John H. Kalivas
Professor of Chemistry
Ph.D. Analytical Chemistry, University of Washington – 1982
Research area: Analytical Chemistry, Chemometrics, Chemical Education
Student experience required for research: Chem 1111 and Chem 1112
Student experience gained from research: Data analysis, modeling, computational chemistry, spectroscopy, teaching
Ideal preparation for: Chemical industry, pharmaceuticals, medical, environmental, and agriculture research, teaching, and preparation for graduate school in Chemistry or other professional school
Multivariate calibration is key to many disciplines including food analysis, food adulteration detection and authentication of product origin, environmental monitoring, industrial process analysis, medical diagnosis such as disease detection, pharmaceutical analysis, forensic analysis, detection of hidden radioactive material, and the list goes on. Work in our laboratory consists of developing new multivariate calibration processes to improve calibration accuracy and precision, the two merits used to judge how well a calibration works. Another issue with multivariate calibration is maintenance. That is, developing a calibration in one set of environmental, instrumental, physical, and chemical conditions (the primary conditions) and then updating the calibration to now work in new secondary conditions is a persistent problem. Our laboratory also works on methodology developments to solve this issue. Linear algebra and Matlab programing are the tools used in our research.
1) Multivariate Calibration
Multivariate calibration involves developing a mathematical relationship between a dependent variable and measured independent variables. For example, analyte concentration is the dependent variable (the m calibration sample values in the column vector y) and measured independent variables are readings over a series of wavelengths (the respective calibration spectra measured over n wavelengths as rows in X). Mathematically, this is expressed as
with estimation of b, the regression or model vector, by
where the superscript + indicates a generalized inverse of X. The methods of principal component regression (PCR), partial least squares (PLS), ridge regression (RR) a variant of Tikhonov regularization (TR), etc. differ in how respective generalized inverses are formed based on the respective selected meta-parameter (tuning parameter).
Once an acceptable regression vector has been obtained, it can be used for analysis of a future sample x , e.g., the measured spectrum of new sample, by
Estimating b is regularly described in analytical chemistry and other fields as a minimization problem in the L2 norm (2-norm, Euclidean norm, ) of
In essence, expression (4) is a minimization of the accuracy error (bias). However, not only is minimizing bias a crucial component in forming a calibration model, but another essential part of calibration is minimizing the variance associated with estimates of y using eq. (3).
Bias and variance are complementary measures in the sense that a decrease in bias results in an increase in variance for prediction of a sample (). As the following figure shows, there is a tradeoff of bias (prediction error) for variance (model complexity). As respective tuning parameters for PCR, PLS, RR, etc. vary to generate regression vectors from eq. (2), the bias decreases at a sacrifice to variance increasing and vice-versa.
Thus, both issues need to be examined when determining an acceptable . This can be accomplished by including variance information in expression (4), i.e., the model with the proper bias/variance tradeoff (harmonious model) should be sought. A possible approach is to use the Tikhonov regularization (TR) expression
A graphic of this process is the plot of the bias measure against the variance factor shown above. An L shaped curve (L-curve) usually results with the best models occurring in the corner region which reflect harmonious models. Our lab has recently shown that the underlying the bias/variance tradeoff is the corresponding balance of the model (or instrumental method) selectivity/sensitivity tradeoff.
Noted in the following Table are some new TR variants our lab has been developing in order to improve the calibration process. Some variants allow variables (wavelengths with spectroscopic data) to be selected forming sparse models. Results from these research projects are advancing the multidisciplinary field of multivariate calibration.
An interesting application of our newly develop pure component TR variant in the fifth row of the above Table is the analysis of food adulterants in extra virgin olive oil samples. This TR variant does not require any calibration standards (reference samples). The method shows great promise in the pharmaceutical industry for analysis of the active pharmaceutical ingredient (API) content in medicine.
2) Calibration Maintenance
Once a multivariate model is estimated, the duration of the model usefulness becomes relevant. The current primary calibration can fail due to a host of reasons such as uncalibrated spectral features appearing in new secondary samples later in time, the calibrated analyte is now lower or higher than the primary calibration concentrations in y, or other new secondary effects resulting from changes in the instrument and sample type. Our research lab works on developing new TR variants to better maintain the current primary model to deal with new chemical, physical, environmental, and/or instrumental effects not in the current calibration domain. Some of these new methods are listed in the above Table. We develop TR variants because the fundamentals of TR allow for flexible regularization processes and can be modified to work in many uniquely different situations.
3) Chemical Education
We have on going chemical education projects in our research laboratory. These consist of developing new laboratory exercises for general chemistry, quantitative analysis, and instrumental analysis. In the past, our laboratory has developed new guided inquiry labs for general chemistry and quantitative analysis including chemical analysis of live trout for their fat and moisture contents. Currently, we are working on new labs for instrumental analysis that provide greener approaches to multivariate calibration using one of our newly developed TR variants.
Service-learning is becoming ever more important in the education of students to become responsible chemists. Service-learning involves students in thoughtfully organized service activities addressing community needs and complementing students' academic studies. Service-learning results from a curriculum that extends the classroom into the community combing education and service and includes class time to reflect on the service experience. Our research desires are to develop new service-learning components in general and analytical chemistry courses.
V.A. Allen, J.H. Kalivas, R.G. Rodriguez, "Post-Consumer Plastic Identification Using Raman Spectroscopy", Applied Spectroscopy, 53, 672-681 (1999).
T. Houghton, J.H. Kalivas, "Implementation of Traditional and Real-World Cooperative Learning Techniques in Quantitative Analysis Including Near Infrared Spectroscopy for Analysis of Live Trout", Journal of Chemical Education, 77, 1314-1318 (2000).
J.M. Clark, K.A. Daum, J.H. Kalivas, "Demonstrated Potential of Ion Mobility Spectrometry for Detection of Adulterated Perfumes and Plant Speciation", Analytical Letters, 36, 215-244 (2003).
J.H. Kalivas, J.B. Forrester, H.A. Seipel, "QSAR Modeling Based on the Bias/Variance Compromise: A Harmonious Approach", Journal of Computer-Aided Molecular Design, 18, 537-547 (2004).
F. Stout, J.H. Kalivas: "Tikhonov Regularization in Standard and General Form for Multivariate Calibration with Applications Towards Removing Unwanted Spectral Artifacts", Journal of Chemometrics, 20, 22-33 (2006).
F. Stout, M.R. Baines, J.H. Kalivas: "Impartial Graphical Comparison of Multivariate Calibration Methods and the Harmony/Parsimony Tradeoff", Journal of Chemometrics, 20, 464-475 (2006).
F. Stout, J.H. Kalivas, K. Heberger: "Wavelength Selection for Multivariate Calibration Using Tikhonov Regularization", Applied Spectroscopy, 61, 85-95 (2007).
J.H. Kalivas: "Progression of Chemometrics in Research Supportive Curricula" in Active Learning: Models from the Analytical Sciences, ACS Symposium Series 970, editor P.A. Mabrouk, Oxford University Press, (2007).
J.H. Kalivas: "An Elementary School Service Learning Project Based on a Research Supportive Curriculum Format in the General Chemistry Laboratory", Journal of Chemical Education, 85, 1410-1415 (2008).
M.R. Kunz, J. Ottaway, J.H. Kalivas, C.A. Georgiou, G.A. Mousdis: “Updating a Synchronous Fluorescence Spectroscopic Virgin Olive Oil Adulteration Calibration to a New Geographical Region”, Journal of Agricultural and Food Chemistry, 59, 1051-1057 (2011).
J. Farrell, K. Higgins, J.H. Kalivas: “Updating a Near-Infrared Multivariate Calibration Model Formed with Lab-Prepared Pharmaceutical Tablet Types to New Tablet Types in Full Production”, Journal of Pharmaceutical and Biomedical Analysis, 61, 114-121 (2012).
J.H. Kalivas: “Overview of Two-norm (L2) and One-norm (L1) Regularization Variants for Full Wavelength or Sparse Spectral Multivariate Calibration Models or Maintenance”, Journal of Chemometrics, 26, 218-230 (2012).
P. Shahbazikhah, J.H. Kalivas: “A Consensus Modeling Approach to Update a Spectroscopic Calibration”, Chemometrics and Intelligent Laboratory Systems, 120, 142-153 (2013).
J. Ottaway, J. Farrell, J.H. Kalivas: “Spectral Multivariate Calibration without Laboratory Prepared or Determined Reference Analyte Values”, Analytical Chemistry, 85, 1509-1516 (2013).
For MATLAB code to perform Tikhonov regularization without reference samples, see http://pubs.acs.org/doi/suppl/10.1021/ac302705m/suppl_file/ac302705m_si_001.pdf
For MATLAB code to perform sum of ranking differences (SRD), see 2013_12_16_SRD.zip