Practical guide to chemometrics 2ed gemperline

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PRACTICAL GUIDE to CHEMOMETRICS SECOND EDITION Edited by PAUL GEMPERLINE Boca Raton London New York CRC is an imprint of the Taylor & Francis Group, an informa business © 2006 by Taylor & Francis Group, LLC Page Wednesday, October 5, 2005 11:12 AM Published in 2006 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2006 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S Government works Printed in the United States of America on acid-free paper 10 International Standard Book Number-10: 1-57444-783-1 (Hardcover) International Standard Book Number-13: 978-1-57444-783-5 (Hardcover) Library of Congress Card Number 2005054904 This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access ( or contact the Copyright Clearance Center, Inc (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data Practical guide to chemometrics / edited by Paul Gemperline. 2nd ed p cm Includes bibliographical references and index ISBN 1-57444-783-1 (alk paper) Chemometrics I Gemperline, Paul QD75.4.C45P73 2006 543.072 dc22 2005054904 Visit the Taylor & Francis Web site at Taylor & Francis Group is the Academic Division of Informa plc © 2006 by Taylor & Francis Group, LLC and the CRC Press Web site at Page v Thursday, March 16, 2006 3:36 PM Preface Chemometrics is an interdisciplinary field that combines statistics and chemistry From its earliest days, chemometrics has always been a practically oriented subdiscipline of analytical chemistry aimed at solving problems often overlooked by mainstream statisticians An important example is solving multivariate calibration problems at reduced rank The method of partial least-squares (PLS) was quickly recognized and embraced by the chemistry community long before many practitioners in statistics considered it worthy of a “second look.” For many chemists, training in data analysis and statistics has been limited to the basic univariate topics covered in undergraduate analytical chemistry courses such as univariate hypothesis testing, for example, comparison of means A few more details may have been covered in some senior-level courses on instrumental methods of analysis where topics such as univariate linear regression and prediction confidence intervals might be examined In graduate school, perhaps a review of error propagation and analysis of variance (ANOVA) may have been encountered in a core course in analytical chemistry These tools were typically introduced on a very practical level without a lot of the underlying theory The chemistry curriculum simply did not allow sufficient time for more in-depth coverage However, during the past two decades, chemometrics has emerged as an important subdiscipline, and the analytical chemistry curriculum has evolved at many universities to the point where a small amount of time is devoted to practical application-oriented introductions to some multivariate methods of data analysis This book continues in the practical tradition of chemometrics Multivariate methods and procedures that have been found to be extraordinarily useful in analytical chemistry applications are introduced with a minimum of theoretical background The aim of the book is to illustrate these methods through practical examples in a style that makes the material accessible to a broad audience of nonexperts © 2006 by Taylor & Francis Group, LLC Page vii Thursday, March 16, 2006 3:36 PM Editor Paul J Gemperline, Ph.D., ECU distinguished professor of research and Harriot College distinguished professor of chemistry, has more than 20 years of experience in chemometrics, a subdiscipline of analytical chemistry that utilizes multivariate statistical and numerical analysis of chemical measurements to provide information for understanding, modeling, and controlling industrial processes Dr Gemperline’s achievements include more than 50 publications in the field of chemometrics and more than $1.5 million in external grant funds Most recently, he was named recipient of the 2003 Eastern Analytical Symposium’s Award in Chemometrics, the highest international award in the field of chemometrics Dr Gemperline’s training in scientific computing began in the late 1970s in graduate school and developed into his main line of research in the early 1980s He collaborated with pharmaceutical company Burroughs Wellcome in the early 1980s to develop software for multivariate pattern-recognition analysis of near-infrared reflectance spectra for rapid, nondestructive testing of pharmaceutical ingredients and products His research and publications in this area gained international recognition He is a sought-after lecturer and has given numerous invited lectures at universities and international conferences outside the United States Most recently, Dr Gemperline participated with a team of researchers to develop and conduct training on chemometrics for U.S Food and Drug Administration (FDA) scientists, inspectors, and regulators of the pharmaceutical industry in support of their new Process Analytical Technology initiative The main theme of Dr Gemperline’s research in chemometrics is focused on development of new algorithms and software tools for analysis of multivariate spectroscopic measurements using pattern-recognition methods, artificial neural networks, multivariate statistical methods, multivariate calibration, and nonlinear model estimation His work has focused on applications of process analysis in the pharmaceutical industry, with collaborations and funding from scientists at Pfizer, Inc and GlaxoSmithKline Several of his students are now employed as chemometricians and programmers at pharmaceutical and scientific instrument companies Dr Gemperline has also received significant funding from the National Science Foundation and the Measurement and Control Engineering Center (MCEC), an NSF-sponsored University/Industry Cooperative Research Center at the University of Tennessee, Knoxville © 2006 by Taylor & Francis Group, LLC Page ix Thursday, March 16, 2006 3:36 PM Contributors Karl S Booksh Department of Chemistry and Biochemistry Arizona State University Tempe, Arizona Steven D Brown Department of Chemistry and Biochemistry University of Delaware Newark, Delaware Charles E Davidson Department of Chemistry Clarkson University Potsdam, New York Anna de Juan Department of Analytical Chemistry University of Barcelona Barcelona, Spain John H Kalivas Department of Chemistry Idaho State University Pocatello, Idaho Barry K Lavine Department of Chemistry Oklahoma State University Stillwater, Oklahoma Marcel Maeder Department of Chemistry University of Newcastle Newcastle, Australia Yorck-Michael Neuhold Department of Chemistry University of Newcastle Newcastle, Australia Kalin Stoyanov Sofia, Bulgaria Paul J Gemperline Department of Chemistry East Carolina University Greenville, North Carolina Romà Tauler Institute of Chemical and Environmental Research Barcelona, Spain Mia Hubert Department of Mathematics Katholieke Universiteit Leuven Leuven, Belgium Anthony D Walmsley Department of Chemistry University of Hull Hull, England © 2006 by Taylor & Francis Group, LLC Page xi Thursday, March 16, 2006 3:36 PM Contents Chapter Introduction to Chemometrics Paul J Gemperline Chapter Statistical Evaluation of Data Anthony D Walmsley Chapter Sampling Theory, Distribution Functions, and the Multivariate Normal Distribution .41 Paul J Gemperline and John H Kalivas Chapter Principal Component Analysis 69 Paul J Gemperline Chapter Calibration 105 John H Kalivas and Paul J Gemperline Chapter Robust Calibration 167 Mia Hubert Chapter Kinetic Modeling of Multivariate Measurements with Nonlinear Regression 217 Marcel Maeder and Yorck-Michael Neuhold Chapter Response-Surface Modeling and Experimental Design .263 Kalin Stoyanov and Anthony D Walmsley Chapter Classification and Pattern Recognition 339 Barry K Lavine and Charles E Davidson © 2006 by Taylor & Francis Group, LLC Page xii Thursday, March 16, 2006 3:36 PM Chapter 10 Signal Processing and Digital Filtering 379 Steven D Brown Chapter 11 Multivariate Curve Resolution 417 Romà Tauler and Anna de Juan Chapter 12 Three-Way Calibration with Hyphenated Data 475 Karl S Booksh Chapter 13 Future Trends in Chemometrics 509 Paul J Gemperline © 2006 by Taylor & Francis Group, LLC Page Tuesday, January 31, 2006 11:49 AM Introduction to Chemometrics Paul J Gemperline CONTENTS 1.1 Chemical Measurements — A Basis for Decision Making .1 1.2 Chemical Measurements — The Three-Legged Platform 1.3 Chemometrics 1.4 How to Use This Book 1.4.1 Software Applications 1.5 General Reading on Chemometrics .5 References 1.1 CHEMICAL MEASUREMENTS — A BASIS FOR DECISION MAKING Chemical measurements often form the basis for important decision-making activities in today’s society For example, prior to medical treatment of an individual, extensive sets of tests are performed that often form the basis of medical treatment, including an analysis of the individual’s blood chemistry An incorrect result can have life-or-death consequences for the person receiving medical treatment In industrial settings, safe and efficient control and operation of high energy chemical processes, for example, ethylene production, are based on on-line chemical analysis An incorrect result for the amount of oxygen in an ethylene process stream could result in the introduction of too much oxygen, causing a catastrophic explosion that could endanger the lives of workers and local residents alike Protection of our environment is based on chemical methods of analysis, and governmental policymakers depend upon reliable measurements to make cost-effective decisions to protect the health and safety of millions of people living now and in the future Clearly, the information provided by chemical measurements must be reliable if it is to form the basis of important decision-making processes like the ones described above © 2006 by Taylor & Francis Group, LLC Page Tuesday, January 31, 2006 11:49 AM Practical Guide to Chemometrics 1.2 CHEMICAL MEASUREMENTS — THE THREELEGGED PLATFORM Sound chemical information that forms the basis of many of humanity’s important decision-making processes depends on three critical properties of the measurement process, including its (1) chemical properties, (2) physical properties, and (3) statistical properties The conditions that support sound chemical measurements are like a platform supported by three legs Credible information can be provided only in an environment that permits a thorough understanding and control of these three critical properties of a chemical measurement: Chemical properties, including stoichiometry, mass balance, chemical equilibria, kinetics, etc Physical properties, including temperature, energy transfer, phase transitions, etc Statistical properties, including sources of errors in the measurement process, control of interfering factors, calibration of response signals, modeling of complex multivariate signals, etc If any one of these three legs is missing or absent, the platform will be unstable and the measurement system will fail to provide reliable results, sometimes with catastrophic consequences It is the role of statistics and chemometrics to address the third critical property It is this fundamental role that provides the primary motivation for developments in the field of chemometrics Sound chemometric methods and a well-trained work force are necessary for providing reliable chemical information for humanity’s decision-making activities In the subsequent sections, we begin our presentation of the topic of chemometrics by defining the term 1.3 CHEMOMETRICS The term chemometrics was first coined in 1971 to describe the growing use of mathematical models, statistical principles, and other logic-based methods in the field of chemistry and, in particular, the field of analytical chemistry Chemometrics is an interdisciplinary field that involves multivariate statistics, mathematical modeling, computer science, and analytical chemistry Some major application areas of chemometrics include (1) calibration, validation, and significance testing; (2) optimization of chemical measurements and experimental procedures; and (3) the extraction of the maximum of chemical information from analytical data In many respects, the field of chemometrics is the child of statistics, computers, and the “information age.” Rapid technological advances, especially in the area of computerized instruments for analytical chemistry, have enabled and necessitated phenomenal growth in the field of chemometrics over the past 30 years For most of this period, developments have focused on multivariate methods Since the world around us is inherently multivariate, it makes sense to treat multiple measurements simultaneously in any data analysis procedure For example, when we measure the ultraviolet (UV) absorbance of a solution, it is easy to measure its entire spectrum © 2006 by Taylor & Francis Group, LLC Page Tuesday, January 31, 2006 11:49 AM Introduction to Chemometrics quickly and rapidly with low noise, rather than measuring its absorbance at a single wavelength By properly considering the distribution of multiple variables simultaneously, we obtain more information than could be obtained by considering each variable individually This is one of the so-called multivariate advantages The additional information comes to us in the form of correlation When we look at one variable at a time, we neglect correlation between variables, and hence miss part of the picture A recent paper by Bro described four additional advantages of multivariate methods compared with univariate methods [1] Noise reduction is possible when multiple redundant variables are analyzed simultaneously by proper multivariate methods For example, low-noise factors can be obtained when principal component analysis is used to extract a few meaningful factors from UV spectra measured at hundreds of wavelengths Another important multivariate advantage is that partially selective measurements can be used, and by use of proper multivariate methods, results can be obtained free of the effects of interfering signals A third advantage is that false samples can be easily discovered, for example in spectroscopic analysis For any well characterized chemometric method, aliquots of material measured in the future should be properly explained by linear combinations of the training set or calibration spectra If new, foreign materials are present that give spectroscopic signals slightly different from the expected ingredients, these can be detected in the spectral residuals and the corresponding aliquot flagged as an outlier or “false sample.” The advantages of chemometrics are often the consequence of using multivariate methods The reader will find these and other advantages highlighted throughout the book 1.4 HOW TO USE THIS BOOK This book is suitable for use as an introductory textbook in chemometrics or for use as a self-study guide Each of the chapters is self-contained, and together they cover many of the main areas of chemometrics The early chapters cover tutorial topics and fundamental concepts, starting with a review of basic statistics in Chapter 2, including hypothesis testing The aim of Chapter is to review suitable protocols for the planning of experiments and the analysis of the data, primarily from a univariate point of view Topics covered include defining a research hypothesis, and then implementing statistical tools that can be used to determine whether the stated hypothesis is found to be true Chapter builds on the concept of the univariate normal distribution and extends it to the multivariate normal distribution An example is given showing the analysis of near infrared spectral data for raw material testing, where two degradation products were detected at 0.5% to 1% by weight Chapter covers principal component analysis (PCA), one of the workhorse methods of chemometrics This is a topic that all basic or introductory courses in chemometrics should cover Chapter covers the topic of multivariate calibration, including partial least-squares, one of the single most common application areas for chemometrics Multivariate calibration refers generally to mathematical methods that transform and instrument’s response to give an estimate of a more informative chemical or physical variable, e.g., the target analyte Together, Chapters 3, 4, and form the introductory core material of this book © 2006 by Taylor & Francis Group, LLC Page 505 Saturday, March 4, 2006 2:04 PM Three-Way Calibration with Hyphenated Data 505 if y_opt= =1 | y_opt= =3, Yold=abs(Yold); end if z_opt= =1 | z_opt= =3, Zold=abs(Zold); end %UNFOLD KEEPING COLUMN SPACE INTACT col_Y=DATA; %UNFOLD KEEPING ROW SPACE INTACT for r=0:nsam-1 row_X=[row_X,DATA(x_size*r+1:x_size*(r+1),:)]; end %UNFOLD KEEPING SAMPLE SPACE INTACT for z=0:nsam-1 DATA_temp=DATA(x_size*z+1:x_size*(z+1),:); tube_Z = [tube_Z,DATA_temp(:)]; end %Major iterative loop while UCCnew > 1e-9 & reps < 2000 %CALCULATE NEW Z for i=1:rank xy=Xold(:,i)*Yold(:,i)'; Q=[Q;xy(:)']; end if z_opt= =1 | z_opt= =3 %Apply non-negativity constraints for i=1:nsam Znew(i,:)=nnls(Q',tube_Z(:,i))'; end else %UNCONSTRAINED SOLUTION Znew=tube_Z'*Q'*inv(Q*Q'); end Q=[ ]; if z_opt= =2 | z_opt= =3 %APPLY UNIMODALITY CONSTRAINTS [val,index]=max(abs(Znew)); for i = 1:rank for j = index(i):-1:2 if ((Znew(j,i)-Znew(j-1,i))* Znew(index(i),i))
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