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Comparison of pattern-recognition techniques for classification of Silurian rocks from Lithuania based on geochemical data

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Comparison of pattern-recognition techniques for classification of Silurian rocks from Lithuania based on geochemical data
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  Introduction There is no widely recognized chemical classification of sedimentary rocks.The geochemical classification of sedimentary rocks is not as well developed as that forigneous rocks,and most systems for sedimentary rock classification utilize features such as grain size and themineralogy ofthe particles and matrix (Rollinson1995),which can be observed in hand specimens or inthin sections.In cases where the geochemistry ofparti-cular sedimentary rocks is being studied it is alwaysuseful to find "boundaries" that demarcate certain rock types or,at least,separate them on the basis ofmajorand/or trace elements.Separation ofrock types is very important in investigations ofthe relationships amongchemical elements,their associations in certain rock types etc.Calcitic,dolomitic and terrigenous materials are themajor constituents ofmost carbonate rocks andmudrocks.These constituents could aid in the esta-blishment ofa general classification.Mineralogicalinvestigations ofsedimentary rocks,combining thinsections,XRD along with major elements like Ca,Mg,Si and Al,could provide a more reliable classification.However,in many cases,determinations ofmajor andtrace element concentrations are not always accompa-nied by thin section or XRD studies.The handling of geochemical information (for example,geochemicalvariables – chemical elements) is most common nowa-days.Considering the fact that the nature ofmost real-world data is very complex and that the relationshipsamong variables (for example,chemical elements) arenonlinear,it is essential to employ an appropriate tech-nique that could handle such data in a statistically "cor-rect" fashion.Whereas multivariate-statistical approa-ches always produce the same result when applied tothe same data set,a technique like the artificial neuralnetwork (ANN) is more like a living system in thatvarious analyses most likely will not produce exactly the same result.ANNs have been applied to solvingproblems in a wide variety offields.Applications of  NORWEGIAN JOURNAL OF GEOLOGYComparison of pattern-recognition techniques for classification of sedimentary rocks 117  Comparison of pattern-recognition techniques for classifi-cation of Silurian rocks from Lithuania based on geoche-mical data Donatas Kaminskas & Björn A. Malmgren Kaminskas,D.& Malmgren,B.A.2003:Comparison ofpattern-recognition techniques for classification ofSilurian sedimentary rocks from Lithua-nia based on geochemical data. Norwegian Journal ofGeology  ,Vol.84 ,pp.117-124.Trondheim 2003.ISSN 029-196X.There is no widely recognized chemical classification ofsedimentary rocks.The geochemical classification ofsedimentary rocks utilizes featuresthat can be observed in hand specimens or in thin sections,such as grain size and the mineralogy ofthe particles and matrix.The main objectivebehind this paper is to compare the performance ofdifferent pattern-recognition techniques,such as artificial neural networks,linear discriminantanalysis,the k-nearest neighbour technique and "soft independent modelling ofclass analogy" in classifying Silurian sedimentary rocks from Lit-huania.The comparison was made separately for major and trace elements.To obtain an idea about the success ofthe various classifiers in correctly predicting samples from each ofthe individual rock types,error rates were also computed for each ofseven petrographically established rock types.For testing the predictive power ofthe artificial neural networks we applied a back propagation network.Error rates were computed based on theaverage percentage ofmisclassifications.The comparison ofpattern-recognition techniques used in this study indicates that not only the techniquefor classification should be applied with care but also that attention must be paid to the objects (rock types) being classified.It was also noticed thatnot only the major elements,as is usually the case,could be used in "recognition" ofcertain rock types.Trace elements could also successfully beused and readily handle the same tasks.The results indicate that two techniques,artificial neural networks and linear discriminant analysis,yield thelowest error rates for both major and trace elements (7-8% for the major elements and 8-14% for the trace elements).The k-nearest neighbourtechnique and soft independent modelling ofclass analogy produce considerably higher error rates for both types ofelements (16-25%).Since nostrict statistical assumptions,for example,multivariate normality ofa data set,are required in the artificial neural networks,this procedure seems tobe the optimum technique for geochemical classification ofthe sedimentary rocks. Kaminskas,D.,Department ofGeology and Mineralogy,Faculty ofNatural Sciences,Vilnius University,Ciurlionio str.21,2009-LT Vilnius,Lithuania (e-mail: donatas.kaminskas@gf.vu.lt); Malmgren,B.A.,Department ofEarth Sciences,Göteborg University,Box 460,SE-405 30 Göteborg,Sweden (e-mail: bjorn.malmgren@marine-geology.gu.se)  ANNs to the Earth sciences are still rare.They havebeen applied,for example,to problems ofwell loginterpretations (Baldwin et al.1989,1990;Rogers et al. 1992),for identifications oflinear features in satelliteimagery (Penn et al.1993),for geophysical inversionproblems (Raiche 1991),for chemostratigraphy (Malmgren & Nordlund 1996),for predictions ofpastsea-water temperatures (Malmgren et al.2001) and foranalyses ofpaleovegetation data (Grieger 2002).For comparison ofthe performance ofdifferent techni-ques applicable to classification ofsedimentary rocksbased on geochemical properties we explored thepotential offour pattern-recognition techniques,ANNs,the k-nearest neighbour technique (k-NN),linear discriminant analysis (LDA) and "soft indepen-dent modelling ofclass analogy" (SIMCA).The study was based on geochemical data from three boreholespenetrating parts ofthe Silurian ofLithuania. Material and methods The three boreholes analysed here,Kurtuvenai-161,Ledai-179 and Jocionys-299,represent different sedi-mentary environments ofthe Wenlock (Silurian) of Lithuania (Fig.1).Initially,samples were collected tocover a wide range ofrock types according to their lit-hology.In total,210 samples were taken:89 from theKurtuvenai-161,69 from the Ledai-179 and 52 from theJocionys-299 boreholes.We used 179 ofthese samplesin this study;the remaining 31 samples were not inclu-ded,since some rock types contained only a few sam-ples.The deepest part ofthe sedimentary basin envi-ronment is represented by the Kurtuvenai-161 bore-hole,the shallowest by the Jocionys-299 borehole andthe transitional by the Ledai-179 borehole (Paskevicius1997).The samples were analyzed for the content ofmajor (Si,Al,Fe,Mn,Mg,Ca,Na,K,Ti and P) elements,oxidesand trace elements (V,Cr,Co,Ni,Cu,Zn,Rb,Pb,Ba,Sr,Y,Zr,Nb and Th) using XRF.Inorganic and organiccarbon contents were determined using IR spectrome-try.All geochemical analyses were carried out at theGeological Institute,Oslo University,Norway.A raw semi-quantitative classification ofthe seven rock types was made according to the calcitic,dolomitic andterrigenous material present in the samples (Table 1).This simplified classification table is usually used forclassification ofcarbonate rocks and mudrocks.Thedetails ofthis mineralogical classification and its prin-ciples can be found in Grigelis (ed.) 1981.Initially,the rock samples were classified according tothe general description ofthe core material.Thin secti-ons and X-ray diffraction were applied to obtain amore detailed classification.Detailed descriptions of sampling,analytical techniques and thin-section stu-dies can be found in Kaminskas (2002). Brief descriptions of the quantitativetechniques Artificial neural networks (ANNs) ANNs are computer systems that have the ability tolearn,using some pertinent learning algorithm,one orseveral output signals from a set ofinput signals.The 118 D. Kaminskas & B. A. MalmgrenNORWEGIAN JOURNAL OF GEOLOGY Fig.1.Study boreholes: location and facial zonation ofWenlock (Silurian) sedimentary environments: 1 – the deepest part; 2 - intermediate zone; 3 – the shallowest part.Dotted lines mark the boundaries between sedimentary environments zones. ...  objective behind the application ofANNs is to attemptat reproducing the output signal(s) from the input sig-nals with a minimum error rate through a specific trai-ning process.ANNs have the ability to overcome pro-blems offuzzy and nonlinear relationships between thesets ofinput and output signals.The initial data-set isdivided into two random portions,a training set,whichis used for training the ANN,and a test set to which thetrained network is applied for estimates ofthe errorrate.An ANN is an information-processing system inspiredby the way the densely interconnected,parallel struc-ture ofthe mammalian brain processes information.The ANN is composed ofa great number ofprocessingelements that are analogous to neurons and are tiedtogether with weighted connections that are analogousto synapses.The most common type ofANNs is themultilayer perceptron,which is most often trainedusing the back propagation (BP) algorithm.The ANNis trained to reproduce the target variable(s) from theinput variables by adaptively updating the synapticweights that are associated with the strength ofthe con-nections.Learning in a BP network is based on the gra-dient-descent method,that is,the weights are adjustedso that the changes at each time will follow the steepest"downhill" direction on the error surface.The opti-mum weights are thus determined iteratively by opti-mizing certain "energy" functions as training proceeds.Comprehensive descriptions ofmultilayer perceptronANN can be found in Wasserman (1989),Webb (2002)and Malmgren & Nordlund (1996,1997).We used the Trajan 4.0 Professional software package(www.trajan-software.demon.co.uk) in our ANN appli-cations. Linear discriminant analysis (LDA) Normally,discriminant analysis amounts to establis-hing linear functions,representing a planar surfacewith p-one dimensions (p=the number ofvariables),that optimally distinguish two predefined groups of observations.In this study,we assigned each oftheobservation vectors in the various test sets to one ofthepredefined rock groups through computations of Mahalanobis' generalized distances between these vec-tors and group mean vectors (Cooley & Lohnes 1971).These generalized distance measures were then conver-ted to mathematical probabilities ofreferability ofatest-set observation to any ofthe predefined groups(Cooley & Lohnes 1971).Each ofthe test-set observati-ons was subsequently assigned to the group for whichthe probability was highest.Malmgren & Kennett(1977) applied this procedure to a taxonomic problemin recent planktonic foraminifera. K-nearest neighbors (k-NN) The k-nearest neighbor is a conceptually simple techni-que based on the Euclidean distance between observati-ons in multidimensional space (Kowalski & Bender1972).The allocation ofthe test-set members to thetraining set classes is dependent upon the distances of the k shortest Euclidean distances between these sets.Inthe application to the current data-set,we set k equal to3,and we monitored the distances from each ofthe testset members to each ofthe training set members.Atest-set member is referred to that training-set class towhich the majority (two or three) ofthe three closesttraining set members belonged,as indicated by theEuclidean distances. 119 NORWEGIAN JOURNAL OF GEOLOGYComparison of pattern-recognition techniques for classification of sedimentary rocks Table 1. The simplified classification table of carbonate rocks and mudrocks according calcite, dolomite and terrigenous material* percentages. Rock typeCalcite Dolomite Terrigenous Remarks(%)(%)material (%)limestone "clayey"65-900-1010-25limestone "clayey" dolomitic50-8010-2510-25Terrigenous material>Dolomitelimestone dolomitic "clayey"50-8010-2510-25Dolomite>Terrigenous materialmudstone>33.30-1025-50mudstone dolomitic>33.325-5025-50Calcite>Dolomitedolostone0-1080-1000-10dolostone "clayey"0-1065-9010-25 * - terrigenous material equals:100-(calcite+dolomite)  Soft independent modeling of class analogy (SIMCA) SIMCA may involve any or several offour distinctlevels (Wold 1976;Wold et al.1984).Level 1 ofSIMCA is devoted to developing mathematical rules for each of a number ofpreset groups (termed classes in SIMCA)in the training set by fitting separate R-mode principalcomponent models to each ofthem.The dimensiona-lity ofa principal component solution is determined by a cross-validation technique.In level 2,the predictionphase,these rules are used to assign new observationsto any ofthe given classes on the basis oftheir degree of fit to the various class models using a distance measure.At both levels,atypical observations ("outliers"),that is,observations with a data structure that does not accordwith a class model,may be identified.In this way,observations ofunknown affinity that cannot be classi-fied with any training set class may be interpreted asbeing referable to a yet unknown class.Levels 3 and 4 ofSIMCA are designed for quantitativepredictions ofone or several variables from a multiva-riate setup through partial least squares (PLS) models(Wold 1982).These levels ofSIMCA are not used here.So far,SIMCA modeling,srcinally developed for dataanalysis in the field ofchemometry,has been applied togeological problems by,for example,Griffiths (1984),Haugen et al.(1989),and Wei (1994). Canonical Variates Analysis (CVA) CVA is a technique for graphical representation oftheinterrelationships among groups ofmultivariate sam-ples,like the rock groups analysed here,on the basis of plots ofthe group means and individual sample pointsalong specific coordinate axes (the canonical variates;Reyment et al.1984).These canonical variate axes arecomputed so as to maximize the ratio ofthe between-towithin-group variance and to be uncorrelated in cano-nical variate space. Estimates ofError Rates  The success ofa classifier may be determined by com-puting the percentage ofmisclassifications,the "errorrate," ofpredictions in a data set which is not part of the training set.Instead ofrelying on a single test set forestimating the performance ofthe various classifiers,which may be misleading (Weiss & Kapouleas 1989),we created five different random test sets from our ori-ginal data.Each such test set contained 20% (37 parti-cles) ofthe original observations.The remaining 80%(146 particles) was used as training sets.We thenemployed a cross-validation technique for estimatingthe ability ofthe classifiers to correctly predict the classreferability ofthe test set samples (Stone 1974;Weiss &Kapouleas 1989).The error rates computed are thusaverage rates ofmisclassification (%) for the five diffe-rent test sets.The training and test sets are automati-cally generated by the Trajan ANN software,and thesame partitions were used to derive the error rates alsofor the LDA,k-NN,and SIMCA. Relative abundance data  Relative abundance data,adding up to a unit value(unity or 100%) in individual samples,have long beenknown to be subject to the so-called constant-sum con-straint (Pearson 1897;Chayes 1960).In our applicati-ons ofCVA,LDA and SIMCA to the major elementdata-set in which the correlation structure ofthe data 120 D. Kaminskas & B. A. MalmgrenNORWEGIAN JOURNAL OF GEOLOGY Fig.2.Graphical illustration ofthe configurations ofthe individual samples from the seven petrographically identified rock types along the axes ofthe first two canonical variates for the major and trace elements.These axes account for 93.5 and 94.2%,respectively,ofthe variability in multivariate space.  matrix suffers from the constant-sum constraint,whichcould seriously impair the outcome ofthese analyses,we used a centred log-ratio transformation to relievethis constraint (Aitchison 1981,1986).Log-ratio trans- formations imply mathematical operations in a so-cal-led simplex space,constituting a limited part ofthe ori-ginal p-dimensional Cartesian space.The results ofk-NN and ANNs are not affected by the constant-sumconstraint,since they do not involve computations ofacovariance or correlation matrix,and in the applicati-ons ofthese techniques the raw,untransformed datawere used.The data-set used was the same for all thesetechniques. Results Canonical variates analysis Figure 2 shows the locations ofindividual rock samplesalong the axes ofthe first two canonical variates for themajor and trace elements,respectively.These canonicalvariates account for most ofthe variability among thegroup mean vectors (93.5 and 94.2%,respectively).Forthe major elements,the dolostone samples can be cle-arly distinguished from the other rock samples alongthe first canonical variate axis.The mudstone dolomiticand dolostone "clayey" samples are likewise separatedfrom most ofthe other samples along the first axis butdisplay some slight overlap with the limestone dolomi-tic "clayey" samples.Along the second axis,most ofthemudstones are separated from the limestone "clayey",limestone "clayey" dolomitic,limestone dolomitic"clayey" and mudstone samples,but some ofthe muds-tone samples overlap with these other rock groups.Thelimestone "clayey",limestone "clayey" dolomitic andlimestone dolomitic "clayey" samples cannot be une-quivocally differentiated on the basis oftheir geoche-mical compositions.The dolostones cannot be as clearly separated from thedolostone "clayey" samples on the basis ofthe trace ele-ments as in the case ofthe major elements.For thetrace elements the dolostone "clayey" also display aconsiderable overlap with the mudstone dolomiticsamples.The limestone "clayey",limestone "clayey"dolomitic,limestone dolomitic "clayey" and mudstonesamples show overlaps similar to the situation for themajor elements,even though most ofthe mudstoneand limestone dolomitic "clayey" samples are also dis-tinguishable from the limestone "clayey" and limestonedolomitic "clayey" samples by their trace elements.Considering the lack ofdiscrete subclusters for both themajor and trace elements it is relevant to ask the ques-tion ofhow well the ANN and statistically based pat-tern recognition techniques are able to distinguishthese various rock types. 121 NORWEGIAN JOURNAL OF GEOLOGYComparison of pattern-recognition techniques for classification of sedimentary rocks Fig.4.Error rates (percentages ofmisclassification in the various rock types) for the artificial neural network (ANN),linear discriminant analysis (LDA),the k-nearest neighbours (k-NN) and soft indepen-dent modeling ofclass analogy (SIMCA) using trace elements.For legend,please refer to Fig.3.Fig.3.Error rates (percentages ofmisclassification in the various rock types) for the artificial neural network (ANN),linear discriminant analysis (LDA),the k-nearest neighbours (k-NN) and soft indepen-dent modeling ofclass analogy (SIMCA) using major elements 
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