MEASUREMENT ANA Applications should offer advantages over existing techniques to solve chemical problems or open new fields for investigation. Computer pattern recognition methods extend the ability of human pattern rec ognition, but, in the end, it is the chemist who must do the chemistry
Bruce R. Kowalski Laboratory for C h e m o m e t r i c s Department of Chemistry University of Washington Seattle, W a s h . 9 8 1 9 5
Analytical chemists are among many scientists who rely heavily on graphics for the interpretation of ex perimental results. Except for conve nience the use of laboratory comput ers has not altered this reliance signif icantly. A primary o u t p u t of comput erized experimentation is still graphi cal representation of numerical data. There are at least two reasons why graphical presentation is not only prevalent b u t desirable. First, many chemists distrust computers and are not willing to allow a computer to re duce the results of experimental toil to a few numbers. Second, the h u m a n has a well-developed visual ability to recognize pictorial p a t t e r n s and devia tions from p a t t e r n s . For the latter rea son, the interactive role of the chemist in data analysis should be strength ened rather than reduced as originally proposed in the early days of comput ers. If an analytical chemist is seeking the relationship between a physical measurement and the concentration of a species in a sample, a simple plot of the measurement vs. concentration usually leads to the correct functional relationship. T h e computer can be 1152 A ·
used to fit the function and report goodness-of-fit and any significant de viations from the relationship. T h e modern analytical chemist, however, is becoming more involved in experi mental design and measurement sys tems. Therefore, data analysis often means finding relationships not only between a measurement and sample composition but multiple measure ments and sample function or origin as well. In these cases the relation ships are not only multivariant but may be nonlinear with respect to the measurements. T h e solution is simple; since the scientist is the best p a t t e r n recognizer, an examination of an Ndimensional plot where each measure m e n t is represented by one of Ν axes should lead to the necessary m a t h e matical relationship. While true in principle, the practical impossibility is obvious. Nevertheless, the need to deal with Ν-space plots cannot be avoided. Plotting each measurement vs. every other leads to N(N — l ) / 2 plots, b u t the pair-wise examination is neither effective nor practical. How t h e n does one attack this dilemma? T h e historical approach is to solve the problem experimentally. This ap
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proach has evolved due to a lack of computers and a love for experimenta tion. But as computer resources be come more available, experimentation becomes more expensive, and the complexity of problems which science must solve grows, advances in com puter science and other fields can pro vide new approaches. In 1969 a series of papers concerned with applications of learning machines (1 ) to the determination of molecular structural features directly from spec tral data (2) appeared in ANALYTICAL C H E M I S T R Y . Shortly thereafter, a re view described early results of such applications (3). T h u s began a search for new mathematical methods to solve multivariant problems in chem istry. While it can be argued t h a t rec ognition of the importance of multivariant data analysis methods in chemistry started much earlier with linear free energy relationships (4) and other studies, there is little doubt t h a t a considerable a m o u n t of interest in new mathematical methods evolved after these early applications of pat tern recognition. Although the scope of all chemical applications is large at this time and potentially even much greater, emphasis will be on the analy sis of data generated by the analytical chemist. After a brief section on pat tern recognition methods, the strengths and limitations of pattern recognition in chemistry will be dis cussed along with future uses and a perspective on how it fits into a much larger discipline the author identifies as chemometrics. Chemometrics in cludes the application of mathemati cal and statistical methods to the analysis of chemical measurements. Methodology For a detailed understanding of the many methods of pattern recognition, the interested reader should refer to the engineering and computer science
Report
BY PATTERN RECOGNITIO literature (5, 6). A number of reviews on methods and applications which provide stepping stones to the more mathematical literature have also ap peared in the chemical literature ( 7 9). It is convenient to divide the opera tions or types of pattern recognition methods into four categories. These operations—display, preprocessing, supervised learning, and unsupervised learning—will be presented with the aid of a simple example. There are several methods from which to choose within each of the four categories. T h e choice depends on an understanding of the method's limitations, criteria, etc. Additionally, there are many use ful chemometric methods t h a t com plement and enhance those of pattern recognition. A broad knowledge of chemometrics is necessary to ensure proper utilization of methods and op timal solutions to data analysis prob lems. If Ν measurements are made on a collection of objects, and the goal is to learn something about the objects, it is useful to study the similarities and dissimilarities among the objects. One way of studying the objects is to repre sent them as labeled points in an Ndimensional plot. Each of the Ν axes would then correspond to a measure ment, and the value of the jth mea surement for the i t h object would serve to position the ith point along the jih axis. This representation for two measurements reduces to the sim ple two-dimensional graphs, an exam ple of which is shown in Figure 1. Here, the concentrations of two en zymes in blood are plotted for a collec tion of 55 patients, each suffering from one of two different liver disor ders. If three clinical measurements are plotted, computer graphics can be used to analyze the three-space plot. Chemists are often concerned with the analysis of much higher dimensional spaces (often >300) which, of course,
cannot be seen but can be manipulat ed with mathematical methods t h a t follow direct analogies to the analysis of low-dimensional spaces. For exam ple, the familiar two-space euclidean distance άαβ between points a and β is Γ 2
"Ji/2
which is derived from the iV-space eu clidean distance,
Ν
άαβ = [ Λ Σ (x„* - χ*) 2 ]
1/2
(2)
which in turn can be derived from the iV-space Mahalanobis metric N
Ma,
Γ
N k=i
(x„* -
x0k)f'
I/P
(3)
It is important to recognize that by using extensions of mathematics com monly used in analyzing two-space plots, we can analyze iV-space plots with the euclidean or some other met ric. If some of the objects are tagged with a known property, the corre sponding points in Ν-space are re-
Figure 1. Concentrations of two enzymes in blood of patients suffering from two (A and B) liver disorders
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ferred to as members of a training set. In Figure 1 the category A patients are distinguished from the category Β pa tients and collectively constitute the training set. Another set consisting of patients with known property, the test set, is frequently used to test the re sults of supervised and unsupervised learning. Also seen in the example are five points representing patients with unknown classification where it is per haps the goal to use relevant clinical measurements to determine the classi fication to which an unknown belongs. This set can be called the evaluation set. Preprocessing If the measurements for each object are assembled in a matrix X with ele ments Xij (ith object and _/th mea surement), the process of operating on X to change the Ν -space data struc ture is known as preprocessing. T h e data in Figure 1 were range scaled so t h a t the extremes within the two mea surements form the limits of the plot. If this simple form of preprocessing was not used, the variation in one measurement would receive undue emphasis due to its dominant range. This simple form of preprocessing is familiar to anyone who has ever plot ted two measurements with dissimilar ranges. Preprocessing is usually applied to reduce the number of measurements used in subsequent analysis, enhance the information representation of the measurements, or both. When mea surements are preprocessed, features are generated from the measurements for each object. T h e number of fea tures can be greater than, equal to, or less than the number of measure ments. T h e features can also be linear or nonlinear combinations of the mea surements. Since the selection of a preprocessing method is dependent upon subsequent operations, further discussion on preprocessing will be in cluded in the next three sections. Display Methods If the goal in the analysis of the clinical d a t a shown in Figure 1 is the separation of the two known catego ries, it is clear t h a t although the two measurements contain some discrimi natory ability, they are not sufficient to satisfy the goal. Adding additional measurements to the study should ob viously be done, but, unfortunately, the addition increases the dimension of the plot, and the unique pattern recognizing abilities of the scientist are no longer applicable. Are we then forced to blindly accept the results of the mathematical analysis methods in the form of tables of numbers so easily generated by computers? Experience in our laboratory has shown t h a t the
Figure 2. Eigenvector projection of eight-measurement data structure ( 6 5 % infor mation retention)
display methods (10) provide a useful b u t unfortunately only partial solu tion to this problem. These methods a t t e m p t to project or map the points in /V-space down to two- or threespace with the criteria t h a t the data structure in the iV-space be preserved as much as possible. When six addi tional clinical measurements (Table I) are obtained on the patients in Figure 1, and a linear projection method is used to project the points from eightspace to two-space, Figure 2 results. T h e eigenvector method, used here, attempts to retain total variance by forming two orthogonal projection axes which are linear combinations of the eight measurements. In Figure 2, 65% of the total variance is preserved. All eight measurements combine to provide a better separation of the two categories. It must be remembered t h a t Figure 2 is an "approximate view" into eight-space, and the need to apply additional pattern recogni tion methods still exists. Before leaving display methods, two additional points can be made. First, by the definition of preprocessing methods, the display methods can be included as special cases. Dimension ality reduction is accomplished by the projection to two-space, and the infor mation content of the two new fea
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tures (coordinates of the points in Fig ure 2) is greater than in any two of the original clinical measurements. This is because the new features are combina tions of all of the measurements. Ei genvector projections generate opti mal linear combinations where nonlin ear mapping methods preserve more information but form nonlinear com binations of the original measure ments. Second, preprocessing can be applied to the measurement space prior to the application of the display
Table 1. Blood Constituents Variance Measurement
wt^
Leucine aminopeptidase 5'-Nucleotidase Glutamate oxaloacetate transaminase Glutamate pyruvate transaminase Ornithine carbamoyl transferase Guanine deaminase Isocitrate dehydrogenase Alkaline phosphatase
1.7 1.5 1.6 1.8 1.3 1.8 1.2 3.5
a W e i g h t = 1.0 means no discrim ination i n f o r m a t i o n .
Figure 3. Eigenvector projection of variance weighted eight-measurement data structure (80 % information retention)
methods. When the scaled measure ments were weighted by variance weighting (7) (Table I) so as to in crease the importance of measure ments t h a t are good individual dis criminators of the two categories, the plot in Figure 3 results. The projection shows a greater degree of separation, but the analysis of the eight-space must continue because some informa tion was lost in projection. Supervised Learning
The result in the clinical data exam ple thus far has been to investigate the separation of categories with display methods while applying some simple preprocessing methods. To attack this application more directly, supervised learning (2, 5, 6) methods can be ap plied that develop classification rules using the examples in the training set. If the results of classification attempts on the training and test sets are ac ceptable to the chemist, the rules can be applied to classify unknowns in the evaluation set via the measurements. Supervised learning methods at tempt to do in iV-space what we have done by examining the first three fig ures; namely, determine the separabil ity of the categories in the measure ment space (or feature space if prepro cessing has been applied).
When the eight-space data in the clinical measurement example are an alyzed by any of the several super vised learning methods used routinely in our laboratory, classification rules that separate points into the two cate gories are easily determined, and the features t h a t are most useful for sepa ration are reported. For example, the linear learning machine (1) iteratively moves a decision surface in the mea surement space until either all of the points in one category lie on one side of the hyperplane and the points in the other category lie on the other, or a limit of time or iterations is exceed ed. In the former case, the training set is said to be linearly separable. The separating surface was found for our example in a very few iterations. In the latter case, it can only be said t h a t perfect separability was not attained. Several other supervised learning methods are known, and a few have found application in chemistry. T h e k-Nearest Neighbor Classification Rule (7) which classifies an unknown point according to a majority vote of its k-nearest neighbors is conceptually simple and has the advantages of being a nonlinear, multicategory clas sifier. The learning machine and knearest neighbor rule are among sev eral supervised learning methods that
can be classed as nonprobabilistic be cause they do not determine or use the underlying probability distributions in the training set measurements. These distribution-free methods have a pos sible advantage when small training sets make the determination of the parameters of distributions uncertain. Their severe disadvantage is t h a t a probability of correct classification, or the classification risk, cannot be re ported. If the measurements can be seen to fit a probability density function, then the parameters of the appropriate dis tribution can be determined from the training set and the preferred Bayes Classification Rule (5) can be used. This is illustrated in Figure 4 which represents two overlapping distribu tions in a single measurement space. In this simple example, points with measurement A and C would be classi fied as category one and two, respec tively, with a probability of 1.0 associ ated with the classification. Point Β would have an equal probability (0.5 for category one and 0.5 for category two) of coming from either category. Probabilistic classification rules have generally been avoided in chemical ap plications most probably due to a lack of sufficient data to establish the pa rameters and the simplicity and gen eral availability of nonprobabilistic methods. A new supervised learning method called statistical isolinear multicomponent analysis (SIMCA) developed by Wold (11) has recently found ap plication to chemical data analysis. SIMCA combines the simplicity and general applicability of the nonproba bilistic methods with the robustness of probabilistic methods. The axes of greatest variance for each category are determined by principal component analysis, and least squares is used to fit the training set members to their respective principal component mod els. In most cases, the number of com ponents is quite small compared to the number of original measurements. Ex perience in our laboratory has shown SIMCA to be the supervised learning method of choice for many chemical applications. There are usually two reasons for poor classification results in a particu lar application. Either the necessary discriminating information is not con tained in the measurements or the in formation representation is not ade quate. In the former case, it is obvious t h a t better measurements are needed. This was seen in the clinical data ex ample when additional measurements led to 100% discrimination. In the lat ter case, preprocessing can be applied to change the representation. Scaling and measurement weighting have al ready been discussed, but the number
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Unsupervised Learning
Figure 4. Overlapping distributions in single measurement
of preprocessing methods from which to choose is greater t h a n all of the rest of the p a t t e r n recognition methods combined. Several preprocessing m e t h o d s have been used to enhance the results of supervised learning in chemical applications. Most promin e n t are those studies t h a t use transform domains such as Fourier (12) and H a d a m a r d (13) on spectral data prior to the determination of molecular structural features. T h e important point to note is t h a t preprocessing is applied to reduce the n u m b e r of measurements or features and/or to improve the information representation. Selection of a preprocessing m e t h o d depends upon a knowledge of the ideal measurement representation for the supervised learning method of choice. In our example, the property of the objects is a category or class membership. This is because the classic pattern recognition application involves classification. If the property of interest is continuous or semicontinuous, such as the ozone concentration over a city, or a biological response to a chemical measured on a continuous scale between two limits, the objects can either be forced into classes based on ranges of the property or other chemometric methods can be used to relate the measurements to the property. T h e r e are actually several cases where classification according to ranges is desirable. For instance, atmospheric contaminant measurements are often conveniently divided into ranges associated with appropriate actions to be taken: low concentration requiring no action, moderate levels leading to a curtailment of industrial activity, and extreme levels de-
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manding industrial shutdowns. T h e application of probabilistic supervised learning methods to predict future levels from current atmospheric measurements could complement current modeling efforts and provide more confidence in implementing suggested actions. Since sample collection and measurements represent the expensive parts of most studies, the application of several complementary d a t a analysis methods is highly recommended for m u l t i m e a s u r e m e n t studies.
W h e n a training set of labeled data points is not available and the goal of a study is to gain an'understanding of the ./V-space data structure in the hope t h a t a new property of the objects will be detected, the unsupervised learning methods of p a t t e r n recognition can be applied. T h e majority of unsupervised learning methods look for clusters of points (clusters are defined by a variety of criteria) in the ./V-space. When the eight-space d a t a in the clinical example is subjected to an unsupervised learning method [Zahn minimal spanning tree method (5)], five distinct groups or clusters of points are detected. These groups are identified in Figure 5 with the aid of the eigenvector projection to twospace (Figure 2). Ignoring the classifications, Figure 5 is an excellent beginning to the analysis of the eight-dimensional data structure. Neither the display method nor the cluster analysis method was given the classifications of the points. Figure 5 is the combination of two complementary analyses of eight-space, each surfacing the inadequacies of the other. T h e two single-point clusters represent two patients with clinical measurements quite different from each other and the rest of the patients. From the positions of the three large clusters, it might be postulated t h a t there are three different types of disorders represented within the collection of patients. Returning to the classifications, one cluster is purely "A", another purely " B " , and the third is predominantly "A". T h e supervised learning
Figure 5. Unsupervised learning results presented with eigenvector projection (same as Figure 2)
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methods had little difficulty in separating the two groups, but it is obvious from Figure 5 t h a t no great void exists between the " A " group and the " B " group. In fact, the mixed cluster even indicates t h a t a few " B ' " s are more like the "A'"s. Finding clusters is a simple task for the computer. Assigning a meaning to the separation of the groups of patients cannot be done by the computer and is by far the most difficult task. In our example, unsupervised learning suggested the discrimination of three liver disorders by the measurements. If, however, the data analysis began with the theory t h a t only one disorder was involved, the theory would certainly be challenged by the results in Figure 5. Unsupervised learning methods have not found extensive application in analytical chemistry. Nevertheless, when used with display methods, they can aid in understanding TV-dimensional data structures and information representations. It is expected t h a t as interactive pattern recognition programs become commonplace in the analytical laboratory, their usefulness will increase. Applications Early applications of p a t t e r n recognition to chemical d a t a involved the determination of molecular structural features from low-resolution mass spectra using the learning machine. Since then, several other pattern recognition methods have been applied to chemical data analysis, and the applications have seen an increase in both b r e a d t h and depth. T h e increase in breadth comes from the analysis of d a t a obtained from other areas of molecular spectroscopy as well as atomic spectroscopy and even nonspectral sources. T h e increase in depth comes from the application of improved preprocessing and supervised learning methods to the analysis of spectral data. Justice and Isenhour (14), for example, compared six supervised learning methods for classification accuracy and cost of implementation. T h e identification of structure features from spectral (molecular spectroscopy only) data can be represented by p a t h 1 in Figure 6. Molecules or mixtures of molecules are therein represented by points in a high-dimensional spectral data space and concurrently in a high-dimensional structure or composition space. For example, the axes in the spectral space can be mass-to-charge ratios (m/e), and a point representing a molecule is positioned by the ion intensity at each m/e from its mass spectrum. In structure space, the axes can correspond to several molecular structural features (carbonyl groups, primary amine ni1158 A .
Figure 6. Chemical applications of multidimensional mapping using pattern recognition trogens, etc.), and the representative point is positioned by t h e frequency of occurrence of each structural feature in the molecule. Therefore, these early chemical pattern recognition applications really a t t e m p t e d the determination of rules t h a t were trained on known structures to provide a m a p ping of molecules from spectral space to structure space. T h e objects under study need not be pure molecules but may be complex mixtures about which one might wish to m a p to a composition space or even to an average structure space. An excellent example of the latter is the work of Tunnicliff and Wadsworth (15) which mapped gasoline samples from mass spectral space to an average structural space for hydrocarbons (commonly called type analysis). T h e reverse mapping of 1 in Figure 6 is, of course, done by the spectrometer but is also represented by work done by Schechter and J u r s (16) which uses p a t t e r n recognition to generate mass spectra from a list of molecular structural features. In this study, candidate structures are used to generate spectra which are matched to the measured spectrum for conformation. Following this mapping perspective, samples (pure molecules or complex mixtures) can be positioned in TV-dimensional spaces where each space represents either what is known about the samples (types of measurements t h a t can be obtained) or what is to be learned. P a t t e r n recognition methods can then be used to m a p these samples from one space to another. Traditionally, the mapping is from one iV-space to only one dimension at a time in another TV'-space. However, this should not be seen as a limitation because, for instance, the method of nonlinear mapping (10) and the method of Schiffman (17) can be used to m a p points from TV-space to TV'-space (TV > TV'). Further, information spaces can be combined, thereby allowing the mapping of points in two or more spaces to another space.
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P a t t e r n recognition has been applied t o all of the mappings shown in Figure 6. T h e determination of the geographical origin of archaeological artifacts from the concentrations of trace elements (18) and the determination of the position in the heart from which a tissue sample was extracted (19), also by elemental composition, are just two examples of using p a t t e r n recognition for path 2 mapping. In these examples, the trace element data are considered as nonspectral data because the data need not be obtained by atomic spectroscopic measurements. Solving material production problems (20) with pattern recognition is potentially a most rewarding area of application. These studies are represented by p a t h 3 in Figure 6 and involve the discrimination of acceptable quality material from unacceptable quality material using chemical and physical properties of the material. These studies do not usually end with the mapping but involve dimensionality reduction of the measurement space to identify the measurements related to the quality of the material. T h e practical goal in most production processes is the manufacture of only quality material. T h e mapping, therefore, is only a means to an end and is seldom t h e end in itself. P a t h s 4 and 5 represent exciting but difficult mappings recently a t t e m p t e d by a few chemical pattern recognizers. In these studies the function is the biological activity of molecules. T h e determination of differences in the biological function of a class of similar molecules from spectral data is an exciting prospect. Although the first att e m p t (21 ) suffered from an unfortunate selection of molecules, the idea is sound, and future research could lead to some very exciting results. T h e understanding of structure activity relationships (SAR) has long been of interest to chemists (22). Most SAR research uses multiple or stepwise regression analysis to relate physical
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and chemical properties of molecules to their biological activity (path 3). Others use regression analysis to fit structural information to biological activity (path 4). Recently, p a t t e r n recognition has been used to relate structural information to biological activity (22), and the future will no d o u b t see an increase in this activity. In describing the philosophy and current chemical applications of pat tern recognition, I was forced, for rea sons of brevity, to ignore several very interesting and high-quality studies conducted by chemists. Additionally, there are even more excellent applica tions being conducted a t the time of this writing. Future
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In some ways, chemistry has fallen behind other fields in the application of new methods to extract useful in formation from raw data. Analytical chemists and spectroscopists buried under t h e burden of interpreting the enormous quantities of data produced by the laboratory computer are well aware of this lag, and many are cur rently working on solutions. Chemists using p a t t e r n recognition methods, as well as optimization, factor analysis, a n d several other chemometric meth ods, are demonstrating t h a t the com puter is capable of aiding significantly in providing better and more useful chemical information with less effort expended by the chemist. T o many chemists, it is painfully obvious t h a t mathematicians, statisticians, and computer scientists cannot and will not solve our problems for us. It is the chemist who m u s t accept the responsi bility of infusing the tools of these in formation scientists into chemistry and even contributing to method de velopment when and if necessary. T h i s interfacing task is clearly a ser vice to chemistry if the end result is a demonstrated enhancement in the ac quisition and extraction of chemical information. With this in mind, what research in p a t t e r n recognition is needed in the future? New and improved chemometric methods are needed to perform the mappings indicated in Figure 6. T h e greatest emphasis in method develop m e n t should be on preprocessing. T h e chemical literature will no doubt see improved methods of display, super vised and unsupervised learning t h a t will enhance the results of the various mappings shown in the last section. Preprocessing method improvements will provide better information repre sentations and will therefore provide features more related to the informa tion desired. T h e scientist is some what biased in thinking t h a t if a spec t r u m or other d a t u m is optimal for h u m a n analysis, then it should be
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1975
ideal for computer analysis. This m a y not be t h e case. T h e scientist seeks simplified spectra to make analysis easier. T h e computer can take advan tage of complex spectra. For instance, many of the successful applications of p a t t e r n recognition t o spectral analy sis use preprocessing methods t h a t transform spectra into waveforms t h a t look much more complicated and are of little use to t h e chemist. Probably t h e most i m p o r t a n t area of future development is the incorpo ration of p a t t e r n recognition methods into on-line measurement systems. In this way, the power of the methods can be used for real problems, and the methods will become familiar tools to chemists and spectroscopists. D a t a from several instruments can be com bined to attack more difficult p r o b lems involving high-dimensional d a t a spaces. In much the same way as t h e chemist routinely uses various spectrometric tools, p a t t e r n recognition and other chemometric methods should be available to the chemist on the same basis. T h e use of interactive computer graphics, the cost of which has been falling sharply in recent years, will be an integral p a r t of on line measurement acquisition and analysis systems. As p a t t e r n recognition programs be come more available to chemists, t h e b r e a d t h and depth of applications will certainly increase. This process is al ready under way as more t h a n 50 chemical laboratories have received p a t t e r n recognition systems from our laboratory ( A R T H U R ) or from C. F. Bender of the Lawrence Livermore Laboratory (RECOG). Applications should either demon strate a clear improvement over exist ing techniques to solve chemical prob lems or open new fields of investiga tion which were previously untouched because the tools were not available. P a t t e r n recognition methods oper ate with defined criteria and a t t e m p t to distill useful information from raw data. If t h e criteria used by the meth ods and their limitations and pitfalls are not clearly understood by chem ists, the dangers are incorrect inter pretation and a misuse of costly mea surements. It is the author's opinion t h a t they should be used to extend the ability of h u m a n p a t t e r n recognition and rely heavily on graphics for the presentation of results. T h e computer can assimilate many more numbers a t one time t h a n can the chemist, b u t it is t h e chemist who, in the end, must do the chemistry. References (1) N. J. Nilsson, "Learning Machines," McGraw-Hill, New York, N.Y., 1965. (2) P. C. Jurs, B. R. Kowalski, T. L. Isenhour, and C. N. Reilley, Anal. Chem., 41,
1949 (1969) and references therein. (3) T. L. Isenhour and P. C. Jurs, ibid., 43, (10), 20A (1971). (4) N. B. Chapman and J. Shorter, Eds., "Advances in Linear Free Energy Relations," Plenum, London, England, 1972. (5) H. C. Andrews, "Mathematical Techniques in Pattern Recognition," WileyInterscience, New York, N.Y., 1972. (6) E. A. Patrick, "Fundamentals of Pattern Recognition," Prentice-Hall, Englewood Cliffs, N.J., 1972. (7) B. R. Kowalski, "Pattern Recognition in Chemical Research," in "Computers in Chemical and Biochemical Research," Vol 2, C. E. Klopfenstein and C. L. Wilkins, Eds., Academic Press, New York, N.Y., 1974. (8) T. L. Isenhour, B. R. Kowalski, and P. C. Jurs, Crit. Rev. Anal. Chem., 4, 1 (1974). (9) P. C. Jurs and T. L. Isenhour, "Chemical Applications of Pattern Recognition," Wiley-Interscience, New York, N.Y., 1975. (10) B. R. Kowalski and C. F. Bender, J. Am. Chem. Soc, 95, 686 (1973). (11) S. Wold, Technical Report No. 357, Dept. of Statistics, University of Wisconsin, Madison, Wis. (12) L. E. Wangen, N. M. Frew, T. L. Isenhour, and P. C. Jurs, Appl. Spectrosc, 25 203 (1971). (13) *B. R. Kowalski and C. F. Bender, Anal. Chem., 45, 2234 (1973). (14) J. B. Justice and T. L. Isenhour, ibid., 46, 223 (1974). (15) D. D. Tunnicliff and P. A. Wadsworth, ibid., 45,12 (1973). (16) J. Schechter and P. C. Jurs, Appl. Spectrosc, 27, 30 (1973). (17) S. S. Schiffman, Science, 185, 112
(1974). (18) B. R. Kowalski, T. F. Schatzki, and F. H. Stross, Anal. Chem., 44, 2176 (1972). (19) J. Webb, K. A. Kirk, W. Niedermeier, J. H. Griggs, M. E. Turner, and T. N. James, J. Molec. Colin. Cardiol., 6, 383 (1974).
(20) B. R. Kowalski, Chem. Technol, 300 (May 1974). (21) K. H. Ting, R.C.T. Lee, G.W.A. Milne, M. Shapiro, and A. M. Guarino, Science, 180, 417 (1973). (22) G. Redl, R. D. Cramer IV, and C. E. Berkoff, Chem. Soc. Rev., 3, 273 (1974).
B r u c e R. K o w a l s k i is associate professor of chemistry a t the University of Washington. After receiving his P h D from t h e University of Washington in 1969, he applied p a t t e r n recognition techniques t o several areas of petroleum research for t h e Shell Development Co. in Emeryville, Calif., and Houston, Tex. In 1971 he joined the General Chemistry Division a t Lawrence Livermore Laboratory a n d t h e n , in 1972, became an assistant professor a t Colorado S t a t e University. H e t h e n moved to Seattle where he has been since December 1973. His research interests include t h e development a n d application of chemometric m e t h ods primarily for t h e analysis of analytical d a t a and to t h e relationship between molecular structure a n d biological activity. Additionally, he is investigating t h e use of improved chelating agents for trace metal analysis.
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