Comparison of Multidimensional Scaling and Principal Component Analysis of Interspecific Variation in Bacteria*

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1 ANNALS OF CLINICAL AND LABORATORY SCIENCE, Vol. 18., No. 6 Copyright 1988, Institute for Clinical Science, Inc. Comparison of Multidimensional Scaling and Principal Component Analysis of Interspecific Variation in Bacteria* DAVID A. LACHER, M.D., and EDWARD D. O DONNELL, Ph.D. Department of Pathology, Medical College of Ohio, Toledo, OH ABSTRACT Multidimensional scaling (MDS) and principal component analysis (PCA) were applied to bacterial taxonomy. The biochemical profiles of 42 isolates consisting of four species of Enterobacteriaceae were used. Both MDS and PCA use proximity measures such as the correlation coefficient or Euclidean distance to generate a spatial configuration (map) of points in multidimensional space where distances between points reflect the similarity among isolates. Multidimensional scaling and principal component analysis were able to discriminate organisms in two dimensions. The test components of the MDS and PCA factors (derived variables composed of linear combination of biochemical tests) were different for a two-dimensional solution. Introduction but these approaches assume statistically independent variables which do not usually occur.6,7 Discriminant analysis techniques have also been applied to bacterial taxonomy but may require reductions of large variable sets prior to analysis.3,17 Principal component analysis (PCA), a m ultivariate tech n iq u e which examines the correlations b e tween tests and reduces variable sets, has been applied to taxonomic studies of bacteria.1,4,10,11,14 Multidimensional scaling (MDS) can also be used to reduce variable sets and has been applied in the social sciences, but rarely to laboratory m edicine.12,13 Different populations of microorganisms can be represented by geometric models.9 A data set of p isolates analyzed by n tests can be visualized as a cloud of /88/ $01.20 Institute for Clinical Science, Inc. The system atic analysis of variation among bacterial species can help construct useful num eric taxonom ic schemes to classify and identify organisms. Bacterial isolates are commonly identified by a profile of biochemical tests. By exam ining th e correlation among these tests, statistical techniques can be useful in bacterial taxonomy. Many statistical techniques have been used to classify microorganisms. Bayesian and relative likelihood models can be applied to identify bacterial isolates, Address rep rin t requests to David A. Lacher, M.D., Departm ent of Pathology, Medical College of Ohio, C.S. #10008, Toledo, OH

2 456 M D S A N D PCA ANALYSIS OF BACTERIA p points in n-dimensional hyperellipsoid space. For efficiency, it is desirable to reduce the dimensional space (reduce the number of tests) while preserving the maximum amount o f information used to discriminate different bacterial groups. Geometrically, multidimensional scaling and principal component analysis seek a lower dimensional representation of the data set while retaining, as much as p o s s ib le, th e o rig in a l d ista n ce between points (the original underlying relationship o f data). Both M DS and PCA can map the p oin ts in higher dim ensional space onto lower dim ensional space. W hen moving to a lower dimensional representation, MDS and PCA generate factors which are linear combinations of variables that reflect features of the data. Tests which significantly influence a factor will be highly correlated and help to interpret the factor Ṫhere are several differences between MDS and PCA.8,12,16 Principal component analysis starts with a correlation matrix, while multidimensional scaling can start with an inter-subject distance matrix or a correlation matrix. The MDS m ethod is based on distances among points w hile PCA is based on angles among vectors. Also, principal component analysis is based on the general linear model, but multidimensional scaling has no such restrictive assumption. In addition, M DS may result in a lower dimensional solution than PCA. However, m ultidim ensional scaling cannot handle large data sets efficiently. A survey of the literature revealed no application of multidimensional scaling to bacterial taxonomy or identification. In this study, multidimensional scaling and previously used principal component analysis are applied to the analysis of variation among four closely related species of E n terobacteriaceae. Both MDS and PCA are compared for their ability to reduce the variable set (reduce dimensionality), to discriminate between species in various dim ensional space, and to explain the test components of the generated factors. Materials and Methods D a ta S e t Multidimensional scaling and principal component analysis were applied to a small test data set consisting of a biochemical profile of 42 selected isolates obtained from various anatom ic sites with the majority from urine cultures and endotracheal aspirates. The isolates consisted of four species of the Enterobacteriaceae family: Serratia marcescens (n = 8), E nterobacter aerogenes (n = 10), Klebsiella pneumoniae (n = 12), and Enterobacter cloacae (n = 12). These isolates were chosen because they are relatively closely related species within the family Enterobacteriaceae. There were no repeat isolates from any patient. The isolates were identified by biochemical tests incorporated into the gramnegative GNI card analyzed on the VITEK AMS instrument.* There are 30 wells in GNI card which contain 29 biochemical broths and one growth control broth. Test results were negative or postive and were coded as 0 and 1, respectively. Ten of 30 tests had uniformly positive or negative results for all isolates and were discarded since there was no discrimination among isolates. In addition, there were tests which correlated perfectly with other tests and this redundancy allowed the elimination of three tests. The 17 remaining biochem ical test results for the 42 isolates can be seen in table I. The biochem ical broths contained DP-300 (DP3 containing 2,4,4 trichloro-2 -hydroxydiphenylether), urea *McDonnell Douglas Health Systems Co., Hazelwood, MO

3 MDS AND PCA ANALYSIS OF BACTERIA 457 T ABLE I Biochemical Pattern Test* S p e c i e s DP3 URE I N O A R A A D O M A L C O U A R G A C E TDA LY S E S C P X B O N P O R N P L I L A C S e r r a t i a m a r c e s c e n s E n t e r o b a c t e r a e r o g e n s K l e b s i e l l a p n e u m o n i a e E n t e r o b a c t e r c l o a c a e * Test codes are 0 for a negative and 1 for a positive result. DP3- DP-300(DP3 containing 2,4,4' trichloro-2 '-hydroxydiphenylether) URE- Urea INO- Inositol AKA- L-arabinose ADO- Adonitol MAL- Malonate COU- p-coumaric ARG- Arginine ACE- Acetamide TDA- Tryptophan LYS- Lysine ESC- Esculin PXB- polymyxin B ONP- o-nitrophenyl-ß-d-galactopyranoside ORN- Ornithine PLI- Plant indican LAC- Lactose (U R E), in o sito l (IN O ), L -arabinose (ARA), a d o n ito l (A D O ), m alon ate (MAL), p-coum aric (COU), arginine (ARG), acetamide (ACE), tryptophan (TDA), lysine (LYS), esculin (ESC), polym yxin B (PXB), o-nitrophenyl-f$-d - galactopyranoside (ONP), ornithine (ORN), plant indican (PLI), and lactose (LAC). All isolates had com plete biochemical profiles. S t a t is t ic a l A n a l y sis M ultidimensional scaling was performed using the SAS ALSCAL program.18 The biochemical test data were

4 458 LACHER AND O DONNELL used to create a Euclidean distance between each pair of isolates using the following formula: du = -v/x (Xir Xjr)2 where i=l dy = Euclidean distance R = biochemical test number Xir = test result for the ith isolate for the rth test X,r = test result for the jth isolate for the rth test The range of the Euclidean distance was from zero (indicating isolates with identical biochemical patterns) to a maximum of the square of the number of biochemical tests (indicating a nonidentical p a tte r n ). T he E u c lid e a n d ista n c e betw een each isolate was used in the SAS ALSCAL program. Dim ensional scores produced by MDS for the isolates were plotted to assess the separation of the four species in various dimensional space (figures 1 and 2). Multiple linear regression, using the dimensional scores as dependent variables and biochemical tests as independent variables, was performed using the BMDP LR program5 to establish the standard regression coefficients for each dim ension (table II). These regression coefficients identify the tests which had significant positive and negative influences on each dimension. Also, stepwise linear regression identified those tests which contributed most significantly in predicting the dimension scores. x xx a a i Principal component analysis, a form of factor analysis, was performed on the biochemical data using the SAS FAC TOR program.15 Unrotated and orthogonal VARIMAX-rotated PCA were performed. Rotations were perform ed to simplify the interpretation of each factor. Factor scores were then plotted for each isolate (figures I and 3). Random bacterial isolates from a single population should produce normally (Gaussian) distributed PCA scores.4 The PCA factor pattern (table III) was examined to identify the tests which had salient loadings (strong influence) for each factor. Results and Discussion The biochemical profiles of isolates of S. marcescens, E. aerogenes, K. pneumoniae, and E. cloacae are seen in table I. Serratia m arcescens is identified if DP-300 or polymyxim B are positive or if ONPG or arabinose are negative. If inositol, adonitol or plant indican are negative or if arginine is positive, E. cloacae is identified. A positive reaction for acetam ide would indicate E. aerogenes. These tests are important in differentiatin g th e four sp ecies and w ou ld be expected to be influential test components of the factors in PCA or dimensions in MDS. Multidimensional scaling was applied to the biochemical pattern of the isolates. Young s S-stress measure (a goodness of fit function) was reduced significantly from a one-dimensional (0.2799) to a two-dimensional solution (0.2355), MDS -2-1 U i a X X X XX PCA F ig u r e 1. One-dimensional plot of multidimensional scaling (MDS) dimensional and principal component analysis (PCA) factor scores for S. marcescens ( ), E. aerogenes (A), K. pneumoniae (X) and E. cloacae ( ) isolates.

5 MDS AND PCA ANALYSIS O F BACTERIA T g 0'5 "', F igure 2. Twoin dimensional plot of multi- 5 dimensional scaling for S A marcescens ( ), E. aero- genes (A), K. pneumoniae (X), and E. cloacae ( ) o.s 4- x isolates DIMENSION 1 but the stress measure did not change significantly for a three-dim ensional solution (0.2348). This indicated that a two-dimensional MDS solution was optimal. Multiple linear regression, using the MDS dimensional coordinates as dependent variables and tests as independent variables, was performed to interpret the tw o-dim ensional solution (table II). Lysine, p-coumaric, and inositol had a strong positive influence (regression T A B L E II Two-dimensional Multidimensional Scaling Standard Regression Coefficients Tests D i m e n s i o n 1 D i m e n s i o n 2 D P ( D P 3 c o n t a i n i n g 2,4,4' t r i c hloro-2' -h y d r o x y d i p h e n y l e t h e r ) Urea I n o s i t o l L - a r a b i n o s e A d o n i t o l M a l o n a t e p - c o u m a r i c A r g i n i n e A c e t a m i d e T r y p t o p h a n Lysine E s c u l i n p o l y m y x i n B o -nitrophenyl- 3-D - g a l a c t o p y r a n o s i d e Orni thine P l a n t i n d i c a n L a c t o s e coefficients >0.10) and malonate, lactate and L-arabinose had a strong negative effect on dimension 1. For dimension 2, ornithine had a positive influence and urea, adonitol, lactate, esculin, and ONPG had a significant negative influence. Stepwise linear regression showed that L-arabinose and lysine best predicted the first dimensional scores. L- arabinose was useful in identifying S. marcescens, and lysine had the highest negative p ercentage for E. cloacae. Ornithine and esculin were the best predictors of dimension 2 scores. Ornithine helped differentiate K. pneumoniae and a negative esculin reaction indicated E. cloacae. Principal component analysis was also applied to the biochemical test reactions of the isolates. The first five factors had eigenvalues greater than one (considered significant factors) and explained 79.4 percent o f the variance. A scree plot (eigenvalue versus factor number) indicated that the first two factors (accounting for 54.2 percent of total variance) could adequately represent the information contained in the biochemical database. This was surprising because principal component analysis was developed to handle continuous, normally distributed variables, unlike the binary qualitative

6 460 LACHER AND O DONNELL F igure 3. T w o - dimensional plot of princip a l c o m p o n e n t fa c to r scores for S. marcescens ( ), E. aerogenes (A), K. pneum oniae (X) and E. cloacae ( ) isolates. FACTOR 1 biochemical test data analyzed in this study. Factoring data where variables are dichotomous may lead to spurious extra factors,8 but PC A efficiently reduced the biochemical data to two dimensions. The orthogonal VARIMAX rotation was applied to the principal component analysis since the unrotated PCA could not simply identify significant tests contributing to the two factor solution (table III). In general, tests with larger positive or negative coefficients should be the important tests which differentiate species. For factor one, L-arabinose, lactate, ONPG, and malonate had strong positive effects (factor loading > 0.50) and p- coumaric, polymix-b and DP-300 had salient negative loadings (less than 0.50). Inositol, esculin, lysine, adonitol and plant-indican had strong positive and ornithine had a strong negative influence on factor 2 scores. The communality estimates, the proportion of the variation explained by each test for the PCA solution, suggested that L-arabinose followed by p-coumaric and lysine were important tests in differentiating the four species. A positive p-coumaric T A B L E III Two-dimensional Varimax-rotated Factor Pattern Test Factor 1 Factor 2 DP-300(DP3 containing 2,4,4' trichloro-2 -hydroxydiphenylether) Urea Inositoi L-arabinose Adonitoi Malonate p-coumaric Arginine Acetamide Tryptophan Lusine Esculin polymyxin B o-nitrophenyl-ß-d -galactopyranoside Orni thine Plant indican Lactose

7 reaction was seen most often in S. marcescens. The influence of tests on the MDS dimensions and PCA factors were different. Multidimensional scaling and principal component analysis were compared for their ability to graphically separate S. m arcescens, E. aerogenes, E. cloacae and K. pneumoniae. The MDS and PCA scores were plotted for a one-dim ensional solution (figure 1). M ultidimensional scaling appeared to be the mirror image of the PCA one-dimensional solution and, hence, compared well to principal component analysis. Serratia marcesc e n s and E. clo a ca e w ere w e ll separated, but K. pneumoniae and E. aerogenes could not be fully differentiated for the one-dimensional solution. T he m u ltid im en sional scores and VARIMAX-rotated factor scores were then compared for a two-dimensional solution (figures 2 and 3). Both MDS and PCA separated the four sp ecies o f Enterobacteriaceae in two-dimensional space. E nterobacter aerogenes and K. pneumoniae appeared to be phylogenetically similar with respect to their biochemical test pattern. When compared to S. marcescens, E. cloacae was more closely related to E. aerogenes and K. pneumoniae. The relationships of these four species based on biochemical data was comparable to DNA relatedness groupings seen among Enterobacteriaceae species.2 Since the MDS plot could not be rotated to match the PCA plot, it appeared that the MDS and PCA twodimensional solutions were different. For MDS, a positive score for dimension 1 indicated S. marcescens. To get a positive score for dimension 1, lysine, p- coumaric and inositol should have a positive reaction and L-arabinose should have a negative result as indicated by the multiple linear regression analysis (vide supra). Serratia marcescens best fit this reaction pattern (table I). A negative score (less than 1.0) for dimension 2 MDS AND PCA ANALYSIS OF BACTERIA 461 indicated E. cloacae. Enterobacter aerogenes and K. pneum oniae w ere separated by the second MDS dimension. E n tero b a cter aerogen es had higher dimension 2 scores than K. pneumoniae. The interpretation of the tw o-dim ensional principal component analysis plot was different from the MDS graph. A negative factor score identified the S. marcescens group, but could not separate it from E. cloacae as the M DS dimension 1 did. The PCA dimension 2 helped separate K. pneumoniae, E. aero g en es and E. c lo a c a e w h ich had decreasing scores, respectively. Principal com ponent analysis and multidimensional scaling were applied to a profile of biochemical tests to reduce the dimensionality of the variable (test) set and to discriminate betw een four bacterial species. Both MDS and PCA could represent the data w ell in two dimensions but gave different interpretations of the dimensions. The analysis of a data set consisting of a large number of different isolates would increase the number of dimensions required to differentiate the organisms. In this study, the identities of the isolates were known a priori. Discriminate analysis of MDS or PCA scores of a training set of known isolates can be used to classify unknown isolates. Other pattern recognition techniques such as SIMCA, K-nearest neighbor and Bayesian analysis can discriminate bacterial isolates.1 Also, MDS or PCA followed by cluster analysis techniques can be used to group (a priori) unknown microorganisms.1,14 Multidimensional scaling and principal component analysis are used to reduce a large number of variables to a few significant variables in order to simplify data analysis. References I. Boyd, J. C., Lewis, J. W., Marr, J. J., Harper, A. M., and Kowalski, B. R.: Effect of atypical

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