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|
1) Harmonious and Parsimonious Multivariate Calibration: The Tao of Analytical Chemistry
Multivariate calibration involves developing a mathematical relationship between a dependent variable and measured independent variables. For example, analyte concentration is the dependent variable and measured independent variables are readings over a series of wavelengths. Mathematically, this is expressed as
with estimation of b by
where the superscript + indicates a generalized inverse of X . The methods of principal component regression (PCR), partial least squares (PLS), ridge regression (RR), etc . differ in how respective generalized inverses are formed based on the selected meta-parameter. Equation (2) can be written as
showing that regression vectors from PCR, PLS, RR, etc. are simply linear combinations of the singular vectors in the basis set V from the singular value decomposition (SVD) of X . Once the optimal regression vector has been obtained, it can be used for analysis of a future sample x by
Estimating b is regularly described in analytical chemistry and other fields as a minimization problem in the 2-norm (Euclidean norm, ) of
In essence, expression (5) 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. (4).
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 variance for bias. As respective meta-parameters for PCR, PLS, RR, etc. vary to generate regression vectors from eqs. (2) or (3), the bias decreases at a sacrifice to variance increasing and vice-versa.
Thus, both issues need to be examined when determining the best . This can be accomplished by including variance information in expression (5), i.e., the model with the proper bias/variance tradeoff (harmonious model) should be sought. A possible approach is to use the Tikhonov regularization expression
By doing so, there is less chance of obtaining an over- or under-fitted model. Little work has been accomplished in this direction for analytical chemistry. A graphic of this process is the plot of the variance factor against the bias measure shown in the following Figure.
An L shaped curve usually results with the best model occurring at the bend which reflects a harmonious model.
Little work has been performed that uses bias and variance information concurrently to determine the model with the best bias/variance tradeoff. Additionally, variable selection is often used to provide robust models by excluding non-analyte related variables; this is especially critical in quantitative structure activity relationships (QSAR) applications. With variable selection, the best model with the least number of variables is said to be parsimonious . Again, this best model is regularly determined in the literature using only bias information ignoring prediction variance.
Our research goal is to develop an approach that provides simultaneous identification of the optimal smooth harmonious and parsimonious model. Results from this research will advance the multidisciplinary field of multivariate calibration. For example, medical diagnostics, environmental and agriculture monitoring, and industrial process analysis all rely on multivariate calibration.
2) Instrument Calibration Standardization
Calibration standardization (transfer) is another important aspect of multivariate calibration. In this case, the concern is to develop a calibration model for the primary instrument using y and corresponding calibration spectra measured on the primary instrument ( X1) and computing . This model is used to predict the sample composition from a spectrum measured on the secondary instrument ( x2 ) by
The secondary instrument is the primary instrument at a later time, under conditions where sample compositions or an external parameter (temperature) have changed, or it can be a different instrument. Prior to using eq. (7), the sample spectrum from the secondary instrument must be transformed to appear as if it was measured on the primary instrument. This can be accomplished by various methods. It has been shown that wavelength selection can be used to enhance the robustness of the calibration model transfer process. Current approaches are cumbersome and limited to a bias criterion. Conversely, using expression (6) with the 1-norm or a weighted 2-norm for variance indicators should provide distinct advantages and form better models that are robust to the secondary circumstances.
An alternative to determining a transformation matrix with or without wavelength selection is to update the primary calibration model to the new instrument or conditions (). This would require measuring spectra under the secondary circumstances for a few new or previously used samples. Using the basis set spanning the new environment, the initial model can be updated using
in conjunction with expression (6) where the vi basis vectors are from the SVD of the spectra measured under the new conditions. Our research involves investigation of eq. (8) to provide a solution to the calibration standardization problem.
3) Chemical Education
Presently lacking from the chemical education community for use in undergraduate courses as well as for use by scientist and engineers is a simple interactive tutorial web-based approach to teach multivariate calibration in all aspects, i.e., calibration design, model building, validation of model, and updating the model (calibration transfer or standardization). Part of our research is to assist in filling part of this void by developing such a web site for model building. This web site will be complemented with tutorial manuscripts and include data sets with worked-out examples. All tutorial data sets and Matlab algorithms will be downloadable. Web site development will involve interaction with professionals from the ISU Instructional Teaching Resource Center and have an inquiry-based learning component. For example, once a user has worked through the tutorial, data sets will be available for the user to model and engage in a real experience of inquiry research. The web site will allow investigators interested in using the described approaches easy access to learn the material.
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 service-learning components in general and analytical chemistry courses.
Commercially available guided inquiry teaching approaches are available for general, organic, and physical chemistry courses at other institutions. To date, there is no such entity available for the analytical chemistry curriculum. Our research desires are to develop such a curriculum in conjunction with peer led team teaching.
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).