Utilization of Chemical Structure Information for Analysis of Spectra Composites

Transcription

1 ESANN 214 proceedings, European Symposium on Artificia Neura Networks, Computationa Inteigence and Machine Learning Bruges (Begium), Apri 214, i6doccom pub, ISBN Avaiabe from Utiization of Chemica Structure Information for Anaysis of Spectra Composites Kristin Domaschke1,2, Andre Rossberg1 and Thomas Vimann3 1- Hemhotz-Zentrum Dresden-Rossendorf, Institute of Resource Ecoogy, PO Box 51 1, 1314 Dresden, Germany 2- current address: Life Science Inkubator Sachsen GmbH & Co KG, project team NanoscopiX, Tatzberg 47, 137 Dresden, Germany 3- University of App Science Mittweida - Dept of Mathematics, Technikumpatz 17, 9648 Mittweida, Germany Abstract In this paper, we propose the utiization of structura information of spectra data during the preprocessing to extend the abiity of subsequent anaysis methods Specificay, we expect a dataset of measured spectra containing mixtures of ony a few spectra components Using the concentration ratios for a sma subset of mixtures and the chemica structura knowedge, theoretica spectra components are generated Then a set, which combines measured and theoretica spectra, is anayzed using a sef-organizing map to predict the unknown mixture ratios of the remaining subset by an associative earning At this time, the initia study on simuated data reached very good resuts 1 Introduction The prediction of concentration of mixture components is an important task in chemica data anaysis In this paper we propose an approach based on Kohonen s Sef-Organizing Map (SOM,[1]) and an utiization of structura chemica knowedge, if the mixture information is avaiabe for a few data of the whoe data set The SOM is one of the most popuar data mining and visuaization methods for vectoria data It provides a non-inear mapping of the possiby high-dimensiona data onto a ow-dimensiona, frequenty two-dimensiona, grid Under certain conditions this mapping preserves the topoogica properties of the data [2] Chemica spectra data are known to be high-dimensiona in genera and, therefore, are predestined for processing using SOMs in order to visuaize them or to detect custers To anayze the dependence of the spectra structure of data on specific chemica parameters, such as the ph-vaues or concentrations, a fused mapping of the spectra data together with further information is frequenty requested For this need, Messen proposed the XY-fused SOM [3] In this approach, two SOMs, one for spectra data and one for chemica parameters, are combined bi-directionay via a merged winner determination Yet, this structure is very compex and fais if ony a sma amount of data is avaiabe for earning, as it is frequenty the case in chemica data anaysis The authors woud ike to thank Dr Vinzenz Brender and Dr Kay Grossmann, of Institute of Resource Ecoogy at Hemhotz-Zentrum Dresden-Rossendorf, for hosting this research 277

2 ESANN 214 proceedings, European Symposium on Artificia Neura Networks, Computationa Inteigence and Machine Learning Bruges (Begium), Apri 214, i6doccom pub, ISBN Avaiabe from Here, the factor anaysis, which is used as standard method for spectra decomposition, can be mentioned Nevertheess, the non-inearity of SOMs seems to have much greater potentia especiay for further research on spectra unmixing probems as the factor anaysis Thus, in this paper we propose the foowing strategy: First, in a preprocessing step, we use the avaiabe mixture information for a sma subset of the spectra data to estimate theoretica pure component spectra, which can serve as additiona data vectors with the identity matrix as known mixture information For this purpose, chemica structure information is expicity taken into account Thereafter, we appy associative earning in sef-organizing maps to estimate the unknown mixture ratios for a spectra of the data set In the ast section of this paper we present the appication of this strategy to a simuated data set 2 21 Preprocessing of spectra using chemica structure information Spectra pattern and structura information in composite spectra We assume n spectra di obtained from some measurements with NB bands coected in the data matrix D = {d1,, dn } Rn NB In our data to be anayzed, these spectra are obtained by extended X-RAY absorption fine structure spectroscopy (EXAFS,[4]) as absorption spectra These measured spectra composites di consist of sparse mixtures of m theoretica components, where m << n These m pure spectra, which are estimated as described ater, are coected in the matrix R Rm NB with R = {r1,, rm } and rj RNB Further we denote by C Rn m with C = {c1,, cn } and ci Rm the unknown component concentration ratios of the component spectra R within the composites D The structura information of the spectra signa can be described by the Lambert-Beer aw [5] In the foowing, this definition is expained for absorption spectroscopic methods, but can be adapted simpy to many other spectroscopic methods, such as fuorescence spectroscopy The spectra signa of an absorbing substance is caed extinction E in absorption spectroscopy and depends proportionay on the thickness of the sampe b, the concentration c and on an extinction coefficient α by mo (1) E(λk ) = b c α(λk ) [cm] mo cm The unit of the extinction coefficient α resuts from the units for b and c We suppose the thickness of the sampe b is standardized to 1cm for each measurement, so we can reduce the equation (1) to mo E(λk ) = c α(λk ) mo If we further assume a high concentration of 1 mo for the substance, we see that the extinction coefficient α(λk ) is equa to E(λk ) and therefor has the same data characteristics as E(λk ) 278

3 ESANN 214 proceedings, European Symposium on Artificia Neura Networks, Computationa Inteigence and Machine Learning Bruges (Begium), Apri 214, i6doccom pub, ISBN Avaiabe from Furthermore, mixture sampes contain more than one absorbing substance, which here are assumed having no interactions between them Then, the absorption of a composite sampe E i, with i is the index of measurements in 1 < i < n, is the sum of the singuar extinctions E i (λ k ) = E 1 (λ k ) + E 2 (λ k ) + + E m (λ k ) resuting in the inear Lambert-Beer aw for the m components E i (λ k ) = m c ij α j (λ k ) (2) j=1 Furthermore, these equations show, that the extinction E and their extinction coefficient α reies on λ k, which is the waveength of the k th band with k = {1,, N B } Depending on the dimension of λ k, which can characterize either ony one or a N B spectra bands, we get either a singe extinction vaue E or an extinction vector E This aso appies to the extinction coefficients α For our data set, the extinction vector E of a sampe i is the measured spectrum d i Further, the m pure components can be identified with their extinction coefficients α j such that r j = α j is vaid Thus we obtain in (2) d i (λ k ) = m c ij r j (λ k ) (3) j=1 D = CR (4) We observe that under certain conditions the measured spectra d i can be determined additivey by the spectra of the pure components r j and their concentration vaues c ij within the composites For a set of measured spectra D equation (3) hods in the same way, as shown in (4) Further we ony consider convex data structures, ie m j=1 c ij = 1 In particuar, it is assumed that the number of a contained components is known in advance Unfortunatey, the concentration matrix C is generay not known for the measured data Hence, we cannot cacuate the matrix R However, the deduced structura reation (4) can be used as chemica structure information for structured preprocessing if a few concentrations are avaiabe 22 Using structura information for structured preprocessing In our probem we assume a spectra data subset D S R m N B, for which the concentrations C S R m m are known Thus, if we have this additiona data at east for as many spectra as components r j with 1 < j < m underying the data, we can compute the pure component spectra R using the structura information in (4) For this purpose, we appy an iterative Jacobi scheme [6], such that for each iteration step t + 1 we obtain R t+1 = O 1 [ D S LR t] (t = 1, 2, ) 279

4 ESANN 214 proceedings, European Symposium on Artificia Neura Networks, Computationa Inteigence and Machine Learning Bruges (Begium), Apri 214, i6doccom pub, ISBN Avaiabe from where the foowing notation is used c11 c21 = c12 c22 c1m c2m = L + O with cm1 cm2 c21 L = c12 cmm c1m c11 c2m, O= cm1 cm2 CS c22 cmm The iteration, starting with some set vaues R, is performed unti krt+1 Rt k <, where > is a chosen toerance, is reached Here, k k denotes the spectra norm Convergence is guaranteed if either max i m X j=1,j6=i m X cij < 1 or max j cii i=1,i6=j cij <1 cii hods [6] As a resut, we obtain the estimates R of the pure component spectra The concentration matrix CR with CR = {e1,, em } and ej Rm is simpy the unity matrix of dimension m consisting of the respective unity vectors ej In this way, we are abe to generate additiona spectra with known concentrations based on the chemica structure information (4) 3 Utiization of the extended data set to SOM-associationearning After the structured preprocessing, we have, on the one hand, the originay given data, consisting of D with the subset DS, for which the concentrations CS are avaiabe Wog we suppose these spectra to be d1 dm with concentration vectors c1 cm On the other hand we generated the pure component spectra R with trivia concentrations CR Thus we have the foowing dataset: d1,1 d V = NB,1 c1,1 cm,1 d1,m dnb,m c1,m cm,m rnb,1 e1,1 em,1 r1,1 r1,m rnb,m, V = e1,m em,m dnb,m+1 c1,m+1 cm,m+1 d1,m+1 d1,n dnb,n c1,n cm,n Hence, the fused dataset V = {v1,, vm+m } contains both informations, the spectra and their known concentrations merged into singe vectors v Rp with p = NB + m and 1 < < m + m The set V coects the remaining n m spectra together with the unknown concentrations cm+1 cn Both datasets are used for associative earning in SOMs [1] In our appication, the SOM grid A is a square attice of edge ength N such that the coordinate vectors are k N 2 The weight vectors or prototypes W = {wk } assigned to 28

5 ESANN 214 proceedings, European Symposium on Artificia Neura Networks, Computationa Inteigence and Machine Learning Bruges (Begium), Apri 214, i6doccom pub, ISBN Avaiabe from A, have the same dimension p as defined for the data vector of V Usua SOM training takes pace as appying the winner determination s(v) = arg min kv wk k k A and subsequent prototype adaptation according to wk = hks (v wk ) kk ska with hks = exp 2σ 2 being the neighborhood function Here < 1 is the earning rate and σ is the neighborhood function To keep the information of the subset V we aso feed these vectors into the training scheme Because of the unknown concentration information for these vectors v k ony the spectra information is used for winner determination For prototype update we appy the spectra information and the concentration estimations given by the current best matching unit After training, the unknown concentrations for the vectors v k can be estimated by association, ie the winner s(v k ) is determined and we simpy set NB +i v knb +i = ws(v for i = 1 m as association step k) 4 Appication of structured information processing for an EXAFS data set For this appication a dataset of n = 14 simuated EXAFS spectra with NB = 1 is used The underying chemica structure information assumes m = 4 components and a sinusoida pure component spectrum according to sin(bj f ) for a given frequency vector f RNB [7] Here we consider b = (125, 25, 5, 1) for the different pure component spectra We generated the simuated spectra as mixtures of these pure components with a predefined mixing matrix C of concentrations In the simuations we provided the concentrations ony for m = 4 simuated spectra to the above described processing agorithm using a SOM-grid A with N = 15 Thus, these data pay the roe of the subset DS For the SOM-training the neighborhood range σ remains non-vanishing aso during the convergence phase of SOM-earning to keep the generaization abiity of the mode despite the sma number of avaiabe training data, which is a common procedure for those cases [8] Further, we appied a prototype correction to ensure the reation (4) for the prototypes during the earning process Thus, the structura knowedge is used again After the appication of the compete anaysis procedure we obtain the estimated concentrations for the remaining 1 spectra We can compare them with the origina ones used for generating the simuated data set As we can see in Fig 1, we get accurate predictions Thus, the association earning by SOMs together with the utiization of the chemica structure information is abe to estimate the unknown concentrations quite we for this data set 5 Concusion We propose a data anaysis framework for spectra data processing in order to estimate mixture concentrations in spectra composites under the assumption of 281

6 ESANN 214 proceedings, European Symposium on Artificia Neura Networks, Computationa Inteigence and Machine Learning Bruges (Begium), Apri 214, i6doccom pub, ISBN Avaiabe from Fig 1: Comparison of the 4 origina component concentrations ( ) and the respective predicted vaues (?) obtained from the structured data processing for the 1 spectra not contained in DS sparsey avaiabe concentration information This approach takes the structura chemica information into account to generate an extended whie reiabe data set, which then can be used for association earning in SOMs We introduced the method and expained, how the structura-chemica information is integrated We exempary demonstrated the method for an artificia dataset Yet, further simuation and stabiity anaysis is required In particuar, the infuence of noisy data has to be considered Thus, the presented work is ony a proof of concepts so far, which has to be evauated further in the next steps of our research References [1] T Kohonen The sef-organizing map Proceedings of the IEEE, 78(9): , 199 [2] Th Vimann, R Der, M Herrmann, and Th M Martinetz Topoogy preservation in sef-organizing feature maps: Exact definition and measurement IEEE Transactions on Neura Networks, 8(2): , 1997 [3] W Messen, R Wehrens, and L Buydens Supervised Kohonen networks for cassification probems Chemometrics and Inteigent Laboratory Systems, 83(2):99 113, 26 [4] A Rossberg, T Reich, and G Bernhard Compexation of uranium (vi) with protocatechuic acid - appication of iterative transformation factor anaysis to exafs spectroscopy Anaytica and bioanaytica chemistry, 376(5): , 23 [5] DA Skoog and JJ Leary Instrumentee Anaytik: Grundagen - Gera te - Anwendungen Springer-Lehrbuch Springer, 1996 [6] H Friedrich and F Pietschmann Numerische Methoden: ein Lehr- und U bungsbuch Water de Gruyter GmbH & Co KG, 21 [7] K Domaschke Mutidimensionae Spektrenanayse mittes neuronae Netze dipoma thesis, Hochschue Zittau/Go ritz - Univerity of Appied Science, 212 [8] Th Vimann Neura maps for faithfu data modeing in medicine - state of the art and exempary appications Neurocomputing, 48(1-4):229 25,