M.S. thesis advisor, Prof. Harold Hager, told me that I’d probably find the methods in Bruce’s class useful in treating the data I was to collect. He was right, but more than that, it wasn’t long before I knew that I’d found something I wanted to do for a living.
A big part of the class was a project, due at the end of the semester in early December. I spent my Thanksgiving vacation working with Infometrix’s Ein*Sight software doing PCA on data from a Liquid-Fed Ceramic Melter I’d worked on at Pacific Northwest National Laboratory. Ein*Sight had a limit of 100 samples and 10 variables but it ran on an IBM AT. I spent a lot of time swapping interesting samples in and out of the analysis and trying to interpret the results. I got an A on the project (Bruce gave lots of A’s!) and my study became a piece of Infometrix sales literature (left). From there I started working with Prof. Larry Ricker on my ChemE Ph.D. with Bruce on my committee. The rest, as they say, is history.
I always liked data analysis. As an undergrad in ChemE my lab partners referred to me as the “Data Magician.” I just liked massaging the numbers to see what I could tease out. Chemometrics gave me a whole new set of tools and opened my world up to high dimension data.
Chemometrics has taken me lots of interesting places over the last 30 years, and I mean that both with regards to the travel and the intellectual challenges. And I’ve been blessed to meet lots of great people. It’s awesome to go to a conference in a faraway place and walk into a room full of friends.
Thanks to all my friends and colleagues for a great 30 year adventure! But, man!, that was fast! Where did the time go? But I’m looking forward to a couple more decades of chemometrics escapades.
May 23, 2015
Like its predecessors, the 10th Annual Eigenvector University included the Tuesday evening PLS_Toolbox/Solo User poster session. Eight posters, which spanned a wide range of applications, were scrutinized by about 40 attendees. A good time was had by presenters and viewers alike as we enjoyed hors d’oeuvres, beverages and scientific discussion.
Amanda Lines of Pacific Northwest National Laboratory (PNNL) captured this year’s top prize with “Remote Raman technology for in-situ identification of nuclear tank waste.” The poster revealed how Raman spectroscopy combined with multivariate calibration can be used to analyze surfaces at distances up to 50 feet. Ms. Lines is shown below with her poster and EVRI Vice-President Neal B. Gallagher.
In a very close contest the runner up Anna Klimkiewicz of the University of Copenhagen presented “A chemometric approach to the optimization of bio-industrial processes.” The work illustrated the application of multivariate analysis to understand and improve performance in an industrial-scale continuous enzyme purification process. Ms. Klimkiewicz can be seen with her poster (and me) below.
Both of these posters clearly presented an interesting story and made especially good use of our PLS_Toolbox. As a reward for their efforts Amanda took home a pair of Bose Noise Canceling Headphones while Anna took home a Bose Bluetooth Speaker system. Well deserved! 👍 We hope you enjoy them.
Thanks to everybody who attended and presented at EigenU!
Feb 25, 2015
The successful candidate is expected to take a lead role on some chemometrics consulting projects and a supporting role on others. Must be able to meet with potential clients, understand their goals and needs, develop a statement of work, and execute the tasks. Good written and oral communications skills, especially the ability to convey complex information to non-experts, required. Potential to attract new projects through new and existing contacts preferred. Must be able to work at home. Location not critical but proximity to our existing locations would be a plus.
EVRI employees enjoy working on interesting projects with a dedicated, fun and lively team of chemometrics and programming experts. EVRI offers a competitive salary and benefits package, plus flexible hours and the ability to work at home.
Applicants should send a C.V. and letter of interest to Barry M. Wise.
Oct 22, 2014
Model_Exporter is EVRI’s software for turning multivariate/chemometric models into formats which can be compiled into online applications. It offers an alternative to our stand-alone prediction engine Solo_Predictor. Model_Exporter allows users of our MATLAB® based PLS_Toolbox and stand-alone Solo to easily create a numerical recipes of their models. These recipes give the step by step procedure that take a measurement and calculate the desired outputs, such as concentration, class assignment, prediction diagnostics, etc. This includes applying all preprocessing steps along with the model (PCA, PLS, PLS-DA etc.) itself. When Model_Exporter is installed, models can be exported into predictor files in a variety of formats via the file menu in the Analysis window as shown below.
Model_Exporter also includes two versions of the freely-distributable Model_Interpreter. Either the C# or Java version of the Model_Interpreter can be used by any 3rd party program to add the ability to parse an exported model in XML format. Simply point the interpreter at an XML exported model and supply the data from which to make a prediction. The interpreter applies the model and returns the results. Model_Interpreter has no licensing fees and is appropriate for use on standard processors and operating systems or on handheld devices run by reduced instruction set processors (e.g. ARM). Your application doesn’t need to know anything about the preprocessing or model being used.
Version 3.0 of Model_Exporter was released in early October along with its associated stand-alone Solo+Model_Exporter version 7.9. This release includes support for Support Vector Machine (SVM) regression and classification models as well as Artificial Neural Network (ANN) regression models.
These changes represent a significant addition to Model_Exporter making it even more unique in the chemometrics world. No other chemometric modeling product offers anything as transparent, flexible or unencumbered by licensing. You can get more info about Model_Exporter by consulting the Release Notes and the Model_Exporter Wiki page.
Users with current maintenance can access these versions now from their account. If expired, maintenance can be renewed through the “Purchase” tab.
If you have any questions, feel free to write us at firstname.lastname@example.org.
Oct 20, 2014
In the last several years we’ve seen a resurgence of interest in Classical Least Squares (CLS) modeling. To address that our Neal Gallagher is developing a course on CLS Methods for the next EigenU. Our interest also stems from the fact that we’ve worked on a number of consulting projects where CLS models are appropriate for calibrating spectroscopic systems. As you might expect, these systems are relatively simple mixtures in gas or liquid phase. Recall the CLS model is
X = CS‘ + E
where X is the measured spectra, C is the matrix of concentrations, S is the pure component spectra and E is noise.
Complicating matters a bit, several of the systems we’ve worked with exhibit significant nonlinearities due to high absorbance features. In spite of that, CLS models can work quite well if set up correctly. What follows is an example that demonstrates this (which I originally did just to clarify how this works in my own mind).
Suppose you have a single component system with a pure component response that is a simple Gaussian peak centered in the spectral range with a maximum value of one when the concentration is also one. Furthermore, suppose that the spectra is linear up to an absorbance of one but rolls off after that. (For xideal > 1 I used xmeasured = 2-exp(-(xideal-1)) but the exact form of the nonlinearity isn’t critical.) The measured spectra for concentrations from 0 to 3 is shown below, with concentration = 1 shown as the thick blue line. It is apparent that the shape changes as the concentration exceeds 1.
If the concentration is estimated using the ideal (concentration < 1) response, the estimate will fall below the actual value as the concentration passes 1, as shown below. If the spectral residuals were observed it would be apparent that there was a problem, but how to fix it?
If the ideal response for each concentration is estimated, then the difference between it and the observed response can be calculated, as shown in the top panel in the figure below. Because each difference spectra has a slightly different shape, the rank of this difference matrix is equal to the number of samples exhibiting non-linear behavior, which in this case is 20 (the samples with concentration 1.1 to 3). However, it is easy to get a basis for the nonlinear deviations using the Singular Value Decomposition (SVD). Furthermore, the singular values indicate that 93.7% of the residual sum of squares is captured in the first factor, and 98.6% is captured in the first two. The ideal response along with the first two basis vectors is shown lower panel.
When the CLS model is augmented with the two basis vectors, the prediction improves dramatically. The figure below shows the predicted concentration of the analyte as well as the “concentration” of the two additional basis vector factors. The correction added by the 1st nonlinear factor becomes quite large at high concentrations, whereas the contribution of the 2nd nonlinear factor remains relatively small. The prediction error in the concentration of the analyte is less than 1%.
In a future blog post we’ll explore some other aspects of CLS models.
Oct 7, 2014
The MathWorks released MATLAB R2014b (version 8.4) last week, and right on its heels we released PLS_Toolbox 7.9. R2014b has a number of improvements that MATLAB and PLS_Toolbox users will appreciate, specifically with graphics. The new MATLAB is more aesthetically pleasing to the eye, easier for the Color Vision Deficiency (CVD) challenged, and smoother due to better anti-aliasing. An example is shown below where the new CVD-friendly Parula color map is used to indicated the Q-residual values of the samples.
But the most significant changes in R2014b are really for people (like us) that program in MATLAB. For instance, TMW didn’t just change the look of the graphics, they actually changed the entire handle graphics system to be object oriented. They also added routines useful in big data applications, and improved their handling of date and time data. When you start the new MATLAB the command window greets you with this:
“Some existing code may need to be revised to work in this version of MATLAB.” That is something of an understatement. In fact, R2014b required the update of almost every interface from PLS_Toolbox 7.8. Revising our code to work with R2014b required hundreds of hours. But the good news for our users is that we were ready with PLS_Toolbox 7.9 when R2014b was released AND, as always, we made our code work with previous versions of MATLAB (back to R2008a). This, of course, is the significant difference between a supported commercial product and freeware. Not only do you get new features regularly, but you can rely on it being supported as operating systems and platforms change.
So if you look at the Version 7.9 Release Notes, you won’t see a lot of major changes. Instead, we took the time to assure compatibility with R2014b and made many minor changes to improve usability and stability.
The new MATLAB will allow our command-line and scripting users to do their science more efficiently and present their result more elegantly. These improvements will benefit us as well, and will ultimately translate into continued improvement in PLS_Toolbox and Solo.