Identification of water samples from different springs and rivers of ...

ISSN 00271314, Moscow University Chemistry Bulletin, 2013, Vol. 68, No. 1, pp. 60–66. © Allerton Press, Inc., 2013. Original Russian Text © Ya.N. Pushkarova, A.B. Sledzevskaya, A.V. Panteleimonov, N.P. Titova, O.I. Yurchenko, V.V. Ivanov, Yu.V. Kholin, 2012, published in Vestnik Moskovskogo Universiteta. Khimiya, 2012, No. 6, pp. 405–412.

Identification of Water Samples from Different Springs and Rivers of Kharkiv: Comparison of Methods for Multivariate Data Analysis Ya. N. Pushkarova, A. B. Sledzevskaya, A. V. Panteleimonov, N. P. Titova, O. I. Yurchenko, V. V. Ivanov, and Yu. V. Kholin Karazin Kharkiv National University, pl. Svobody 4, Kharkiv, 61022 Ukraine email: [email protected] Received September 5, 2012

Abstract—The application of artificial neural networks for identifying water samples from different springs and rivers of Kharkiv based on the data about metal ions concentrations was studied. Using the riverwater samples as an example, we demonstrated that the artificial neural networks enabled the correct identification of water samples, even if there were some gaps in the initial data. The procedure for determining the optimal number of neurons for synthesizing neural networks was proposed. Keywords: qualitative chemical analysis, identification, artificial neural network, linear discriminant analysis DOI: 10.3103/S0027131412060077

INTRODUCTION

networks. Artificial neural networks have received much more attention recently. Thanks to their adap tive structure and learning capability, they are success fully used to solve classification tasks (see, e.g., [5–9]). One of the tools needed to identify water quality is qualitative chemical analysis, especially the identifica tion and discrimination of water samples according to their composition, origin, characteristics, etc. The expo nential growth in the number of publications reviewed by ScienceDirect (http://www.sciencedirect.com/) and containing such word combination as “quality of water” in their main headings, and abstracts evidences that many more people have become interested in the problem of water quality (Fig. 1). In this connection, chemometric methods for identifying and estimating quality of water samples (principal component analy sis; factor, cluster, and discriminant analysis; artificial neural networks; etc.) are becoming increasingly sig nificant [10–20]. The work considers the application of neural net works for identifying the origin of the river (polluted by

The role played by the qualitative chemical analysis has become more important over the past two decades. This can be explained by the increasing demands in the identification of compositions of different com plex mixtures used in various fields: monitoring of the environmental condition; checking the authenticity of biomedical preparations; identifying and protecting food, beverages, and edible raw material; etc. [1]. Thus, our idea of what the qualitative chemical analy sis should include has also changed. According to [2– 4], the modern qualitative analysis allows finding and identifying analytes, as well as carrying out sample dis crimination. Considering all of the abovediscussed issues should result in a certain classification of the objects used in this analysis: upon detection, samples are divided into groups that either contain analyte in the concentration that exceeds the threshold limit or does not have it at all; upon identification, conclusions are drown either on the identity level between the ana lyte and the standard value or the whether the analyte belongs to a certain class of objects; and, upon dis crimination, all objects being analyzed are divided into groups of objects with similar characteristics. Therefore, the trend towards gaining an under standing of qualitative analysis as the classification of different objects based on their characteristics has become more definite. This often concerns the pro cessing of data obtained as a result of the chromato graphic analysis and various spectroscopic methods, as well as sensory systems, such as the electronic nose and electronic tongue. When processing these data, one cannot avoid applying modern chemometric methods, e.g., pattern recognition and classification algorithms, discriminant analysis, and artificial neural

1

the industrial wastes) and springwater samples of Kharkiv based on the concentrations of eight metals. The objects under study were chosen due to the changes in the chemical composition of their surface and ground waters that they undergo during the inten sive anthropogenic activities. The aims of the work are as follows: the investiga tion of how efficient the training neural networks are 1 The

identification of the origin of water samples consists of assigning them to a certain class that is known beforehand, i.e., it is the identification of water samples (cf. the following defini tion: “identification is assigning an analyte to a certain sub stance (standard) or a group of compounds” [4].

60

Number of sources

IDENTIFICATION OF WATER SAMPLES FROM DIFFERENT SPRINGS

61

11008 publications with word combination “quality of water” used in main 1000 headings and abstracts 800 600 400 200 1990

1995

2000 Year

2005

2010

Fig. 1. Data on publications on water quality that can be found in ScienceDirect (as on May 30, 2012).

for identifying water samples; checking the stability of different algorithms of the neural networks to the pres ence of gaps in the initial data about the water samples; and the formulation of advice about choosing the opti mal number of neurons for the synthesis of neural net works. The calculations were performed using the MATLAB 6.5 package [21, 22]. PROCESSED DATA The data array under study includes 22 riverwater samples and 24 springwater samples taken from the rivers and springs of Kharkiv in different seasons over 2008–2010. The ion concentrations of the following metals contained in the water samples were deter mined: copper, zinc, lead, cadmium, manganese, iron, cobalt, and nickel (Appendixes 1, 2). The number of water samples (500 mL in volume each) taken from every river and spring ranged from two to seven. The time of transfer and storage from the moment of sampling until they were analyzed was no more than 24 hours. The pH of the solution was adjusted by adding con centrated HNO3; the pH was equal to two. The samples were then evaporated to a volume of 20–22 mL, trans ferred to graduated flasks with volumes of 25 mL, filled by bidistilled water, and carefully mixed. The content of metal ions in the water samples under study was determined using atomic absorption spectroscopy [23–26] by an S115M1 spectrometer (SELMI, Ukraine) in propane–butane–air and acetylene–air flames. Calibrated solutions containing 0.1–1.0 mg/L metal ions were prepared from samples with the stan dard composition of the solution (the concentration of metal ions was equal to 1 g/L) by diluting initial aque ous solutions with bidistilled water [27]. The relative standard deviation of the determined concentrations did not exceed 0.01–0.02. Since the concentration of metal ions ranged from thousands to dozens of mg/L, the autoscaling trans MOSCOW UNIVERSITY CHEMISTRY BULLETIN

formation of the initial data was performed as follows before any classification algorithms were applied: xi – x norm xi = , i = 1, 2, …, N, std ( x ) where xnorm is the modified dimensionless concentra tion of the element in the ith water sample (the xnorm value has zero mean and unit variance); xi is the con centration of this element in the ith sample; x is the average concentration of this element in the samples; std(x) is the standard deviation of the concentration of this element in the samples; and N is the number of water samples. CLASSIFICATION OF WATER SAMPLES BY APPLYING TRAINING ALGORITHMS The water samples were identified using training algorithms of the neural networks (probabilistic neural network, dynamic network, cascade network, feedfor ward network, and recurrent neural network) and lin ear discriminant analysis. An artificial neural network is a set of neurons con nected to each other. The synthesis of a neural network includes two stages, i.e., choosing the network archi tecture (determining the number of layers, neurons, and types of activation functions) and choosing the way of training (choosing the weighting coefficients and the rules to correct them). For many neural net works, the training procedure is anticipated by initial ization of weight coefficients and biases. In this work, the Nguyen–Widrow algorithm of neurons initializa tion was used [28]. The LevenbergMarquardt algo rithm was used as training method for the cascade net work, feedforward network and dynamic network (the training of the recurrent neural network is based on the backpropagation learning rule [29, 30]). The training was completed when the value of mean squared error 0.01 achieved. Detailed data about the neural net works under study and the learning algorithms can be found in the publications [21, 31, 32]. The methods

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Table 1. Parameters of neural networks and values of minimal unreliability for identification of water samples Number of neurons for classification of river/springwater samples

Neural network

Activation functions for hidden/output layers

P, % for river/springwater samples

Cascade neural network

9/10

hyperbolic tangent/hyperbolic tangent

17/0

Feedforward neural network

9/11

hyperbolic tangent/linear

17/0

Recurrent neural network

11/12


17/17

Dynamic neural network

11/11


0/0

Probabilistic neural network

16/18

Gaussian/competitive layer

0/0

for supervised learning imply the presence of training and testing subsets. A training subset is a set of objects for which are known assigning to certain classes; this P, % 1 80 60

2

40 20 0 30

40

50

60

70

80 T, %

Fig. 2. Dependencies of classification error on the per centage of samples in training subset for the probabilistic neural network: 1. riverwater samples; 2. springwater samples.

P, % 1 60 2 40

subset is used to determine the optimal parameters of the algorithm. The testing subset is the set of objects for which are not known assigning to certain classes; this subset is used to checking the efficiency of the algorithm. The first stage of applying the supervised training algorithms includes the determination of the optimal size of the training subset. In order to develop the training subset, a probabilistic neural network was used, which is characterized by simple architecture, short training period, and the possible use of the obtained results for other types of neural networks. The probabilistic neural network demands the optimization of only one parameter, i.e., the degree of smoothing δ (the recommended value 0.1 [33]). Furthermore, the number of neurons in the hidden layer equals the num ber of samples in the training subset. The results of a qualitative chemical analysis can not be estimated using a metrological characteristic, such as uncertainty, which is common for quantitative analyses [34]. It has been suggested that unreliability should be used, rather than uncertainty [35, 36]; the high degree of reliability corresponds to the low num ber of false conclusions on its basis [37]. In this work, the unreliability of identification was calculated based on the percentage of water samples classified wrongly as follows: P = n/N × 100, %, where n is the number of the misclassified water sam ples in the testing subset; N is the total number of sam 2

20 0 8

9

10 11 12 Number of neurons

13

Fig. 3. Dependences of classification error on number of neurons for dynamic neural network: 1. riverwater sam ples, 2. springwater samples.

ples in the testing subset . Figure 2 demonstrates the dependencies of classifi cation error on the percentage of samples in the train ing subset (T, %) for the river and spring waters (T is the part of samples in the training subset from their total number). Thus, the size of the training subset used to train different types of neural networks was 75%. This is 2 It

is assumed that a properly trained neural network demon strates no errors in the classification of samples from the training sample.

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equal to 16 and 18 water samples taken from rivers and springs, respectively. The training and testing parame ters for the embodied neural networks and the mini mum classification errors of the water samples are given in Table 1. The optimal number of neurons in the hidden layer (the number of neurons in the output layer was taken as the one corresponding to the num ber of classes, i.e., the number of the rivers and springs under study) and the optimal combination of the acti vation functions for the hidden and output layers were determined. Using these parameters enabled correct network training and the satisfactory identification of the water samples from the testing subset (except the recurrent neural network). The optimal number of neurons is the number of neurons needed for the minimum unreliability of the classification or identification of the water samples under study. The model for determining the optimal number of neurons, i.e., the dependence of the frac tion of the misclassified water samples on the number of neurons in the hidden layer for dynamic neural net work is given in Fig. 3. Using the linear discriminant analysis [38] to iden tify the water samples resulted in an unacceptably high P values (67 and 33% for river and springwater sam ples, respectively). Therefore, the probabilistic and dynamic neural networks are most appropriate for identifying water samples based on data about the microelement content. STABILITY OF ALGORITHMS FOR CLASSIFYING DATA WITH GAPS Four riverwater samples were used to estimate the stability of algorithms for classification. The latter were analyzed in 2011, nickel ion concentrations were not determined (Appendix 3). To train the neural net works, 22 water samples (Appendix 2) and the activa tion functions given in Table 1 were used. The unknown concentrations of nickel ions were replaced by the average value of their concentrations obtained from samples in training subset (0.0144 mg/L). The characteristics of identifying riverwater samples based on data with gaps include the minimum unre liability values and the optimal number of hidden neu rons (Table 2). The worst results were obtained using linear discriminant analysis; reliable identification is achieved by the dynamic neural network. Thus, using riverwater samples as an example, we demonstrated that artificial neural networks can enable the correct identification of water samples, even if there are some gaps in the characteristics of the training subset. ADVICE ON CHOOSING THE NUMBER OF NEURONS When analyzing the optimal structure of the neural networks (Table 1, 2), it can be concluded that the optimal number of neurons obtained during the clas MOSCOW UNIVERSITY CHEMISTRY BULLETIN

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Table 2. Results of identifying riverwater samples after removing some concentrations of metal ions Number of neurons

P, %

Cascade neural network

14

25

Feedforward neural network

15

25

Recurrent neural network

15

25

Dynamic neural network

14

0

Probabilistic neural network

22

25

Linear discriminant analysis

–

75

Algorithm

sification of objects based on the data from the multi variate experiment can be calculated using the follow ing formula: n training n classes n neurons = + n properties ± , n testing 2 where ntraining is the number of samples in the training subset, ntesting is the number of samples in the testing subset, nproperties is the number of characteristics, and nclasses is the number of classes. Let us note that the method suggested for calculat ing the optimal number of neurons is heuristic and should be controlled when analyzing new experimen tal data. Therefore, we demonstrated that neural networks are efficient for identifying water samples based on the concentrations of eight metal ions, even if the data on concentrations of one metal ion are absent. The dynamic and probabilistic neural networks are most efficient for solving such problems. The results dis cussed in this work allowed the following rules to be proposed for simplifying the calculations of optimal parameters of the neural networks in order to make it easier to classify multivariate experimental data arrays: (i) two activation functions (a linear and hyperbolic tangent) are sufficient to implement the neural net works (all except the probabilistic neural network); (ii) the optimal number of neurons lies in a range that can only be calculated based on the initial data on the task (the number of samples in the training and testing subsets, number of characteristics, and number of classes); (iii) the optimal size of the testing subset deter mined using the probabilistic neural network can be used to train different types of neural networks. The results obtained during our investigation can be of use for detecting the falsification of mineral water or determining whether its actual origin corresponds to that claimed.

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PUSHKAROVA et al. APPENDIX 1

Metal ion concentrations in springwater samples (mg/L, 10–1) Metal Spring Sarzhin Yar, Khar’kovskaya–1 (2010) Khar’kovskaya–2 (2010)

Panteleymonovskaya Church (2010)

Edible Plant of Acids (2010)

ul. Uborevicha (2009)

Yunost’ Park (2009)

Zn

Cu

Mn

Fe

Cd

Pb

Co

Ni

0.090 0.130 0.120 0.120 0.070 0.050 0.070 0.080 0.190 0.080 0.080 0.080 0.100 0.050 0.060 0.100 0.140 0.230 0.230 0.140 0.180 0.140 0.340 0.150

0.100 0.080 0.080 0.050 0.050 0.040 0.040 0.050 0.180 0.750 0.230 0.190 0.930 0.070 0.080 0.400 0.150 0.220 0.050 0.040 0.050 0.020 0.040 0.030

0.300 0.240 0.260 0.200 0.180 0.130 0.080 0.190 0.080 0.610 0.700 0.220 0.180 0.410 0.210 0.140 0.240 0.130 0.110 0.020 0.030 0.040 0.150 0.030

0.480 0.720 0.500 1.020 0.570 0.590 0.330 0.570 0.640 0.760 1.200 0.550 0.370 0.280 0.280 0.260 0.780 0.430 0.080 0.150 0.150 0.100 0.520 0.290

0.024 0.024 0.018 0.019 0.012 0.016 0.018 0.021 0.029 0.024 0.022 0.019 0.025 0.019 0.026 0.012 0.026 0.024 0.083 0.053 0.049 0.052 0.123 0.086

0.250 0.280 0.250 0.230 0.230 0.190 0.160 0.230 0.350 0.290 0.280 0.350 0.250 0.000 0.000 0.160 0.160 0.130 0.110 0.150 0.270 0.170 0.210 0.070

0.084 0.063 0.078 0.084 0.069 0.069 0.103 0.063 0.078 0.056 0.063 0.094 0.078 0.078 0.063 0.078 0.078 0.100 0.133 0.125 0.063 0.000 0.125 0.125

0.080 0.090 0.090 0.110 0.120 0.110 0.120 0.120 0.200 0.200 0.200 0.200 0.200 0.090 0.100 0.100 0.140 0.140 0.120 0.140 0.140 0.110 0.380 0.060 APPENDIX 2

Metal ion concentrations in riverwater samples (mg/L) Metal River Nemyshlya (2008)

Kharkiv (2009)

Lopan (2009)

Udy (2010)

Zn

Cu

Mn

Fe

Cd

Pb

Co

Ni

0.0150 0.0130 0.0080 0.0120 0.0120 0.0050 0.1040 0.0150 0.0070 0.0100 0.0470 0.1090 0.0650 0.0100 0.0110 0.0120 0.0170 0.0050 0.0300 0.0090 0.0080 0.0110

0.0055 0.0045 0.0073 0.0073 0.0078 0.0034 0.0103 0.0043 0.0052 0.0052 0.0043 0.0069 0.0069 0.0078 0.0087 0.0056 0.0056 0.0032 0.0286 0.0063 0.0110 0.0080

0.0230 0.0410 0.0170 0.0130 0.4330 0.0020 0.0070 0.0030 0.0030 0.0030 0.0050 0.0030 0.1330 0.0060 0.0400 0.2790 0.0030 0.0000 0.0150 0.0230 0.0130 0.0280

0.1000 0.1200 0.0280 0.0380 0.0190 0.0220 0.0190 0.0170 0.0160 0.0170 0.0110 0.0170 0.0220 0.0170 0.0230 0.0690 0.1460 0.0110 0.0970 0.0460 0.0430 0.0460

0.0021 0.0015 0.0024 0.0022 0.0022 0.0017 0.0019 0.0017 0.0039 0.0030 0.0032 0.0052 0.0060 0.0030 0.0023 0.0000 0.0000 0.0000 0.0090 0.0000 0.0021 0.0015

0.0350 0.0440 0.0350 0.0470 0.0460 0.0410 0.0410 0.0340 0.0310 0.0230 0.0310 0.0430 0.0380 0.0280 0.0380 0.0000 0.0000 0.0000 0.2000 0.0380 0.0100 0.0250

0.0084 0.0088 0.0094 0.0063 0.0140 0.0105 0.0112 0.0090 0.0085 0.0097 0.0070 0.0068 0.0078 0.0075 0.0107 0.0125 0.0000 0.0071 0.0554 0.0089 0.0047 0.0078

0.0200 0.0180 0.0140 0.0130 0.0200 0.0160 0.0120 0.0080 0.0100 0.0070 0.0120 0.0140 0.0130 0.0190 0.0160 0.0110 0.0040 0.0040 0.0300 0.0390 0.0070 0.0090


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65 APPENDIX 3

Metal ion concentrations in riverwater samples for which the concentration of nickel ions was not determined (mg/L) (2011) Metal

Zn

Cu

Mn

Fe

Cd

Pb

Co

Nemyshlya

0.0520

0.0330

0.0960

0.2130

0.0035

0.0250

0.0050

Kharkiv

0.0340

0.0300

0.0660

0.1800

0.0035

0.0160

0.0070

Lopan

0.0360

0.0340

0.0370

0.1600

0.0035

0.0240

0.0080

Udy

0.0420

0.0330

0.0470

0.0690

0.0031

0.0090

0.0030

River

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