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 recognition, but, in the end, it is the chemist who must do the chemistry
Bruce R. Kowalski Laboratory for Chemometrics Department of Chemistry University of Washington Seattle, Wash. 98195
Analytical chemists are among many scientists who rely heavily on graphics for the interpretation of experimental results. Except for convenience the use of laboratory computers has not altered this reliance significantly. A primary output of computerized experimentation is still graphical representation of numerical data. There are a t least two reasons why graphical presentation is not only prevalent but desirable. First, many chemists distrust computers and are not willing to allow a computer to reduce the results of experimental toil to a few numbers. Second, the human has a well-developed visual ability to recognize pictorial patterns and deviations from patterns. For the latter reason, the interactive role of the chemist in data analysis should be strengthened rather than reduced as originally proposed in the early days of computers. 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. The computer can be 1152A
used to fit the function and report goodness-of-fit and any significant deviations from the relationship. The modern analytical chemist, however, is becoming more involved in experimental design and measurement systems. Therefore, data analysis often means finding relationships not only between a measurement and sample composition but multiple measurements and sample function or origin as well. In these cases the relationships are not only multivariant but may be nonlinear with respect to the measurements. The solution is simple; since the scientist is the best pattern recognizer, an examination of an N dimensional plot where each measurement is represented by one of N axes should lead to the necessary mathematical relationship. While true in principle, the practical impossibility is obvious. Nevertheless, the need to deal with N-space plots cannot be avoided. Plotting each measurement vs. every other leads to N ( N - 1)/2 plots, but the pair-wise examination is neither effective nor practical. How then does one attack this dilemma? The historical approach is to solve the problem experimentally. This ap-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
proach has evolved due to a lack of computers and a love for experimentation. But as computer resources become more available, experimentation becomes more expensive, and the complexity of problems which science must solve grows, advances in computer science and other fields can provide new approaches. In 1969 a series of papers concerned with applications of learning machines ( I ) to the determination of molecular structural features directly from spectral data ( 2 )appeared in ANALYTICAL CHEMISTRY.Shortly thereafter, a review described early results of such applications ( 3 ) .Thus began a search for new mathematical methods to solve multivariant problems in chemistry. While it can be argued that recognition 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 that a considerable amount of interest in new mathematical methods evolved after these early applications of pattern recognition. Although the scope of all chemical applications is large a t this time and potentially even much greater, emphasis will be on the analysis of data generated by the analytical chemist. After a brief section on pattern recognition methods, the strengths and limitations of pattern recognition in chemistry will be discussed along with future uses and a perspective on how it fits into a much larger discipline the author identifies as chemometrics. Chemometrics includes the application of mathematical 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
literature (5, 6). A number of reviews on methods and applications which provide stepping stones to the more mathematical literature have also appeared in the chemical literature (79). I t is convenient to divide the operations 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. The choice depends on an understanding of the method's limitations, criteria, etc. Additionally, there are many useful chemometric methods that complement and enhance those of pattern recognition. A broad knowledge of chemometrics is necessary to ensure proper utilization of methods and optimal solutions to data analysis problems. If N 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 represent them as labeled points in an Ndimensional plot. Each of the N axes would then correspond to a measurement, and the value of the j t h measurement for the i t h object would serve to position the i t h point along the j t h axis. This representation for two measurements reduces to the simple two-dimensional graphs, an example of which is shown in Figure 1. Here, the concentrations of two enzymes in blood are plotted for a collection of 55 patients, each suffering from one of two different liver disorders. 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 manipulated with mathematical methods that follow direct analogies to the analysis of low-dimensional spaces. For example, the familiar two-space euclidean distance dap between points CY and /3 is
which is derived from the N-space euclidean distance,
which in turn can be derived from the N-space Mahalanobis metric
I t is important to recognize that by using extensions of mathematics commonly used in analyzing two-space plots, we can analyze N-space plots with the euclidean or some other metric. If some of the objects are tagged with a known property, the corresponding points in N-space are re-
Figure 1. Concentrations of two enzymes in blood of patients suffering from two (A and 6)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 B patients and collectively constitute the training set. Another set consisting of patients with known property, the test set, is frequently used to test the results of supervised and unsupervised learning. Also seen in the example are five points representing patients with unknown classification where it is perhaps the goal to use relevant clinical measurements to determine the classification to which an unknown belongs. This set can be called the eualuation set.
Display Methods If the goal in the analysis of the clinical data shown in Figure 1 is the separation of the two known categories, it is clear that although the two measurements contain some discriminatory ability, they are not sufficient to satisfy the goal. Adding additional measurements to the study should obviously 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 that the 1154A
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Preprocessing If the measurements for each object are assembled in a matrix X with elements X , , (ith object and j t h measurement), the process of operating on X to change the N-space data structure is known as preprocessing. The data in Figure 1 were range scaled so that the extremes within the two measurements 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 plotted 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 measurements are preprocessed, features are generated from the measurements for each object. The number of features can be greater than, equal to, or less than the number of measurements. The features can also be linear or nonlinear combinations of the measurements. Since the selection of a preprocessing method is dependent upon subsequent operations, further discussion on preprocessing will be included in the next three sections.
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EIGENVECTOR I Figure 2. Eigenvector projection of eight-measurement data structure (65% information retention)
display methods ( 1 0 ) provide a useful but unfortunately only partial solution to this problem. These methods attempt to project or map the points in N-space down to two- or threespace with the criteria that the data structure in the N-space be preserved as much as possible. When six additional 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. The 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. I t must be remembered that Figure 2 is an “approximate view” into eight-space, and the need to apply additional pattern recognition 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. Dimensionality reduction is accomplished by the projection to two-space, and the information content of the two new fea-
ANALYTICAL CHEMISTRY, VOL. 47, NO, 13, NOVEMBER 1975
tures (coordinates of the points in Figure 2 ) is greater than in any two of the original clinical measurements. This is because the new features are combinations of all of the measurements. Eigenvector projections generate optimal linear combinations where nonlinear mapping methods preserve more information but form nonlinear combinations of the original measurements. Second, preprocessing can be applied to the measurement space prior to the application of the display
Table I . Blood Constituents Measurement
Leucine aminopeptidase 5’-Nucleotidase G Iu ta mate oxaloacetate transaminase Glutamate pyruvate transaminase Orn ith ine car bamoy I transferase Guanine deaminase lsocitrate dehydrogenase Alkaline phosphatase
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EIGENVECTOR 1 Figure 3. Eigenvector projection of variance weighted eight-measurement data structure (80 YO information retention)
methods. When the scaled measurements were weighted by variance weighting ( 7 ) (Table I) so as to increase the importance of measurements that are good individual discriminators 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 information was lost in projection. Supervised Learning The result in the clinical data example thus far has been to investigate the separation of categories with display methods while applying some simple preprocessing methods. T o attack this application more directly, supervised learning ( I , 5,6) methods can be applied that develop classification rules using the examples in the training set. If the results of classification attempts on the training and test sets are acceptable to the chemist, the rules can he applied to classify unknowns in the evaluation set via the measurements. Supervised learning methods attempt to do in N-space what we have done by examining the first three figures; namely, determine the separability of the categories in the measurement space (or feature space if preprocessing has been applied).
When the eight-space data in the clinical measurement example are analyzed by any of the several supervised learning methods used routinely in our laboratory, classification rules that separate points into the two categories are easily determined, and the features that are most useful for separation are reported. For example, the linear learning machine ( I ) iteratively moves a decision surface in the measurement 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 exceeded. 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 that perfect separability was not attained. Several other supervised learning methods are known, and a few have found application in chemistry. The 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 classifier. The learning machine and knearest neighbor rule are among several supervised learning methods that
can be classed as nonprobabilistic because they do not determine or use the underlying probability distributions in the training set measurements. These distribution-free methods have a possible advantage when small training sets make the determination of the parameters of distributions uncertain. Their severe disadvantage is that a probability of correct classification, or the classification risk, cannot be reported. If the measurements can be seen to f i t a probability density function, then the parameters of the appropriate distribution 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 distributions in a single measurement space. In this simple example, points with measurement A and C would be classified as category one and two, respectively, with a probability of 1.0 associated with the classification. Point B 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 applications most probably due to a lack of sufficient data to establish the parameters and the simplicity and general availability of nonprobabilistic methods. A new supervised learning method called statistical isolinear multicomponent analysis (SIMCA) developed by Wold ( 1 1 ) has recently found application to chemical data analysis. SIMCA combines the simplicity and general applicability of the nonprobabilistic 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 models. In most cases, the number of components is quite small compared to the number of original measurements. Experience 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 particular application. Either the necessary discriminating information is not contained in the measurements or the information representation is not adequate. In the former case, it is obvious that better measurements are needed. This was seen in the clinical data example when additional measurements led to 100% discrimination. In the latter case, preprocessing can be applied to change the representation. Scaling and measurement weighting have already been discussed, but the number
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
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I
Category 2
Category 1
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8 Measurement
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Figure 4. Overlapping distributions in single measurement
of preprocessing methods from which to choose is greater than all of the rest of the pattern recognition methods combined. Several preprocessing methods have been used to enhance the results of supervised learning in chemical applications. Most prominent are those studies that use transform domains such as Fourier (12) and Hadamard (13) on spectral data prior to the determination of molecular structural features. The important point to note is that preprocessing is applied to reduce the number of measurements or features and/or to improve the information representation. Selection of a preprocessing method 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. There 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 de1156A
manding industrial shutdowns. The 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 data analysis methods is highly recommended for multimeasurement studies.
Unsupervised Learning When a training set of labeled data points is not available and the goal of a study is to gain an’understanding of the N-space data structure in the hope that a new property of the objects will be detected, the unsupervised learning methods of pattern recognition can be applied. The majority of unsupervised learning methods look for clusters of points (clusters are defined by a variety of criteria) in the N-space. When the eight-space data 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. The 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 that 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”. The supervised learning
Figure 5. Unsupervised learning results presented with eigenvector projection (same as Figure 2)
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
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methods had little difficulty in separating the two groups, but it is obvious from Figure 5 that no great void exists between the “A” group and the “B” group. In fact, the mixed cluster even indicates that 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 that 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 N-dimensional data structures and information representations. I t is expected that as interactive pattern recognition programs become commonplace in the analytical laboratory, their usefulness will increase. Applications
Early applications of pattern recognition to chemical data 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 breadth and depth. The increase in breadth comes from the analysis of data obtained from other areas of molecular spectroscopy as well as atomic spectroscopy and even nonspectral sources. The increase in depth comes from the application of improved preprocessing and supervised learning methods to the analysis of spectral data. Justice and Isenhour (141, for example, compared six supervised learning methods for classification accuracy and cost of implementation. The identification of structure features from spectral (molecular spectroscopy only) data can be represented by path 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 ( r n l e ) , and a point representing a molecule is positioned by the ion intensity a t each mle from its mass spectrum. In structure space, the axes can correspond to several molecular structural features (carbonyl groups, primary amine ni1158A
Figure 6. Chemical applications of multidimensionalmapping using pattern recognition
trogens, etc.), and the representative point is positioned by the frequency of occurrence of each structural feature in the molecule. Therefore, these early chemical pattern recognition applications really attempted the determination of rules that were trained on known structures to provide a mapping of molecules from spectral space to structure space. The objects under study need not be pure molecules but may be complex mixtures about which one might wish to map 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). The reverse mapping of 1 in Figure 6 is, of course, done by the spectrometer but is also represented by work done by Schechter and Jurs ( 1 6 ) which uses pattern 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 N-dimensional spaces where each space represents either what is known about the samples (types of measurements that can be obtained) or what is to be learned. Pattern recognition methods can then be used to map these samples from one space to another. Traditionally, the mapping is from one N-space to only one dimension a t a time in another ”-space. However, this should not be seen as a limitation because, for instance, the method of nonlinear mapping (10) and the method of Schiffman ( I 7) can be used to map points from N-space to ”-space (N2 N’). Further, information spaces can be combined, thereby allowing the mapping of points in two or more spaces to another space.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
Pattern recognition has been applied to all of the mappings shown in Figure 6. The 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 pattern 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 path 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. The practical goal in most production processes is the manufacture of only quality material. The mapping, therefore, is only a means to an end and is seldom the end in itself. Paths 4 and 5 represent exciting but difficult mappings recently attempted by a few chemical pattern recognizers. In these studies the function is the biological activity of molecules. The determination of differences in the biological function of a class of similar molecules from spectral data is an exciting prospect. Although the first attempt (21) suffered from an unfortunate selection of molecules, the idea is sound, and future research could lead to some very exciting results. The 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, pattern recognition has been used to relate structural information to biological activity (22),and the future will no doubt see an increase in this activity. In describing the philosophy and current chemical applications of pattern recognition, I was forced, for reasons of brevity, to ignore several very interesting and high-quality studies conducted by chemists. Additionally, there are even more excellent applications being conducted a t the time of this writing.
Future In some ways, chemistry has fallen behind other fields in the application of new methods to extract useful information from raw data. Analytical chemists and spectroscopists buried under the burden of interpreting the enormous quantities of data produced by the laboratory computer are well aware of this lag, and many are currently working on solutions. Chemists using pattern recognition methods, as well as optimization, factor analysis, and several other chemometric methods, are demonstrating that the computer 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 that mathematicians, statisticians, and computer scientists cannot and will not solve our problems for us. I t is the chemist who must accept the responsibility of infusing the tools of these information scientists into chemistry and even contributing to method development when and if necessary. This interfacing task is clearly a service to chemistry if the end result is a demonstrated enhancement in the acquisition and extraction of chemical information. With this in mind, what research in pattern recognition is needed in the future? New and improved chemometric methods are needed to perform the mappings indicated in Figure 6. The :reatest emphasis in method development should be on preprocessing. The chemical literature will no doubt see improved methods of display, supervised and unsupervised learning that nill enhance the results of the various mappings shown in the last section. Preprocessing method improvements nill provide better information representations and will therefore provide batures more related to the informa;ion desired. The scientist is somenhat biased in thinking that if a spec:rum or other datum is optimal for _iuman _ _analysis, then it should be
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ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
ideal for computer analysis. This may not be the case. The scientist seeks simplified spectra to make analysis easier. The computer can take advantage of complex spectra. For instance, many of the successful applications of pattern recognition t o spectral analysis use preprocessing methods that transform spectra into waveforms that look much more complicated and are of little use to the chemist. Probably the most important area of future development is the incorporation of pattern 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 t o chemists and spectroscopists. Data from several instruments can be combined t o attack more difficult problems involving high-dimensional data spaces. In much the same way as the chemist routinely uses various spectrometric tools, pattern recognition and other chemometric methods should be available to the chemist on the same basis. The use of interactive computer graphics, the cost of which has been falling sharply in recent years, will be an integral part of online measurement acquisition and analysis systems. As pattern recognition programs become more available to chemists, the breadth and depth of applications will certainly increase. This process is already under way as more than 50 chemical laboratories have received pattern recognition systems from our laboratory (ARTHUR) or from C. F. Bender of the Lawrence Livermore Laboratory (RECOG). Applications should either demonstrate a clear improvement over existing techniques to solve chemical problems or open new fields of investigation which were previously untouched because the tools were not available. Pattern recognition methods operate with defined criteria and attempt to distill useful information from raw data. If the criteria used by the methods and their limitations and pitfalls are not clearly understood by chemists, the dangers are incorrect interpretation and a misuse of costly measurements. I t is the author’s opinion that they should be used to extend the ability of human pattern recognition and rely heavily on graphics for the presentation of results. The computer can assimilate many more numbers a t one time than can the chemist, but it is the 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, A n d . Chem., 41,
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1949 (1969) and references therein. (3) T. L. Isenhour and P. C. Jurs, ibid., 43, (lo), 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,” Vol2, 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. Reu. Anal. Chem., 4 , l
(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. Colln. Cardiol., 6,383 (1974).
(20) B. R. Kowalski, Chem. Technol., 300 (May 1974). (21) K. H. Tine. R.C.T. Lee. G.W.A.
Milne, M. Shypiro, and A.’M. Guarino, Science, 180,417 (1973). (22) G. Redl, R. D. Cramer IV, and C. E. Berkoff, Chem. Sot. Reu., 3,273 (1974).
(1974). (9) P. C. Jurs and T. L. Isenhour, “Chemi-
cal 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. Wan en, N. M. Frew, T. L. Isenhour, and P. Jurs, Appl. Spectrosc.,
8.
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). (151 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 ~~
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Bruce R. Kowalski is associate professor of chemistry at the University of Washington. After receiving his P h D from the University of Washington in 1969, he applied pattern recognition techniques to several areas of petroleum research for the Shell Development Co. in Emeryville, Calif., and Houston, Tex. In 1971 he joined the General Chemistry Division at Lawrence Livermore Laboratory and then, in 1972, became a n assistant professor at Colorado State University. He then moved t o Seattle where he has been since December 1973. His research interests include the development and application of chemometric methods primarily for the analysis of analytical data and t o the relationship between molecular structure and biological activity. Additionally, he is investigating the use of improved chelating agents for trace metal analysis.
Trm
Shaker Model BT
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DISTILLED IN GLASS’” Gentle Swish to Violent Swirl Replicable Operation Handles Flasks, Beakers, Separatory Funnels, and Fleakers
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Burrell Shakers perform any action from a slight tilt, gentle agitation to a pitched, violent swirl. All at a constant speed for as long as necessary. Results can be replicated by simply duplicating the initial angle and speed settings. Exclusive Build-Up design permits short or long side arms, the top platform and separatory clamps to be easily added or removed. Burrell WristAction’” Shakers , . . the PERFECT Shaker.
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ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMB 3 1975
