Anal. Chem. 1997, 69, 856-862
Neural Network Classification and Quantification of Organic Vapors Based on Fluorescence Data from a Fiber-Optic Sensor Array Jon M. Sutter and Peter C. Jurs*
Department of Chemistry, The Pennsylvania State University, 152 Davey Laboratory, University Park, Pennsylvania 16802
Computational neural networks have been developed to classify and quantify nine organic vapors. The neural network analyses used data that consisted of the change in fluorescence from a sensor array that consisted of 19 fiber optics with immobilized dye in polymer matrices. Plots of change in fluorescence intensity versus time were measured as pulses of analyte were presented to the sensor array. Descriptors were calculated from the intensity vs time plots, and they were used to build neural network models that accurately classified and quantified each of the nine analytes. Most of the data were used to train the neural networks (training set members), some were used to assist termination of training (cross-validation set members), and some were used to validate the models (prediction set members). Classification rates approaching 100% were achieved for the training set data, and 90% of the members in the prediction set were correctly classified. In addition, 97% of the prediction set observations were assigned a correct relative concentration. It is well-known that animals have very effective olfactory systems that can detect low concentrations of odorants, even down to parts per trillion in some cases. The mammalian nose classifies odorants using a complex series of biological processes of which little is known. However, the nose is known to utilize a large array of olfactory receptor cells that act as both neurons and transducers. The olfactory receptor cells interact with the odorant and transmit a signal to the mitral cells located in the olfactory bulb. These cells then transmit a signal to the neurons in the frontal lobe or the limbic system where the information is processed and the odorant is classified or a response is triggered. The olfactory receptors are not highly selective. In other words, there is not a different receptor that responds to and classifies every unique odor presented to the mammalian nose. It is the spatial and temporal pattern generated by a large number of similar receptors that signals the presence of an odor.1 Recently there has been interest in designing vapor-sensing instruments that mimic the effectiveness of the mammalian nose.2-4 The concept of an array of sensors is common to most of the designs to date; however, the designs depend on different types of sensors. Researchers have investigated electrochemi(1) Kauer, J. S. Trends Neurosci.. 1991, 14, 79-85. (2) Newman, A. R. Anal. Chem. 1991, 63, 585A-588A. (3) Lundstro¨m, I.; Erlandsson, R.; Frykman, U.; Hedborg, E.; Spetz, A.; Sundgren, H.; Welin, S.; Winquist, F. Nature 1991, 352, 47-50. (4) Dickinson, T. A.; White, J.; Kauer, J.; Walt, D. R. Nature 1996, 382, 697.
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cal,5,6 conductive polymer,7,8 piezoelectric,9,10 and surface acoustic wave sensors.11-15 Work has also appeared dealing with the selection of subsets of sensors with SAW devices.14,15 The sensor array used in this study consists of an array of optical sensors. Temporal information is used in the analysis process. The use of both optical sensors and temporal information is novel to the realm of sensor arrays meant to act as artificial noses. Optical sensors could prove to be beneficial for several reasons: they can be placed on fiber optics up to 2 km long, they are rugged, and they are free of electrical interferences.16 A temporal response seems to be important in the mammalian nose, since slight changes in odors are detected by spatial and temporal patterns of the olfactory receptor cells. Data collected over time increase the amount of information gained from the interaction of the odorant with the sensors and could consequently increase the chances of classifying the odorant correctly. In a previous study,17 an array of fiber-optic sensors was used to produce data which were then submitted to a neural network analysis to classify and quantify nine odorants. The data were a result of a change in the wavelength shift of maximum absorbance of a solvatochromic dye (Nile Red) when an odorant interacted with the microenvironment of the dye. The response of the fiberoptic sensors is similar to the response of the olfactory receptor cells in the mammalian nose. The neural network analysis of the odorants is akin to the mitral cells of the mammalian nose which process the responses from the receptor cells. In that work, a single, very large, feed-forward, three-layer neural network was used. The training was done using the backpropagation method to classify each analyte as one of the nine possibilities as well as to predict its concentration. The networks (5) Stetter, J. R.; Jurs, P. C.; Rose, S. L. Anal. Chem. 1986, 58, 860-866. (6) Singh, S.; Evor, H. L.; Gardner, J. W. Sens. Actuators B 1996, 30, 185190. (7) Freund, M. S.; Lewis, N. S. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 26522656. (8) Hodgins, D. Sens. Actuators B 1995, 27, 255-258. (9) Carey, W. P.; Beebe, K. R.; Kowalski, B. R. Anal. Chem. 1987, 59, 15291534. (10) Freeman, N. J.; May, I. P.; Weir, D. J. J. Chem. Soc., Faraday Trans. 1994, 90, 751-754. (11) Rose-Pehrsson, S. L.; Grate, J. W.; Ballantine, D. S., Jr.; Jurs, P. C. Anal. Chem. 1988, 60, 2801-2811. (12) Grate, J. W.; Rose-Pehrsson, S. L.; Venezky, D. L.; Klusty, M.; Wohltjen, H. Anal. Chem. 1993, 65, 1868-1881. (13) Grate, J. W.; Klusty, M. Anal. Chem. 1991, 63, 1719-1727. (14) Grate, J. W.; Abraham, M. H. Sens. Actuators 1991, 3, 85-111. (15) Zellers, E. T.; Batterman, S. A.; Han, M.; Patrash, S. J. Anal. Chem. 1995, 67, 1092-1106. (16) Seitz, W. R. CRC Crit. Rev. Anal. Chem. 1988, 19, 135-173. (17) White, J.; Kauer, J. S.; Dickinson, T. A.; Walt, D. R. Anal. Chem. 1996, 68, 2191-2202. S0003-2700(96)00982-1 CCC: $14.00
© 1997 American Chemical Society
were trained to a certain root-mean-square (rms) error or for 50 000 iterations, either of which can lead to overtraining. The most successful network used had a 100-12-12 architecture containing 1368 adjustable parameters. This network attained 100% classification of the nine analyte identities during training but 83% for a test set. The input data to the neural network were 10 averages of time slices taken from the fluorescence data. No attempt was made to determine whether subsets of the input data would be sufficient; that is, no feature selection was done. In the current study, the same change in fluorescence intensity data were used. However, each fluorescence signature was represented by a set of calculated descriptors designed to highlight the most important features of the data. A separate neural network was created for the classification of each of the nine analytes, and one additional neural network model was created to assign a relative concentration. The separate models were used in an attempt to reduce the number of adjustable parameters being employed and consequently to reduce the probability of chance effects. A cross-validation set was used to prevent possible overtraining of the networks. In addition, the use of one neural network for identification of each analyte allows analysis and interpretation of the results obtained. Examples include determination of which sensors are most involved in the identification of each analyte and which types of descriptors are most capable of capturing important information and, ultimately, providing information that could be used for design of later fiberoptic sensor arrays. It was believed that these techniques would improve the classification and quantification of the nine organic vapors. These points are reinforced in the remainder of this report. EXPERIMENTAL SECTION Nine low molecular weight organic vapors (amyl alcohol, amyl acetate, butyl alcohol, butyl acetate, pentyl alcohol, pentyl acetate, benzene, toluene, xylene) were presented separately to the sensor array. The sensor array consisted of a bundle of fiber-optic sensors with a dye immobilized in a polymer mixture on one end. The 19 different polymers used for the fiber-optic sensors are shown in Table 1. The dye was Nile Red, which is known to undergo a change in fluorescence when its environment changes. When the odorant was pulsed onto the polymer and dye mixture, the microenvironment was altered and the fluorescence of the dye changed. The result was a set of 19 plots (one for each fiber) of the change in fluorescence intensity vs time (the intensity was recorded every 133 ms for a total of 64 time slices) for each analyte introduced to the instrument. A detailed explanation of the instrument used, data collection, polymers used, sensor fabrication, and chemical information is given in ref 17. The data set consisted of nine trials for each of the nine analytes at three concentrations and a blank (air) for each trial at each concentration, yielding a total of 270 runs. Each analyte was presented separately to the sensor array at high concentration (saturated vapor), medium concentration (1:1 dilution with air), and low concentration (2:1 dilution with air). The blank was a run of air with no odorant. Each time an odorant was presented to the sensor array, a plot of the change in fluorescence intensity vs time was recorded for the 19 fibers. It was necessary to analyze the responses and pick the fibers that appeared to have the most consistent behavior between trials. Three tests were performed to select the fibers that exhibited the most consistent behavior. First, the plots of intensity change vs
Table 1. Polymers Used for Each Fiber-Optic Sensor fiber
polymera
no. of dips
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Dow (in 2 mL of toluene) PS802 Dow (in 2 mL of toluene) PS802 PC (in 2 mL of chloroform) PS802/PS078.9 (77:23) PC (in 2 mL of chloroform) PS802/PS078.9 (77:23) PEM (in 0.5 mL of chloroform) PS802/MMA (90:10) PEM (in 0.5 mL of chloroform) PS802/MMA (90:10) PABS (in 1 mL of chloroform) PS802/HEMA (90:10) PABS (in 1 mL of chloroform) PS802/HEMA (90:10) PSAN (in 1 mL of chloroform) PS851 PSAN (in 1 mL of chloroform)
3 1 5 2 3 1 5 2 3 1 5 2 3 1 5 2 3 2 5
a Key: Dow, dimethylsiloxane dispersion coating; PS802, (8085%)dimethyl(15-20%)(acryloxypropyl)methylsiloxane copolymer; PC, polycaprolactone; PS078.9, diethoxylmethylsilyl-modified polybutadiene in toluene; PEM, poly(methyl methacrylate); PABS, poly(acrylonitrilebutadiene-styrene); PSAN, poly(styrene-acrylonitrile 75:25); PS851, (97-98%)dimethyl(2-3%)(methacryloxypropyl)methylsiloxane copolymer.
time of consecutive trials for the same analyte at the same concentration were visually inspected to see if the shape of the curve was consistent throughout the lifetime of the fiber. Second, plots for each concentration of each analyte were inspected at trial three to see if the intensity decreased with decreasing concentration. Trial three was used since this was approximately the midlife of the fiber, and any settling-in effects should be complete by this time. The third test required the maximum intensity of the saturated concentration of trial nine, the medium concentration of trial six, and the low concentration of trial two to decrease. The intensity plots seemed to decrease slightly with the lifetime of the fiber. Therefore, if this order was maintained for these particular trials, then the fiber should have given consistent results throughout data collection. These three tests were performed for all analytes, and the 10 fibers that passed the most tests were used for constructing the neural network models. Data from 10 fibers (numbers 1, 4, 5, 6, 7, 8, 10, 12, 15, and 16) were selected for use. Eight of these were also used in the previous work.17 The next step of the study was to create descriptors that numerically encode the important characteristics of the fluorescence intensity change vs time plots. Two types of models were created, one to classify the odorant and one to quantify the odorant. The fluorescence plots were normalized for the classification models, and raw data were used for the quantification model. The descriptors, listed in Table 2, were simple values that were derived from the change in fluorescence plots of the 10 fibers selected. The data were smoothed using a simplified leastsquares method,18,19 the descriptors were recalculated, and all corresponding pairs (smoothed and raw data descriptors) were pairwise correlated (R > 0.95) except the steepest positive slope and the steepest negative slope. The slopes of the smoothed data were added to the total descriptor pool. A total of 170 descriptors were available for each observation. (18) Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627-1639. (19) Steinier, J.; Termonia, Y.; Deltour, J. Anal. Chem. 1972, 44, 1906-1909.
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Table 2. Descriptors Derived from the Fluorescence Data That Were Used in This Study descriptor
explanation
AVER STSL SNSL MPOS MNEG ANEG APOS TSPS TSNS AVE1 AVE2 AVE3 AVE4 AVE5 AVE6 S. STSL S. SNSL
average change in intensity for all 64 time slices steepest positive slope of the fluorescence plots steepest negative slope of the fluorescence plots most positive change in fluorescence most negative change in fluorescence average of all the negative changes in fluorescence values average of all the positive changes in fluorescence values time slice of the steepest positive slope time slice of the steepest negative slope average change in fluorescence intensities of time slices 3-12 average change in fluorescence intensities of time slices 13-22 average change in fluorescence intensities of time slices 23-32 average change in fluorescence intensities of time slices 33-42 average change in fluorescence intensities of time slices 43-52 average change in fluorescence intensities of time slices 53-62 steepest postitve slope of the smoothed fluorescence intensities steepest negative slope of the smoothed fluorescence intensities
that corresponded to the minimum rms error of the crossvalidation set members.23 Also to avoid overtraining, the ratio of the number of observations in the training set to the total number of weights and biases was kept above 2.0.23 This is necessary to keep the probability of getting good results due to chance at a low level. For a detailed explanation of the type of neural network used in this study see refs 19 and 20.
After the descriptor pool was created, all the redundant information was removed. If a pair of descriptors were highly correlated, one of them was removed, and if a descriptor had the same or similar value for all trials, it was removed. The 270 trials were split into a 210-member training set, a 30-member crossvalidation set, and a 30-member prediction set. The training and cross-validation sets were used for descriptor reduction and model development, and the prediction set was used for model validation. The members of the prediction set and cross-validation set were selected semirandomly. It was important to have each odorant represented in the cross-validation and prediction sets for accurate model development and validation. The selection should be random, however, to avoid biasing the results. Therefore, each analyte and blank for each concentration was guaranteed to be in both the prediction set and cross-validation set, but the trial number was randomly selected. A separate model was trained to classify each analyte (a total of nine models), and one model was trained to quantify the analytes. Small subsets of descriptors were selected using the results of multiple linear regression models as the selection criterion. The descriptor subset corresponding to the model that yielded the smallest rms error was then submitted to a neural network analysis. Several different descriptor subset sizes and neural network architectures were investigated for each analyte. The neural network models were evaluated by calculating the rms error of the training set members and the rms error of the crossvalidation set members. After the best neural network model for each analyte was selected, it was validated using the rms error of the prediction set. The neural network architecture used in this study was a fully connected, feed-forward, three-layer system20 (Figure 1). The rms error of the training set members was minimized by adjusting the weights and biases using a quasi-Newton algorithm.21,22 To avoid overtraining, the rms error of the cross-validation set members was calculated periodically throughout training, and when the cross-validation set error began to rise, training was terminated and prediction was done using the weights and biases
RESULTS AND DISCUSSION Classification of Analytes. The first step of the study was to create nine neural network models to classify each of the nine odorants. The models had to be able to predict whether the odorant of interest was present and to predict the absence of the other eight odorants in order to be successful. As stated earlier, the descriptors were simple numerical representations of the normalized fluorescence intensity change plots. Several different models with different descriptor subset sizes were evaluated for each analyte. Small subsets of descriptors were chosen from the overall descriptor pool using multiple linear regression for the training set and cross-validation set members. Several thousand subsets were investigated using simulated annealing24 or genetic algorithm25 search routines that selected subsets based on the rms error of regression. The descriptor subsets that yielded the best regression models were then submitted to a neural network analysis to improve the overall prediction of the models. The neural network model that gave the smallest rms errors for the training set and cross-validation set members and had the smallest number of adjustable parameters was used for further analysis. After selection of the descriptor subset, the number of neurons in the hidden layer was adjusted, which resulted in many different neural network architectures that were appraised on the basis of the rms errors of the training set and cross-validation set members. The final step was model validation, which was done by calculating the rms error of the prediction set members. The final nine neural network models performed their classifications based on 6-12 descriptors drawn from the overall pool of 170 descriptors. A total of 87 descriptors were used (of which
(20) Xu, L.; Ball, J. W.; Dixon, S. L.; Jurs, P. C. Environ. Toxicol. Chem. 1994, 13, 841-851. (21) Wessel, M. D.; Jurs, P. C. Anal. Chem. 1994, 66, 2480-2487. (22) Sutter, J. M.; Dixon, S. L.; Jurs, P. C. J. Chem. Inf. Comput. Sci. 1995, 35, 77-84.
(23) Livingstone, D. J.; Manallack, P. T. J. Med. Chem. 1993, 36, 1295-1297. (24) Sutter, J. M.; Jurs, P. C. In Data Handling in Science and Technology (Vol 15). Adaption of Simulated Annealing to Chemical Optimization Problems; Kalivas, J. H., Ed.; Elsevier: Amsterdam, 1995; Chapter 5. (25) Luke, B. T. J. Chem. Inf. Comput. Sci. 1994, 34, 1279-1287.
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Figure 1. Typical computational neural network architecture. Table 3. Descriptors Used for Classifying and Quantifying all Nine Analytesa 1 STSL SNSL MPOS MNEG ANEG APOS TSNS AVE1 AVE2 AVE3 AVE4 AVE5 AVE6 S. STSL S. SNSL AVER
t Q p p, x
4
5
6
p, al, pl, Q
7
8
10
b
p, pl
b
p, x t
x
b, be
al
12
15
16
t p a x al, be, Q al
t a, p, t, x
p
p, pl
b al pl, be
b, Q pl
pl a
b p p
al
al, bl Q
t a
bl
bl al, bl, pl be, x b t
t a, be
Q
pl
t
Q
b b, be x t, x al
t
bl al
Q a a, pl, x bl, x
b t pl
al
bl pl Q
b, pl
a The boxes that contain the letter a represent the presence of that descriptor (rows of table) using that fiber number (columns of table) in the neural network model for amyl acetate (e.g., descriptor ANEG using fiber 4). b, p, al, bl, pl, be, t, and x represent butyl acetate, pentyl acetate, amyl alcohol, butyl alcohol, pentyl alcohol, benzene, toluene, and xylene, respectively. Q represents a descriptor from the quantifying neural network model.
64 were unique) for the input layers of the nine neural network models that classified the nine analytes. Table 3 identifies all the descriptors used to classify each of the nine different analytes, where the letter codes identify which descriptors were used in which neural network. For example, the neural network for classifiying butyl acetate uses 11 descriptors, so there are 11 b’s in Table 3. Of the 17 descriptors calculated for the 10 fibers, 15 were used by at least one of the nine models. The number of entries in each row of Table 3 shows how many times that descriptor was used. The most often used descriptor was AVE4, with 15 entries across seven different fibers. The number of entries in each column of Table 3 shows how many times each fiber was used. The most often used fiber was fiber 8, with 16 entries across 10 different descriptors. Overall, the nine network architectures ranged from 6 to 12 descriptors in the input layer, four to eight neurons in the hidden
layer, and one neuron in the output layer. The exact architecture of each neural network is shown in the final column of Table 4. The number of adjustable parameters in the networks range from a low of 37 for the 7-4-1 network for butyl alcohol to a high of 105 for the 11-8-1 network for pentyl acetate. Since there are 210 observations being used for training, the ratio of observations to adjustable parameters is well below the level where chance effects are likely to be important. Each network was trained so that a value of 0.05 meant the odorant was absent and a value of 0.95 meant the odorant was present. Any value greater than 0.50 was considered a positive test for the odorant corresponding to that neural network model, and any value less than 0.50 was considered to be one of the other eight odorants. If all nine values from the different neural networks were below 0.50, the analyte was considered to be air. Analytical Chemistry, Vol. 69, No. 5, March 1, 1997
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Table 4. Results of the Nine Classification Neural Networks training set
cross-validation set
prediction set
odorant
false +
false -
false +
false -
false +
false -
CNN architecture
amyl acetate butyl acetate pentyl acetate amyl alcohol butyl alcohol pentyl alcohol benzene toluene xylene
0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 0 0
0 2 0 0 0 1 0 0 0
0 0 0 0 1 0 0 0 1
7-5-1 11-5-1 11-8-1 11-7-1 7-4-1 12-6-1 6-5-1 12-7-1 10-6-1
total wrong
0
1
1
1
3
2
all 9
0
1
0
1
1
2
Table 4 shows the classification results achieved by the nine individual neural networks. A false positive classification occurred when an analyte was selected that was not the odorant of interest, and a false negative occurred when the odorant of interest was not selected. As can be seen in Table 4, a few false positives and false negatives were generated. The training set yielded zero false positives and one false negative out of a total of 210 members. The cross-validation set yielded one false positive and one false negative. The prediction set yielded three false positives and two false negatives. When all nine neural network results were considered simultaneously (see last row of Table 4), however, several of the false positives disappeared because the value closest to 0.95 was selected as the odorant when more than one value from different neural network models was greater than 0.50. The final result was zero, zero, and one false positive for the training set, cross-validation set, and prediction set respectively. There was no change in the number of false negatives when all nine models were considered simultaneously. The nine neural networks successfully predicted the presence of the corresponding odorant and the absence of the other eight in nearly all situations (99.5% of the training set, 96.7% of the cross-validation set, and 90% of the prediction set members were correctly classified). The successful classification of the prediction set members suggests that these neural network models have generalized the information given and could be used to predict a future unknown compound given that it was one of the nine analytes used to build the models. The most important information in the fluorescence intensity vs time data should be obtained during and perhaps immediately following the pulse of odorant. The descriptors should provide relevant information for each analyte so that the classification can be done effectively. Data that are gathered in the region of the pulse correspond to the physical interaction between the odorant and the polymer matrix, which is when the fluorescence of the dye is altered. Any distinguishing information from the various analytes should occur in this region. It is also possible that information immediately following the pulse could provide important information; therefore, it is not surprising that many (25 of the 87 or 28.7%) descriptors are AVE3 and AVE4 for several different fibers. It appears that the optimization routines are selecting descriptors that contain the appropriate information for classification and that chance effects are not present. Figure 2 shows that these regions are at the pulse and immediately following the pulse of odorant. The intensity plot of the first trial of amyl acetate shown in Figure 2 is the fluorescence intensity change vs time for fiber 8. The horizontal lines in Figure 2 860 Analytical Chemistry, Vol. 69, No. 5, March 1, 1997
Figure 2. Change in fluorescent intensity vs time of the first trial of amyl acetate for fiber 8. The time key at the bottom of the plot represents the time frames of the labeled occurrences. The crossed diagonal lines of the time key represents a region in which the pulse of the odorant and the AVE3 descriptor overlap.
represent the corresponding time slices of each of the labeled events (e.g., the odorant is pulsed from approximately time slice 12 to time slice 28). The descriptor matrix shown in Table 3 also reveals that fibers 8, 4, and 1 are important for classifying the nine analytes. It can be seen in Figure 3 that fibers eight, four, and one contain information that can be used together to separate (or classify) the nine analytes. It is important to realize that no one sensor effectively classifies all nine analytes. It is the combination of several important features from several sensors that provides a signature for each particular odorant. It is also important to remember that the neural networks only separate one analyte from the others; for example, amyl acetate is either predicted to be present or absent. The previous study of these data17 used one neural network to classify and quantitate the nine odorants. It used as inputs 10 average intensity values for time slices across the fluorescence intensity plot from 10 of the 19 fibers, so each observation was represented by 100 values. The hidden layer of the neural network had 12 units, and the output layer had 12 units (9 for the 9 analytes presence or absence and three for relative concentra-
Figure 3. Change in fluorescent intensity vs time plots of all nine organic analytes for (a) trial 1 and fiber 8, (b) trial 6 and fiber 4, and (c) trial 3 and fiber 1.
Figure 4. Change in fluorescent intensity vs time plots of all nine organic analytes for trial 4 and fiber 12 at (a) high, (b) medium, and (c) low concentration.
tion). This 100-12-12 neural network had 1368 adjustable parameters in all (far more than the number of training set
members, leading to the possiblity of results due to chance). Between 70 and 83% of the observations were correctly classified, Analytical Chemistry, Vol. 69, No. 5, March 1, 1997
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and 97-100% were assigned a correct concentration for the 30member prediction set. Quantification of Analytes. The second step of the study was to develop a neural network model to predict the relative concentrations of the classified analytes. The same pool of 170 descriptors was used for this portion of the study, but the fluorescence plots had not been normalized prior to descriptor calculation. Regression analysis was used to select several different descriptor subsets of varying sizes. The dependent variable was set to 0.05, 0.50, and 0.95 for the low, medium, and high concentration analytes, respectively. The best descriptor subsets were then submitted to a neural network analysis to improve the overall quantification. The compounds that were classified as air were not included in the quantification analysis. The best set of descriptors chosen for assigning relative concentrations was the set of nine designated by the letter Q in Table 3. Of the nine descriptors, one comes from fiber 1, three from fiber 4, three from fiber 12, and two from fiber 15. The descriptor AVER was not used in any of the classification networks but was used twice in the quantification network. It is apparent that the fibers chosen are not highly selective for the nine different analytes, but rather have a similar response for each analyte with a different intensity for each concentration. Figure 4 contains the intensity plots from fiber 12 for all nine analytes at the three concentrations for the fourth trial. The different analytes have similar shapes and the intensity changes occur because of changes in concentration. This is exactly what one would expect to be the best situation for quantification. Evidence shows that indeed the relative concentration of these nine analytes can be successfully predicted. This 9-3-1 neural network (34 adjustable parameters) correctly assigned relative concentrations for 98.4 (three wrong), 100, and 97% (one wrong) of the training set, crossvalidation set, and prediction set members, respectively. This success rate demonstrates conclusively that there is adequate information contained in the fluorescence intensity plots to determine the relative concentrations of these nine odorants.
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It is important to remember that the odorants have already been classified at this point, and therefore, only the intensity differences for the three concentrations are important. As Figure 4 shows, the response of fiber 12 is nonlinear, but this does not pose a problem for neural network analysis, which is a nonlinear approach to modeling. CONCLUSIONS This study suggests that the time-dependent fluorescence intensity data from the sensor array are sufficiently diverse to provide a signature for each of the nine analytes. Each of the nine three-layer, feed-forward neural networks mapped the signature of the odorant to an accurate classification. The pool of descriptors also contains information that is not highly selective for the nine analytes but which is capable of providing accurate quantitative information. This work shows that an array of fiberoptic sensors effectively generates discriminatory information for these analytes, since 99.5, 96.7, and 90% were correctly classified and 98.4, 100, and 97% were correctly quantified among the training set, cross-validation set, and prediction set members, respectively. Future work will include using more sophisticated descriptors to represent the fluorescent intensity change plots, investigating a larger and more diverse set of organic vapors, and using other types of neural networks that may be more suitable for this type of pattern recognition. ACKNOWLEDGMENT The authors thank Joel White, John Kauer, David Walt, and Todd Dickinson for collecting the data and for helpful discussions concerning the data. This project was funded by the Office of Naval Research. Received for review September 24, 1996. December 20, 1996.X
Accepted
AC960982J X
Abstract published in Advance ACS Abstracts, February 1, 1997.
