ࡱ> G KRbjbjَ *.I]4 ((((((((4 $  ((((( ((((((((((r*rr2r(((( ( APPLICATION OF NEURAL NETWORKS IN THE IDENTIFICATION OF MORPHOLOGICAL TYPES Franjo Prot and Ksenija Bosnar University of Zagreb Ankica Ho{ek and Konstantin Momirovi} Institute of criminological and sociological research A sample of 737 healthy males, 19 to 27 years old, fairly representative for the Yugoslav population of this age and gender, was described over a set of 23 morphological characteristic selected so to assess factors of longitudinal and transversal dimensions of skeleton, muscular mass and fat tissue. An algorithm for a neural network for cluster analysis with coded name Triatlon was applied in order to detect the morphological types. The essence of the applied clustering algorithm is a taxonomic neural network based on adaptive multilayer perceptron as a core engine working on the basis of starting classification obtained by a rational method of fuzzy clustering of variables, and then of fuzzy clustering of objects described on fuzzy clusters of variables. Triatlon conclude that five clusters are necessary and sufficient for the taxonomic description of this data set, and that by only three hidden neurons can produce an acceptable classification of objects. After 15 iteration Triatlon produce an excellent fuzzy classification of variable, but initial fuzzy clustering of objects is obtained after 71 iteration. However, multilayer perceptron consider this classification as good, but not satisfactory, and start learning process in order to obtain a better classification. The final classification is obtained after 24 learning attempts. However, coefficient of efficacy of Triatlon in this case was only 0.920, markedly lower then in applications of this program in other taxonomic problems. In spite of complex position of types in the space of manifest morphological characteristics and not always clear pattern and structure of discriminant factors obtained types can be identified as follows: (1) Typus asthenicus, defined by low development of skeleton, low muscular mass and low fat tissue; (2) Typus sthenicus, defined by strong development of skeleton, high amount of muscular mass and above average fat tissue due to the high amount of fat cells; (3) Typus gracilis, defined primarily by small measures of transversal dimensions of skeleton; (4) Typus disharmonicus, defined by inconvergent development of morphological characteristics and low fat tissue; (5) Typus leptomorphicus, defined by above average development of longitudinal dimensions of skeleton. KEY WORDS morphological types / neural networks / cluster analysis 1. INTRODUCTION In a previous paper (Momirovi}, Ho{ek, Prot and Bosnar, 2002) a sample of 737 healthy males, 19 to 27 years old, was described, by a procedure which minimize error of measurement, by 23 anthropometric variables Morphological types were determined by neural network SIMTAX. The algorithm implemented in this network classify objects in the standardized image space by iterative application of Lebart's multilayer perceptron. Initial classification was obtained on the basis of position of objects on the envelope of hyperelipsoid defined by Orthoblique transformation of principal components of data matrix, also transformed to standardized image space. Dimensionality of latent, and in the same time taxonomic space was determined by number of spectral values greater then inflection point of their distribution. Three taxon were obtained, with classification efficacy of 0.991 in image and 0.986 in real space. First taxon, of 35% of examines, was identified as sthenomorphia, second taxon, of 29% of examines, as asthenomorphia, and third taxon, of 36% of examines, as picnomorphia. Obtained taxons were similar, but not identical, with taxons K, M and R obtained by a method of fuzzy clustering applied by A. Ho{ek (1978) on a set of 200 examines described by the same set of anthropometric measurements, but not to the taxons obtained by Zlobec (1975) by concurrent application of a simple fuzzy clustering method and to taxons obtained by Ward's method of hierarchical clustering and Friedman and Rubin method of local optimization. The aim of this paper is to present results of an alternative attempt to solve the old and at yet unsolved problem of morphological types by an other taxonomic neural network who analyze objects in real space on the basis of results obtained by an initial fuzzy classification similar to classification methods applied in works of Zlobec (1975) and Ho{ek (1978). 2. METHODS A sample of 737 healthy males, 19 to 27 years old, fairly representative for the Yugoslav population of this age and gender, was described over a set of 23 morphological characteristic, defined by the following variables: CODED NAMEVARIABLEWEIGHTBody massHEIGHTBody heightLLENGTHLeg lengthBIACROBiacromial spanBICRISBicristal spanTRISKINTriceps skinfoldSCAPSKINSubcapular skinfoldAXSKINAxilar skinfoldCRUPARMUpper arm circumferenceCRLWARMLower arm circumferenceCRUPLGUpper leg circumferenceCRLWLGLower leg circumferenceHANDLGHand lengthHANDDMHand diameterABDSKINAbdominal skinfoldLWLSKINLower leg skinfoldCHCIRCChest circumferenceDIWRISTDiameter of wristDIAELDiameter of elbowDIAKNEDiameter of kneeFOOTLFoot lengthFOOTDMDiameter of footARMLGArm length An algorithm for a neural network for cluster analysis with coded name Triatlon was applied in order to detect the morphological types. The essence of the applied clustering algorithm is a taxonomic neural network based on adaptive multilayer perceptron as a core engine working on the basis of starting classification obtained by a rational method of fuzzy clustering of variables, and then of fuzzy clustering of objects described on fuzzy clusters of variables. 3. RESULTS Triatlon conclude that five clusters are necessary and sufficient for the taxonomic description of this data set, and that by only three hidden neurons can produce an acceptable classification of objects. After 15 iteration Triatlon produce an excellent fuzzy classification of variable, but initial fuzzy clustering of objects is obtained after 71 iteration. However, multilayer perceptron consider this classification as good, but not satisfactory, and start learning process in order to obtain a better classification. The final classification is obtained after 24 learning attempts. The whole process is presented, in an abbreviated form, in the following tables. Table 1. Starting input to hidden layer axons  f1f2f3WEIGHT.313-.919.230HEIGHT-.471-.116-.445LLENGTH-.021.620.579BIACRO-.250-.147-.031BICRIS.327-.126-.030TRISKIN.038-.103-.024SCAPSKIN.042-.015.219AXSKIN.092-.197-.001CRUPARM.040-.341-.084CRLWARM.201-.036.128CRUPLG-.600-.145.065CRLWLG-.058-.181.001HANDLG-.306.284.253HANDDM.322.387.318ABDSKIN-.070.265.152LWLSKIN.195-.034-.012CHCIRC-.074-.236-.183DIWRIST-1.054-.049.125DIAEL-.025.004.135DIAKNE1.053.242.025FOOTL.137.319.248FOOTDM.286-.019.156ARMLG.113.199.306 Table 2. Starting hidden layer to output axons g1g2g3g4g5f1.449.236.172-.817-.214f2.331-.544.093-.152.750f3.201.521-.736.006.382 Table 3. Initial and classification in first iteration g1g2g3g4g5g1541510025g2181501149g31221592615g411011615g56001276 Table 4. Number of objects and accordance of starting classifications numberprognosisaccordanceg110454.519g2192150.781g3214159.743g4133116.872g59476.809 Table 5. Final input to hidden layer axons  g1g2g3WEIGHT.7671.916-.834HEIGHT.007.785.242LLENGTH-.118-.958-.097BIACRO.015.062-.543BICRIS.011.898.155TRISKIN.019.631-.057SCAPSKIN.316-.936-.635AXSKIN-.469-.029-.180CRUPARM-.024-.098-.347CRLWARM-.352.258.267CRUPLG.257-.993-.603CRLWLG-.112.188-.025HANDLG.070.061-.442HANDDM-.250-1.110.439ABDSKIN-.261-.086.924LWLSKIN.168.178-.038CHCIRC.074-.474.280DIWRIST.946-.578-.219DIAEL.192.346-.092DIAKNE-1.684-.263-.288FOOTL-.023-.070.207FOOTDM-.020-.078.245ARMLG-.064-1.493.341 Table 6. Final hidden layer to output axons g1g2g3g4g5g1-.353-.125-.258.876-.159g2-.058-.001.698.053-.712g3.600-.761.128.187.091 Fisherian discriminant analysis in the whole variable space, incorporated in program, gives the following identification structures: Table 7. Centroids of final taxons  g1g2g3g4g5WEIGHT-.692.860-.432-.075.070HEIGHT-.266.390-.386-.147.294LLENGTH-.169.356-.546-.185.457BIACRO-.641.677-.347-.037.115BICRIS-.120.332.159-.248-.208TRISKIN-.344.889-.075-.566-.124SCAPSKIN-.4541.009-.261-.480-.069AXSKIN-.245.841-.197-.639.046CRUPARM-.704.913-.215-.193-.090CRLWARM-.480.733-.207-.315.049CRUPLG-.781.869-.310-.109.036CRLWLG-.575.701-.196-.137-.022HANDLG-.389.180-.547.056.595HANDDM-.052.099-.632-.174.733ABDSKIN-.139.247-.225-.039.092LWLSKIN-.252.537.010-.246-.190CHCIRC-.571.736-.385-.053.047DIWRIST-.607.172-.868.945.254DIAEL-.436.455-.283.081.031DIAKNE.172.753.119-1.557.377FOOTL-.197.301-.496-.122.430FOOTDM.009.105-.346.040.188ARMLG-.046.250-.639-.179.570 Table 8. Discriminant coefficients  g1g2g3g4g5WEIGHT-.450.796.711.671-1.908HEIGHT.050-.214.612.087-.499LLENGTH-.043.040-.589-.183.759BIACRO-.386.381.007-.091-.055BICRIS-.010-.149.679.080-.589TRISKIN-.099.027.444.037-.440SCAPSKIN-.295.530-.922.126.443AXSKIN.142.246.016-.436.012CRUPARM-.203.262-.101-.092.049CRLWARM.188-.209.366-.255-.038CRUPLG-.773.202-.555.013.914CRLWLG-.027.008.188-.098-.086HANDLG-.611.138.203-.058.160HANDDM.413-.304-.652-.196.873ABDSKIN.618-.691.151-.064.214LWLSKIN-.048.035.043.155-.193CHCIRC.185-.213-.326.094.339DIWRIST-.382.078-.712.763.202DIAEL-.132.053.172.171-.294DIAKNE.399.408.242-1.549.458FOOTL.128-.160-.010.014.080FOOTDM.320-.087-.138.044-.048ARMLG.530-.121-1.143-.045.931 Table 9. Structure of discriminant functions  g1g2g3g4g5WEIGHT-.530.641-.310-.041.052HEIGHT-.203.291-.277-.079.218LLENGTH-.129.265-.392-.100.339BIACRO-.490.505-.249-.020.085BICRIS-.092.247.114-.135-.154TRISKIN-.263.663-.054-.307-.092SCAPSKIN-.348.752-.187-.260-.051AXSKIN-.188.627-.141-.346.034CRUPARM-.538.681-.154-.104-.067CRLWARM-.367.546-.149-.171.037CRUPLG-.598.648-.222-.059.027CRLWLG-.440.523-.141-.074-.016HANDLG-.298.134-.392.030.442HANDDM-.039.074-.453-.094.544ABDSKIN-.106.184-.162-.021.068LWLSKIN-.193.401.007-.133-.141CHCIRC-.437.549-.276-.029.035DIWRIST-.464.128-.623.512.189DIAEL-.333.339-.203.044.023DIAKNE.131.562.085-.844.280FOOTL-.150.224-.356-.066.319FOOTDM.007.078-.249.022.140ARMLG-.035.187-.458-.097.423 Table 10. Pattern of discriminant functions  g1g2g3g4g5WEIGHT-.172.484-.279-.044-.065HEIGHT-.112.192-.163-.072.132LLENGTH.025.236-.307-.067.124BIACRO-.392.249-.051-.067.153BICRIS.097.255-.048-.076-.208TRISKIN.279.700-.366-.164-.395SCAPSKIN.339.819-.530-.119-.459AXSKIN.346.696-.436-.184-.340CRUPARM-.224.484-.149-.097-.095CRLWARM-.155.388-.124-.138-.011CRUPLG-.454.340-.033-.102.122CRLWLG-.262.325-.067-.085.010HANDLG-.713-.248.204-.093.713HANDDM-.230-.071-.100-.109.496ABDSKIN.098.214-.220.004-.087LWLSKIN.179.437-.222-.058-.314CHCIRC-.067.457-.302-.020-.120DIWRIST-.157.109-.456.350.018DIAEL-.134.243-.161.018-.027DIAKNE.115.441.031-.589.153FOOTL-.095.142-.200-.062.201FOOTDM.300.229-.382.064-.161ARMLG.141.226-.396-.048.121 Table 11. Correlations of discriminant functions g1g2g3g4g5g11.000-.615.221-.411.251g2-.6151.000-.106-.354-.094g3.221-.1061.000-.308-.693g4-.411-.354-.3081.000-.273g5.251-.094-.693-.2731.000 Table 12. Standardized discriminant coefficients  g1g2g3g4g5WEIGHT-.344.593.510.364-1.417HEIGHT.038-.160.439.047-.371LLENGTH-.033.030-.423-.099.563BIACRO-.295.284.005-.049-.041BICRIS-.008-.111.487.043-.437TRISKIN-.076.020.319.020-.326SCAPSKIN-.226.395-.662.069.329AXSKIN.109.183.012-.236.009CRUPARM-.155.196-.072-.050.036CRLWARM.144-.155.263-.138-.028CRUPLG-.592.150-.399.007.678CRLWLG-.021.006.135-.053-.064HANDLG-.468.103.146-.031.118HANDDM.316-.226-.468-.106.648ABDSKIN.473-.515.108-.035.159LWLSKIN-.037.026.031.084-.143CHCIRC.142-.159-.234.051.252DIWRIST-.292.058-.511.413.150DIAEL-.101.039.123.092-.218DIAKNE.305.304.174-.839.340FOOTL.098-.119-.007.007.059FOOTDM.245-.065-.099.024-.036ARMLG.406-.090-.820-.024.691 Table 13. Contingency matrix of Neural network and Fisherian classification g1g2g3g4g5g11100303g20162405g314413600g41401372g517200133 Therefore, classification of entities in morphological space is really a hard task for any clustering algorithm, as can be seen from the measure of efficacy of final classification obtained by Triatlon, a taxonomic neural network with almost perfect behavior in the classification of objects in other fields of anthropological space (Momirovi}, 2002). Table 14. Number of objects and efficacy of final classification numberprognosiserrorg11161106g21711629g315413618g41441377g515213319 Coefficient of efficacy of Triatlon in this case was only 0.920, markedly lower then in other applications of this program in biochemistry, physiology, psychology, sociology and criminology. However, in spite of complex position of types in the space of manifest morphological characteristics and not always clear pattern and structure of discriminant factors obtained types can be identified as follows: (1) Typus asthenicus, defined by low development of skeleton, low muscular mass and low fat tissue; (2) Typus sthenicus, defined by strong development of skeleton, high amount of muscular mass and above average fat tissue due to the high amount of fat cells; (3) Typus gracilis, defined primarily by small measures of transversal dimensions of skeleton; (4) Typus disharmonicus, defined by inconvergent development of morphological characteristics and low fat tissue; (5) Typus leptomorphicus, defined by above average development of longitudinal dimensions of skeleton. Therefore, morphological types in real space are differnt of those obtained in image space by Momirovi}, Ho{ek, Prot and Bosnar (2002) but are similar, altough not identical, with taxons obtained by method of fuzzy clustering applied by A. Ho{ek (1978). 4. DISCUSSION It seems, in any case, that manifes morphological space is not an ideal envinronment for the determination of morphological types. Some reasons for this apparently paradoxical statment is the true nature of anthropometric variables. Namely, most of them are partially included one to other to an udetermined manner, and most of them, altough manifestly different, have the same genetical origin. This results in very uncertain position of objects in the space of manifest morphological characteristics, partly because of latent degeneration of this space due to the near singularity of some of segments spanned by specific morphological vectors. REFERENCES Ho{ek, A. (1978): Povezanost morfolo{kih taksona sa manifestnim i latentnim dimenzijama koordinacije. Disertacija, Fakultet za fizi~ku kulturu Sveu~ili{ta u Zagrebu. Ho{ek, A. (2002): O odre|ivanju antropolo{kih taksona. Glasnik Antropolo{kog dru{tva Jugoslavije, 37:147-156. Momirovi}, K.; Zakraj{ek, E. (1973): Odre|ivanje taksonomskih skupina direktnom oblimin transformacijom ortogonaliziranih originalnih i latentnih varijabli. Kineziologija, 3, 1: 83-92. Momirovi}, K. (1978): XTQ procedures for the determination of polar taxonomic variables. Informatika 78, 3, 104. Momirovi}, K.; Zakraj{ek, E.; Ho{ek, A.; Stojanovi}, M. (1979): Comparative evaluation of some taxonomic algorithms for the determination of morphological types. Collegium Antropologicum, 3: 59-65. Momirovi}, K. (1981): A class of algorithms for the determination of polar taxons. In Multidimensional data analysis, 475-491. Le Chesney: SRCE, INRIA et ISDUN. Momirovi}, K.; Gredelj, M. (1982): Jednostavan postupak za detekciju konzistentnih rojeva. Zbornik radova VI simpozija iz informatike 'Jahorina 82', 282: 1-7. Sarajevo: Elektrotehni~Ki fakultet. Momirovi}, K. (1986): COMTAX: Algoritam i program za detekciju i komparaciju polarnih i distinktnih taksona. Statisti~ka revija, 36, 3-4: 141-149. Momirovi}, K. (1993): O jednom taksonomskom algoritmu u parcijalnom image prostoru. Zbornik radova 6 i 7 Sekcije za klasifikacije Saveza statisti~kih dru{tava Jugoslavije, 22-30. Beograd: savezni zavod za statistiku. Momirovi}, K.; Ho{ek, A.; Prot, F.; Bosnar, K. (2002): O morfolo{kim tipovima mladih odraslih mu{karaca (Morphological types of adult young men). Technical report, Institute of criminological and sociological research, Belgrade. Momirovi}, K.; Ho{ek, A.; Popovi}, D. A.; Boli. E. (2002): Cluster analysis by neural networks. Proceedings of 10th International Congress of Physical Education and Sport. Komotini: Democritus University of Trace. Momirovi}, K. (2002): A taxonomic neural network. Technical report, Institute of criminological and sociological research, Belgrade. Popovi}, D. A.; Momirovi}, K. (2002): Taksonomske neuronske mre`e. Tehni~ki izve{taj, Fakultet za fizi~ku kulturu Univerziteta u Pri{tini. Stojanovi}, M.; Solari}, S.; Momirovi}, K.; Vukosavljevi}, R. (1975): Pouzdanost antropometrijskih mjerenja. Kineziologija, 5, 1-2:91-122. Szirovicza, L.; Gredelj, M.; Momirovi}, K. (1978): MORPHOTAX: Algoritam i program za taksonomsku analizu u prostoru multivarijatno raspore|enih varijabli. Informatica 78, 7, 105. [talec, J.; Momirovi}, K. (1971): Ukupna koli~ina valjane varijance kao osnov kriterija za odre|ivanje broja zna~ajnih glavnih komponenata. Kineziologija, 1, 1: 83-90. Zlobec, L. (1975): Komparativna analiza nekih taksonomskih algoritama. Magistarski rad, Elektrotehni~ki fakultet u Zagrebu.  Some other taxonomic neural networks were also applied. Hopfield neural network Hoptax produces unsatisfactory clustering with coefficient of efficacy of only .882. A perfect coefficient of efficacy was obtained by neural network Dualtax, but with very difficult identification of taxons defined in principal component space. Similar results to these obtained by Triatlon were obtained by Intruder, a very simple neural network, but identification structures obtained by Triatlon are more informative then the structures obtained by Intruder due to the intermediary fuzzy clustering of both variables and subjects. Of course, both hierarchical methods and classic methods of local optimization produce quite unsatisfactory results; Ward method produces five clusters with coefficient of efficacy of only .822, and McQueen's method produces five clusters with a relatively good coefficient of efficacy (.917), but not clearly defined in morphological space.  Identification structures in taxonomic algorithms must be, at least initially, defined in the whole space of variables because necessary inversion operations in intrataxon space can produce, in the case of perfect or almost perfect classification, very unstable results due to the possible weak conditionality of matrix of intrataxon dispersion. 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