Using Support Vector Machines to Enhance the Performance of X-Ray Diffraction Data Analysis in Crystalline Materials Cubic Structure Identification

Transcription

1 194 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.7 No.7, July 007 Usng Support Vector Machnes to Enhance the Performance of X-Ray Dffracton Data Analyss n Crystallne Materals Cubc Structure Identfcaton Mohammad Syukur Faculty of Mathematcs and Natural Scences, Unversty of Sumatera Utara, 0155 Medan, Sumut, Indonesa Summary Crystallne materals cubc structure dentfcaton s very mportant n crystallography and materal scence research. For a long tme researchers n the feld have used manual approach n matchng the result data from X-Ray Dffracton (XRD) method wth the known fngerprnt. These manual matchng processes are complcated and sometmes are tedous because the dffracted data are complex and may have more than one fngerprnt nsde. Ths paper proposes the use of support vector machnes to enhance the performance of the matchng process between the dffracted data of crystallne materal and the fngerprnts. It s demonstrated, through experments, that support vector machnes gves more accurate and relable dentfcaton results compared to the use of neural network. Key words: Support Vector Machne, X-Ray Dffracton Data Analyss, Cubc Structure Identfcaton, Materal Scences, Artfcal Intellgence Applcaton. 1. Background Crystallography s one of the areas of research n physcs that deals wth the scentfc study of crystals. It has always been one of the most challengng research felds snce eghteenth century. The sgnfcant dscovery of X- ray by Röntgen n 1895 [8] had yelded to a new way of dong crystallography research. Snce then X-ray dffracton method has been proposed and appled to many dfferent sub-area of crystallography such as dentfcaton of crystallne phases, qualtatve and quanttatve analyss of mxtures and mnor consttuents, dstncton between crystallne and amorphous states, sde-chan packng of proten structures, dentfcaton of crystallne materal, etc. The last area s the focus of ths paper. X-ray dffracton data nterpretaton for most crystallne materals s a very complex and dffcult task. Ths s due to the condton that dfferent crystallne materal may contan more than one cubc structures component type and after beng dffracted usng X-ray dffracton method, the dffracted data are complex. Hence, the data can be very ambguous and s not easy to track and understand. Numerous artfcal ntellgence technques and applcaton have been appled and developed to solve the problems n varous domans. In our prevous work [5], an attempted has been made to use neural network to perform automatc cubc structure dentfcaton on the crystallne materals. Though t was a success, there s stll left room for mprovement. Ths paper proposes the use of support vector machne (SVM) to enhance the performance of crystallne materals cubc structure dentfcaton. The result of usng SVM s compared wth the result usng neural network. Support vector machnes have been proven to be a powerful method to solve dentfcaton and classfcaton problems. It ncludes gene dentfcaton [10], paraphrase dentfcaton [11], proten classfcaton usng X-ray crystallography [9], and many more. The man ntent of ths paper s to showcase the superor results on the use of support vector machne over neural network n crystallne materals cubc structure dentfcaton.. Cubc Structure Identfcaton usng X-Ray Dffracton Data In prncple, there are four cubc structures type for crystallne materals, the Smple Cubc (SC), Body Centered Cubc (BCC), Face Centered Cubc (FCC) and Damond [1]. In our prevous work [], a formula has been proposed to calculate the fngerprnts for these four cubc structures. The formula utlzes the Mller ndex (h,k,l) [6]. The proposed formula can be wrtten as follows: ( h + k + l ) sn θ = λ 4a (1) Snce the wavelength of the ncomng X-ray (λ) and lattce constant (a) are both constants, we can elmnate these Manuscrpt receved July 5, 007 Manuscrpt revsed July 5, 007

2 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.7 No.7, July quanttes from Eq. 1 and derve the rato of two sn θ as follows: sn θ h + k + l m m m m R = = m, n sn θ h + k + l n n n n () where θ m and θ n are the dffractng angles for two peak assocated wth the dffractng planes {h m,k m,l m } and {h n,k n,l n } respectvely for rato R m,n. The fngerprnt for each crystallne materal s cubc structure s calculated by takng 10 peaks from the X-ray dffracton data and calculates the two peaks combnatons from that 10 peaks. That s, each fngerprnt s actually contans 45 values of the quadratc snus rato from Eq. C 10 snce equal to 45. Table 1,, 3 and 4 depct the fngerprnt for Face Centered Cubc (FCC), Damond, Body Centered Cubc (BCC) and Smple Cubc (SC) respectvely. R 1, = R 1, = Table 1: Face Centered Cubc (FCC) Fngerprnt R,3 = R,4 = R,5 = R,6 = 0.50 R,7 = R 3,9 = R,8 = R 3,10 = R,9 = R 5,9 = R,10 = R 5,10 = Table : Damond Fngerprnt R,3 = R,4 = R,5 = R,6 = R,7 = R 3,9 = R,8 = R 3,10 = R,9 = R 5,9 = R,10 = R 5,10 = R 1, = R 1, = Table 3: Body Centered Cubc (BCC) Fngerprnt R,3 = R,4 = R,5 = 0.48 R,6 = R,7 = R 3,9 = R,8 = R 3,10 = R,9 = R 5,9 = R,10 = R 5,10 = Table 4: Smple Cubc (SC) Fngerprnt R,3 = R,4 = R,5 = R,6 = R,7 = R 3,9 = R,8 = R 3,10 = R,9 = R 5,9 = 0.00 R,10 = R 5,10 = Support Vector Machne Support Vector Machne (SVM) can be regarded as an excellent statstcal learnng performance and superor classfcaton performance. Smply put, the support vector machne that we used n ths paper can be summarzed as follows: t dvdes two specfed tranng samples whch belong to two dfferent categores through constructng an optmal separatng hyperplane ether n the orgnal space or n the mapped hgher dmensonal space [4]. The basc dea of constructng ths optmal separatng hyperplane s to guarantee maxmum dstance between each tranng sample and the separatng hyperplane. The SVM algorthm and ts learnng procedure can be comprehended as follows: If the data are lnearly separable n nput space, a bnary classfcaton task s taken nto account. Let {( x, y )}(1 N) be a lnearly separable set, where

3 196 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.7 No.7, July 007 d x R, y { 1,1} and y are labels of categores. The general expresson of the lnear dscrmnaton functon n d-dmenson space s defned as g ( x) = w x + b, and the correspondng equaton of separatng hyperplane s w x + b = 0 where w s normal to the hyperplane, b / w s the perpendcular dstance from the hyperplane to the orgn, and w s the Eucldean norm of w. Further normalze g(x) and let all the x meet g(x) 1 wll results to the samples whch are closest to optmal separatng hyperplane that meet g(x) = 1. Hence, the separatng nterval s equal to / w and solvng the optmal separatng hyperplane tself s equvalent to mnmzng w. The objectve functon used for ths s as follows: 1 mn Φ ( w ) = w (3) subject to the constrants: y ( w x + b) 1, = 1,..., N (4) The constrants n Eq. 4 can be replaced by the Lagrange multplers of the Lagrangan algorthm to further solved the constrants problem where w = α y x and x are the samples only appearng n the separatng nterval planes. These samples are called support vectors and ts classfcaton functon s defned as follows: f ( x) = sgn α y x x + b (5) If data are not lnearly separable n the nput space, smply use the followng objectve functon: N 1 mn Φ( w, ξ ) = w + C ξ (6) = 1 Where, ξ s slack varable and C s a penalty factor. Smultaneously, through a non-lnear transform Φ ( ), the nput space s mapped nto a hgher dmensonal space called feature space n whch optmal separatng hyperplane can be solved. In addton, the nner product calculaton s changed nto K( x, x j ) = Φ( x ) Φ( x j ) where K ( x, x j ) kernel functon s defned as nner product n Hlbert space. Thus the fnal classfcaton functon can be represented as follows: 4. Experments As mentoned earler, the man ntent of ths paper s to showcase the superor results on the use of support vector machne over neural network n crystallne materals cubc structure dentfcaton. In our prevous work [5], we had appled a back-propagaton neural network to dentfy the cubc structure of three samples, Alumnum (Al), Slcon (S), and a mxture of Al and S. In ths experment, more samples are used n addton to that three samples such as Iron (Fe), Tungsten (W), Sodumchlorde (NaCl), and CopperZnc (CuZn). From the new samples, a mxture sample s also created from three samples Al, S, and Fe to evaluate the performance of support vector machne n dentfyng a more complex pattern data. The experments are carred out usng the same equpments and envronment settngs as wth our prevous work whch s usng a Phlps X-Ray devce dffractometer control PW1710. The devce was also usng PW179 seres of X-Ray generator, anode Cu tube, and PCAPD (PW1877) software verson 3 ntegrated wth our proposed applcaton nstalled. In the overall experments, we use the same tube voltage and also the same tube current,.e. 30kV and 0mA respectvely. The SVMlght package [3] was used to construct the support vector machne (SVM) classfers. For a gven set of bnary-labeled tranng examples, SVM maps the nput space nto a hgher dmensonal feature space and seeks a hyperplane n the feature space to separate the postve data nstances from the negatve ones. Dfferent values for the γ and C parameters were tested to optmze the performance of SVM to dentfy the cubc structures from the presented crystallne materal s sample. Snce the fngerprnt tranng dataset was mbalanced, the cost factor was set to 5.8 for gvng more weght to tranng errors on postve examples than errors on negatve ones. In the end, after expermentng several dfferent value for C and γ, we use γ = and C = 0.55 as the SVM parameter n ths experment. Whle the rest of the parameters were set to ther default values as specfed n SVMlght package. As for the neural network, we kept the same settng from our prevous work [5] for comparson wse. That s, the neural network was constructed wth 8 nodes n the hdden layer, 5 n the frst hdden layer and 3 n the second hdden layer. It uses standard teratve gradent algorthm for back-propagaton tranng. f ( x) = sgn α y K( x, x ) x + b (7)

4 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.7 No.7, July Analyss & Results After feedng all the samples nto the X-Ray dffractometer, the resulted dffracton data for each sample and ts rato R m,n values are shown on Table 5, 6, 7, 8 and 9 for Iron (Fe), Tungsten (W), Sodumchlorde (NaCl), CopperZnc (CuZn), and the mxture of Al, S, and Fe respectvely. Whle the R m,n rato values for Al, S and mxture of Al and S are avalable at [5]. Table 5: The resulted R m,n rato values for the sample of Iron (Fe) R 1, = R,4 = R,5 = R,3 = R,6 = Table 6: The resulted R m,n rato values for the sample of Tungsten (W) R 1, = R,3 = R,4 = 0.50 R,5 = R,6 = 0.65 R,7 = R,8 = Table 7: The resulted R m,n rato values for the sample of Sodumchlorde (NaCl) R 1, = R,3 = R,4 = R 4,9 = 0.73 R,5 = 0.41 R 4,10 = R,6 = R,7 = 0.10 R 3,9 = R,8 = 0.00 R 3,10 = R,9 = R 5,9 = 0.15 R,10 = R 5,10 = Table 8: The resulted R m,n rato values for the sample of CopperZnc (CuZn) R 1, = R,3 = R,4 = R 4,9 = R,5 = R 4,10 = R 6, 10 = R,6 = R,7 = 0.51 R 3,9 = R,8 = 0.3 R 3,10 = R 7, 10 = 0.76 R,9 = 0.01 R 5,9 = R, 10 = 0.18 R 5, 10 = Table 9: The resulted R m,n rato values for the mxture sample of Alumnum (Al), Slcon (S), and Iron (Fe) R 1, = R,3 = R,4 = R,5 = R,6 = R 5,9 = R,7 = R 4,9 = R 5,10 = R,8 = 0.86 R 3,9 = R 4,10 = R 5,11 = R,9 = 0.75 R 3,10 = R 4,11 = R 5,1 = R,10 = 0.50 R 3,11 = 0.99 R 4,1 = 0.96 R 5,13 = R,11 = 0.6 R 3,1 = 0.66 R 4,13 = 0.77 R 5,14 = R 1, 11 = 0.15 R,1 = 0.01 R 3,13 = 0.50 R 4,14 = 0.50 R 5,15 = 0.31 R 1,1 = R,13 = R 3,14 = 0.4 R 4,15 = 0.34 R 5,16 = R 1,13 = R,14 = R 3,15 = 0.10 R 4,16 = 0.8 R 5,17 = R 1,14 = R,15 = R 3,16 = 0.05 R 4,17 = 0. R 5,18 = 0.75 R 1,15 = R,16 = R 3,17 = 0.00 R 4,18 = 0.00 R 5,19 = 0.50 R 1,16 = R,17 = R 3,18 = R 4,19 = R 10,11 = R 1,17 = R,18 = R 3,19 = R 10,1 = R 1,18 = R,19 = R 9,11 = 0.83 R 10,13 = R 1,19 = R 9,1 = 0.73 R 10,14 = R 8,11 = 0.79 R 9,13 = R 10,15 = R 8,1 = R 9,14 = R 10,16 = 0.615

5 198 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.7 No.7, July R 6,11 = R 6,1 = R 6,13 = R 6,14 = 0.45 R 6,15 = 0.41 R 6,16 = R 6,17 = R 6,18 = R 6,19 = R 11,1 = R 11,13 = R 11,14 = R 11,15 = 0.70 R 11,16 = R 11,17 = R 11,18 = R 11,19 = R 7,11 = R 7,1 = 0.59 R 7,13 = R 7,14 = R 7,15 = R 7,16 = R 7,17 = R 7,18 = R 7,19 = R 1,13 = R 1,14 = 0.84 R 1,15 = R 1,16 = R 1,17 = 0.75 R 1,18 = R 1,19 = 0.65 R 8,13 = R 8,14 = R 8,15 = R 8,16 = 0.54 R 8,17 = 0.59 R 8,18 = R 8,19 = R 13,14 = R 13,15 = 0.84 R 13,16 = 0.81 R 13,17 = R 13,18 = R 13,19 = R 14,15 = R 14,16 = R 14,17 = R 14,18 = R 14,19 = 0.74 R 9,15 = R 9,16 = R 9,17 = R 9,18 = R 9, 19 = R 15,16 = R 15,17 = R 15,18 = R 15,19 = 0.79 R 16,17 = R 16,18 = R 16,19 = 0.81 R 17,18 = R 17,19 = R 18,19 = 0.97 R 10,17 = R 10,18 = R 10,19 = Table 10: SVM and Neural Network Comparson Results SVM Neural Network Sample Name Type Accuracy Type Accuracy Al + S Al + S + Fe FCC 91% FCC 86% Damond 9% Damond 84% FCC 90% FCC 78% Damond 8% Damond 67% BCC 73% SC 51% Al FCC 93% FCC 9% S Damond 9% Damond 91% Fe BCC 89% BCC 78% W BCC 91% BCC 89% NaCl FCC 94% FCC 9% CuZn SC 90% SC 87% The last step s to pass the resulted data for each crystallne materal sample nto the traned SVM and neural network. Table 10 shows the comparson results of SVM and neural network. From result outlned on Table 10, we can clearly see that support vector machne (SVM) outperform neural network n terms of the accuracy of dentfyng the cubc structure type from each crystallne materal sample. Both SVM and neural network successfully detect the correct cubc structure type for sngle component crystallne materal, but neural network suffers and faled to detect the correct cubc structure type for mult component crystallne materal especally the one wth three cubc structure components nsde. In the experment wth the mxture sample of Alumnum (Al), Slcon (S), and Iron (Fe), neural network dentfy that the sample contan three cubc structure component of FCC, Damond and SC wth accuracy rate of 78%, 67%, and 51% respectvely. Snce the cubc structure type of Iron (Fe) s BCC, the result gven by neural network s wrong. Whle SVM gves more accurate result of FCC, Damond and BCC wth the accuracy rate of 90%, 8%, and 73% respectvely. Neural network falure s probably due to the fact that the fngerprnt structure of BCC and SC s almost the same and among the mxture sample component, Iron (Fe) s the crystallne materal that has the smallest number of R m,n rato values. And after beng mxed wth the two other components, t makes ts rato pattern dffcult to track. SVM results also outperform the neural network n the mxture of two component of Alumnum (Al) and Slcon (S). Though both successfully detect the correct cubc structure types (FCC and damond), but the accuracy of SVM s slghtly hgher, 91% and 9% respectvely for FCC and damond. As for sngle component crystallne materal samples, both SVM and neural network gves equvalent results. 6. Summary In ths paper we propose the use of support vector machne to enhance the performance of cubc structures dentfcaton on mult component crystallne materal. The complexty of mult component crystallne materal R m,n rato needs a sophstcated and powerful methods to accurately classfy ts cubc structure type. And support vector machne whch exhbts more excellent performances such as no local optmum problem, no overft or under-ft problem, better convergence property, less tranng samples, hgher correct dentfcaton rate, and hgher relablty suts ths job.

6 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.7 No.7, July Ths work proves that the use of artfcal ntellgence technques such as support vector machne and neural network towards crystallne materals cubc structure dentfcaton research to be very useful and can smplfy and fasten up the work on crystallography research area. Our future research drecton ncludes applyng these artfcal ntellgence technques to other problems n crystallography research area. Acknowledgments Author would lke to acknowledge Unversty of Sumatera Utara for provdng space and the equpments used n ths research. Also, author would lke to thank Muhammad Ferm Pasha for the frutful dscusson and nsghtful comments on the support vector machne part. Mohammad Syukur receved the B.Sc. degree n Physcs from Unversty of Sumatera Utara, Indonesa and M.Sc. degrees n Materals Physcs from Bandung Insttute of Technology, Indonesa n 1974 and 198, respectvely. He s currently a senor lecturer and the head of Crystallography & Radaton Physcs Research Laboratory at Faculty of Mathematcs and Natural Scences, Unversty of Sumatera Utara, Indonesa. Hs research nterests nclude Materal Physcs, X-Ray Dffracton methods, Artfcal Intellgence Applcaton and Crystallography. He has wrtten two book chapters and numerous refereed research papers. References [1] Suryanarayana, C. and Norton, M.G. X-Ray Dffracton - A Practcal Approach. Plenum Press - NewYork, [] Syukur, M. and Zarls, M. A Standard Calculaton for Lattce Analyss on Cubc Structures Sold Materals usng X-Ray Dffracton Method and ts Expermental Study. Journal of Sold State Scence and Technology Letter, Vol. 6, No., [3] Joachms, T. Makng large-scale SVM Learnng Practcal. Advances n Kernel Methods - Support Vector Learnng, B. Schölkopf and C. Burges and A. Smola (Eds.), MIT Press, [4] Vapnk, V.N. Statstcal Learnng Theory. New York: John Wley and Sons, [5] Syukur, M., Pasha, M.F. and Budarto, R. A Neural Network-Based Applcaton to Identfy Cubc Structures n Mult Component Crystallne Materals usng X-Ray Dffracton Data. Internatonal Journal of Computer Scence and Network Securty (IJCSNS), 7(): 49-54, 007. [6] Cullty, B.D. Elements of X-ray Dffracton. Addson- Wesley - London, [7] The Internatonal Center for Dffracton Data, [8] Ewald, P.P. Ffty Years of X-Ray Dffracton. Internatonal Unon of Crystallography, [9] Gubb, J., Shlton, A., Parker, M. and Palanswam, M. Proten Topology Classfcaton usng Two-Stage Support Vector Machnes. Genome Informatcs Vol.17, No., pp , 006. [10] Krause, L., McHardy, A.C., Nattkemper, T.W., Pühler, A., Stoye, J. and Meyer, F. GISMO - gene dentfcaton usng a support vector machne for ORF classfcaton. Nuclec Acds Research, 35(): , 006. [11] Brockett, C. and Dolan, W.B. Support vector machnes for paraphrase dentfcaton and corpus constructon. Proceedngs of The 3rd Internatonal Workshop on Paraphrasng (IWP005), 005.