2nd NOSE II Workshop Linköping, 18 - 21 May 2003 Signal processing methods for drift compensation Ricardo Gutierrez-Osuna Department of Computer Science Texas A&M University Outline Sources of "drift" Compensation approaches Univariate methods Multivariate methods Discussion This material is based upon work supported by the National Science Foundation under CAREER Grant No. 9984426 / 0229598 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 2 - Texas A&M University What is drift? "A gradual change in any quantitative characteristic that is supposed to remain constant" [Holmberg and Artursson, 2003], and references therein 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 3 - Texas A&M University Sources of "drift" True drift • Aging • Poisoning (reorganization of sensing layer) (irreversible binding) Experimental noise • • • • • • Short-term drift (warm-up, thermal trends) Memory effects (hysteresis, sampling sequence) Environmental (pressure, temp., seasonal) Odor delivery (flow rate, outgass, condensation) Matrix effects (background, humidity) Sample degradation (oxidation, decarbonation) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 4 - Texas A&M University Approaches for drift compensation Drift-free sensors • Duh! Reference sensors • Differential or ratiometric measurements [Choi et al., 1985] Excitation • Temperature modulation [Roth et al., 1996] Frequent re-calibration • Unavoidable Careful experimental design • Avoid systematic errors Feature extraction • Transient response analysis [Wilson and DeWeerth, 1995] Signal processing • The focus of this tutorial 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 5 - Texas A&M University Signal processing for drift compensation Univariate • Compensation applied to each sensor independently • • • • Frequency analysis Baseline manipulation Differential measurements (w/ calibrant) Multiplicative correction (w/ calibrant) Multivariate • Compensation applied to the response across sensors • • • • Adaptive clustering System identification Calibration transfer (w/ calibrant) Orthogonal signal correction and deflation (w/ calibrant) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 6 - Texas A&M University 2nd NOSE II Workshop Linköping, 18 - 21 May 2003 Univariate Techniques Frequency analysis Drift, noise and odor information occur at different time scales [Artursson et al., 2000] • Noise = high frequencies • Drift = low frequencies • Perform separation in the frequency domain • Filter banks [Davide et al., 1996] • Discrete Wavelet Transform • Drawbacks • Requires long-term time series to be collected • Time series has "gaps“, variable sampling rates 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 8 - Texas A&M University Baseline manipulation (1) Basics • The simplest form of drift compensation • “Remove" the sensor response in the recovery cycle prior to sample delivery • Also used for pre-processing [Gardner and Bartlett, 1999] • A local technique, processes one "sniff" at a time 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 9 - Texas A&M University Baseline manipulation (2) Differential • Corrects additive δA or baseline drift xˆ s (t) = y s (t) - y s (0) = (x s (t) + δ A ) − (x s (0) + δ A ) = x s (t) − x s (0) { { measured response ideal response (w/o drift) y(t) x(t) t=0 t=0 t=0 time 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 10 - Texas A&M University Baseline manipulation (3) Relative • Corrects multiplicative (1+δM) or sensitivity drift xˆ s (t) = y s (t) x s (t) (1+ δM ) x s (t) = = y s (0) x s (0) (1+ δM ) x s (0) y(t) x(t) t=0 t=0 t=0 time 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 11 - Texas A&M University Baseline manipulation (4) Fractional • Percentual change in the sensor response x s (t) - x s (0) y s (t) = x s (0) • Properties • Yields a dimensionless measurement • Normalizes sensor responses, but can amplify noisy channels • Fractional conductance shown to be the most suitable method for MOS sensors [Gardner, 1991] 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 12 - Texas A&M University Reference gas [Fryder et al., 1995] Equivalent to diff. BM, except a calibrant is used • Calibrant must be chemically stable over time AND highly correlated with samples [Haugen et al., 2000] y(t) Sample Calibrant x(t) New baseline time 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 13 - Texas A&M University Calibration schedule Calibrant Samples Traditional (time intensive) Efficient (systematic memory errors) Efficient (random memory errors) Time, € adapted from [Salit and Turk, 1998] 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 14 - Texas A&M University Multiplicative correction [Haugen et al., 2000] Basic idea • Model temporal variations in a calibration gas with a multiplicative correction factor • Apply the same correction to the samples • Perform this process first on short-term trends, then on long-term fluctuations Properties • Heuristic, global technique • Practical for industrial applications • Compensates for short- and long-term drift 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 15 - Texas A&M University Short-term correction (1) U STC Sequence 1 Sequence 2 Sequence 3 index Sequence 1 Sequence 2 Sequence 3 index USCT 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 16 - Texas A&M University Short-term correction (2) For each sequence • Compute a correction factor for each calibration sample qn,seq = U1,calseq Un,calseq • Build regression model for series {q1,seq, q6,seq, q11,seq,…} qˆ n,seq = ax n + b with x n = mod(n,Nsam + 1) • Correct all samples ˆ USTC n,seq = Un,seq qn,seq Name U1cal U2 q6,seq U3 U4 U5 U6cal q̂9,seq U7 U8 U9 U10 U11cal U12 U13 U14 U15 … Class Index xn Calibration 1 0 Sample 2 0 Sample 3 0 Sample 4 0 Sample 5 0 Calibration 6 1 Sample 7 1 Sample 8 1 Sample 9 1 Sample 10 1 Calibration 11 2 Sample 12 2 Sample 13 2 Sample 14 2 Sample 15 2 … … … (seq subindex omitted for clarity) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 17 - Texas A&M University Long-term correction (1) USCT LTC Sequence 1 Sequence 2 Sequence 3 index Sequence 1 Sequence 2 Sequence 3 index ULTC 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 18 - Texas A&M University Long-term correction (2) For each sequence • Compute a correction factor for the first calibration sample fseq cal 1,1 cal 1,seq U = U • Correct all samples ˆ ULTC n,seq = Un,seq qn,seq fseq 14243 USTC n,seq Name U1,1cal U2,1 U3,1 … cal f2 U6,1 U7,1 U8,1 … U1,2cal U2,2 f3 U3,2 … U6,2cal U7,2 U8,2 … U1,3cal U2,3 U3,3 … U6,3cal U7,3 U8,3 … Class Index Calibration 1 Sample 2 Sample 3 xn 0 0 0 Calibration Sample Sample 6 7 8 1 1 1 Calibration Sample Sample 1 2 3 0 0 0 Calibration Sample Sample … Calibration Sample Sample 6 7 8 … 1 2 3 1 1 1 … 0 0 0 Calibration Sample Sample … 6 7 8 … 1 1 1 … 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 19 - Texas A&M University Seq 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 Performance of multiplicative correction PCA plot of uncorrected milk samples measured over 2 days: pasteurized milk ({) , oxidized pasteurized milk (), calibration samples (U). PCA plot of drift corrected milk samples measured over 2 days: reference milk ({), oxidized milk (), calibration samples (U). from [Haugen et al., 2000] 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 20 - Texas A&M University 2nd NOSE II Workshop Linköping, 18 - 21 May 2003 Multivariate Techniques Adaptive clustering Basic idea • Model the distribution of examples with a codebook • Assign an incoming (unknown) sample to the "closest" class • Adapt class parameters to incorporate information from the newly classified example 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 22 - Texas A&M University Adaptive clustering (1) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 23 - Texas A&M University Adaptive clustering (2) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 24 - Texas A&M University Adaptive clustering (3) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 25 - Texas A&M University Adaptive clustering (4) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 26 - Texas A&M University Adaptive clustering (5) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 27 - Texas A&M University Adaptive clustering (6) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 28 - Texas A&M University Adaptive clustering (7) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 29 - Texas A&M University Adaptive clustering (8) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 30 - Texas A&M University Adaptive clustering (9) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 31 - Texas A&M University Adaptive clustering (10) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 32 - Texas A&M University Adaptive clustering (11) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 33 - Texas A&M University Adaptive clustering (12) 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 34 - Texas A&M University Adaptive clustering methods Mean updating • One cluster center per class [Holmberg et al., 1996] Kohonen self-organizing maps • One SOM common to all classes [Davide et al., 1994; Marco et al., 1997] • A separate SOM for each class [Distante et al., 2002] Adaptive Resonance Theory • ART is slightly different; new clusters can be created [Gardner et al., 1996] 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 35 - Texas A&M University Adaptive clustering: discussion Algorithm relies on correct classification • Miss-classifications will eventually cause the model to lose track of the class patterns All odors need to be sampled frequently to prevent their patterns to drift too far This problem has also been addressed in the machine learning literature • see [Freund and Mansour, 1997] and refs. therein 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 36 - Texas A&M University System identification [Holmberg et al., 1996] Basic idea • Chemical sensor responses co-vary over time • This "common-mode" behavior can be modeled with a dynamic model (e.g., ARMAX) A S C B k − n) = ∑∑ b y (k − n) + ∑ c e(k − n) ∑ a y14(2 1 424 3 1 424 3 4 3 n =0 n s sensor s i=1 n = 0 i≠ s in i all other sensors n =0 n white noise • where ys(k) is the response of sensor 's' at time k, and yi(k) is the response from all other sensors • Model parameters {A,B,C} may be adapted over time with a recursive least-squares procedure [Holmberg et al., 1997] 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 37 - Texas A&M University System identification: classification Each odor/sensor pair has a unique dynamic behavior that can be used as a fingerprint • Build a dynamic model for each sensor/odor • When an unknown odor is presented, predict its behavior of each sensor with each of the models • The method requires that multiple (consecutive) samples of the unknown odor be collected • The model with lowest prediction error corresponds to the true odor 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 38 - Texas A&M University System identification: illustration MODEL DYNAMIC BEHAVIOR FOR EACH ODOR/SENSOR APPLY EACH O/S MODEL TO UNKNOWN SAMPLE CHOOSE ODOR MODEL WITH LOWEST ERROR Unknown ERROR 1 Unknown ERROR 2 Unknown Odor A A1Y=B1Y’+C1E ERROR 3 Odor B A2Y=B2Y’+C2E Odor C A3Y=B3Y’+C3E time time 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 39 - Texas A&M University Calibration transfer Learn a regression mapping (e.g., MLPs, PLS) from drifting calibrant samples onto a baseline t0 • MLPs for PyMS [Goodacre and Kell, 1996] • PLS for e-noses [Tomic et al., 2002] • MLPs for e-noses [Balaban et al., 2000] Training phase: Drifting calibrant samples at times t1, t2, …tN Training phase: Baseline calibrant sample at time t0 Recall phase: Drifting odor samples at times t1, t2, …tN Recall phase: Corrected odor samples at times t1, t2, …tN 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 40 - Texas A&M University Orthogonal signal correction [Wold et al., 1998] Basic idea • Assume dataset matrices • Y: sensor-array data (independent variables) • C: concentration vector or class label (dependent) • Subtract from Y factors that account for as much of the variance in Y as possible AND are orthogonal to C 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 41 - Texas A&M University Orthogonal signal correction: intuition Y3 Direction orthogonal to concentration vector Y1 Subspace correlated with concentration vector C Y2 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 42 - Texas A&M University Orthogonal signal correction: an example 6 4 2 PCA2 0 -2 -4 -6 -8 2 3 4 4 3 2222 odors 3 4 2 4 4 4 2 3 2 42 2 4423242224 4 3 4 3 3 4 2 3 4 1 11 3 3 1 22 111 4333233 222 3 4 422433233442 22 11 11 1 433 5 55 5 1 1 111 32 34 23 3 324 55 5 5 51 1 1 424 2 34 14 2343 5 5 5 5 1 5 1 55 1 51 4 3 4 4 5 5 55 11111 3 3 234 4342 4 55 5 4 1 1 3 1 2 1 1 4 5 5 2 5 3 3 3 5 322 1 55 5 1 24 2 5 3 5 4 1 5 5 55 4 5 1 5 5 3 2 5 3 11 5 1 drift 1 -10 -10 -5 0 1 5 10 15 PCA1 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 43 - Texas A&M University Component correction [Artursson et al., 2000] Basic idea • Drift is associated with the principal components of variance in a calibration gas • These directions are removed from the multivariate sensor response by means of a bilinear transformation Algorithm T x corrected = x − (x ⋅ v cal )v cal • where vcal is the first eigenvector of the calibration data xcal 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 44 - Texas A&M University Component correction results from [Art, 2000] PCA scatter plot of uncorrected samples for eight gas mixtures. Arrows indicate the direction of drift. The center cluster (+) is the calibration gas. PCA scatter plot after component correction. The calibration gas (+), no longer shown in the figure, has been used to estimate and remove the principal direction of drift (vcal). 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 45 - Texas A&M University Component correction results (2) 3 2 4 3 3 4 4 4 3 3 2 4 523 4 555 8 2 6 5 1516 1 1 616 61 1 PCA2 0 -1 2 2 2 1 777 7 7 -4 -4 Rioja Joven 2000 Rioja Crianza 1999 Rioja Reserva 1998 Ribera Joven 2000 Ribera Crianza 1999 Ribera Reserva 1998 Water 12% v/v EtOH/Water 3 444 4 3 34 4 3 3 3 3 0 -3 -6 (1) (2) (3) (4) (5) (6) (7) (8) 3 8 8 -2 7 777 4 -2 0 PCA1 2 4 6 2 2 666 61 5 55 5 2 22 1161 1 66 55 5 -1 8 8 -5 -4 -3 -2 -1 0 1 PCA1 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 46 - Texas A&M University 2 2 2 3 4 Component deflation [Gutierrez, 2000] Basic idea • Identify variables 'x' whose variance can be attributed to drift or interferents • E.g., response to a wash/reference gas, time stamps, temperature, pressure, humidity, etc. • Measure 'y', the sensor-array response to an odor • Remove variance in 'y' that can be explained by 'x' (by means of regression/deflation) Related to target rotation [Esbensen et al., 1987] • "…removal of undesired information provided that there are variables uniquely connected to that information" [Christie, 1996] 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 47 - Texas A&M University Component deflation algorithm Find linear projections x’=Ax and y’=By that are maximally correlated {A,B} = argmax[ρ(Ax,By )] • How? Canonical Correlation Analysis (CCA) or PLS • Interpretation: x’ and y’ are low-dimensional projections that summarize the linear dependencies between x and y Find regression model ypred=Wy’ W = argmin y − Wy' 2 • Interpretation: ypred contains the variance in the odor vector y that can be explained by y’ and, as a result of the CCA stage, by x Deflate y and use the residual z as a corrected sensor response z = y − y pred = y − WBy 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 48 - Texas A&M University Component deflation: interpretation x3 Ax x2 x1 B W z=y y WBy By class1 class3 z2 y2 class2 z1 y1 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 49 - Texas A&M University Component deflation: motivation Exploit transient information in wash/reference cycle • To capture temporal trends, augment vector x with the time stamp of each sample (also in [Artursson et al., 2000]) Sensor response (V) Wash Reference Odour 3 2.5 2 1.5 50 WTS Kernels 100 xW 150 xR 200 250 Time (s) y x 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 50 - Texas A&M University Component deflation performance Database • Three months of data collection • Four cooking spices • Twenty four days • Four samples per day and spice • Ten metal-oxide sensors Class 1 Class 2 Class 3 Class 4 Date Date PLS CCA Plot shows one particular transient feature • Examples are sorted RAW • By odor class • Within a class, by date Date Date 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 51 - Texas A&M University Influence of aging and training set size Training set Day: 1 2 i Test set j k W Width=1 Predictive accuracy 1 M D Width=5 Width=10 0.9 CCA 0.8 PLS 0.7 RAW 0.6 0.5 2 4 6 Distance 8 10 2 4 6 Distance 8 10 2 4 6 Distance 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 52 - Texas A&M University 8 10 Discussion of univariate methods Frequency decomposition • Mostly useful for diagnostics and analysis Baseline manipulation • Attractive for its simplicity, but not an effective driftcorrection approach for chemical sensors Differential measurements wrt calibrant • First-order approximation, but does not exploit crosscorrelations Multiplicative correction wrt calibrant • Empirically shown to work, heuristic, does not exploit cross-correlations 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 53 - Texas A&M University Discussion of multivariate methods (1) Adaptive clustering • Requires equiprobable and frequent sampling • Correct identification is essential to ensure that the adapting distributions track the odors • Does not use information from a calibrant System identification • Builds a separate drift model for each odor, but requires multiple consecutive samples • Can be used as a template-matching classifier • Does not use information from a calibrant 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 54 - Texas A&M University Discussion of multivariate methods (2) Calibration transfer • Shown to work in MS and e-nose data • Black-box approach Orthogonal Signal Correction and Deflation • In my experience, the best approach • Why? Time tested in chemometrics, uses multivariate and calibrant information, and IT IS SIMPLE 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 55 - Texas A&M University References (1) M. Holmberg and T. Artursson, "Drift Compensation, Standards and Calibration Methods," in T. C. Pearce, S. S. Schiffman, H. T. Nagle and J. W. Gardner (Eds.), Handbook of Machine Olfaction: Electronic Nose Technology, Weinheim, Germany: Wiley-VCH, 2002, pp.325-346. S.-Y. Choi, K. Takahashi, M. Esani and T. Matsuo, "Stability and sensitivity of MISFET hydrogen sensors," in Proc. Int. Conf. Solid State Sensors and Actuators, Philadelphia, PA, 1985. M. Roth, R. Hartinger, R. Faul and H.-E. Endres, "Drift reduction of organic coated gas-sensors by temperature modulation," Sensors and Actuators B 36(1-3), pp. 358-362, 1996. D.M. Wilson and S.P. DeWeerth, "Odor discrimination using steady-state and transient characteristics of tin-oxide sensors," Sensors and Actuators B 28(2), pp. 123-128. 1995. J.W. Gardner and P.N. Bartlett, Electronic Noses. Principles and Applications, New York: Oxford University Press, 1999. J.W. Gadner, "Detection of Vapours and Odours from a Multisensor Array using Pattern recognition. Part 1. Principal Components and Cluster Analysis," in Sensors and Actuators B 4, pp. 109-115, 1991. M. Fryder, M. Holmberg, F. Winquist and I. Lündstrom, "A calibration technique for an electronic nose," in Eurosensors IX, 1995, pp. 683-686. M.L. Salit and G.C Turk, "A Drift Correction Procedure," Analytical Chemistry 70(15), pp. 31843190, 1998. J.E. Haugen, O. Tomic and K. Kvaal, "A calibration method for handling the temporal drift of solidstate gas sensors," Analytica Chimica Acta 407, pp. 23-39, 2000. T. Artursson, T. Eklöv, I. Lundström, P. Mårtensson, M. Sjöström and M. Holmberg, "Drift correction for gas sensors using multivariate methods," Journal of Chemometrics 14(5-6), pp. 711723, 2000. 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 56 - Texas A&M University References (2) F.A.M. Davide, C. Di Natale, M. Holmberg and F. Winquist, "Frequency Analysis of Drift in Chemical Sensors," in Proc. 1st Italian Conf. on Sensors and Microsystems, Rome, Italy, 1996, pp. 150-154. R. Goodacre and D.B. Kell, "Correction of mass spectral drift using artificial neural networks," Analytical Chemistry 68, pp. 271-280, 1996. O. Tomic, H. Ulmer and J.E. Haugen, "Standardization methods for handling instrument related signal shifts in gas-sensor array measurement data," Analytica Chimica Acta 472, 99-111, 2002. M.O. Balaban, F. Korel, A.Z. Odabasi and G. Folkes, "Transportability of data between electronic noses: mathematical methods," Sensors and Actuators B 71, pp. 203-211, 2000. S. Wold, H. Antti, F. Lindgren and J. Öhman, "Orthogonal signal correction of near-infrared spectra," Chemometrics and Intelligent Laboratory Systems 44, pp. 175-185, 1998. K. Esbensen, L. Lindqvist, I. Lundholm, D. Nisca and S. Wold, "Multivariate Modeling of Geochemical and Geophysical Data," Chemometrics and Intelligent Laboratory Systems 2, pp. 161175, 1987. O.H.J. Christie, “Data Laundering by Target Rotation in Chemistry-Based Oil Exploration,” Journal of Chemometrics 10, pp. 453-461, 1996. M. Holmberg, F. Winquist, I. Lundström, F. Davide, C. DiNatale, and A. D'Amico, "Drift counteraction for an electronic nose," Sensors and Actuators B 36(1-3), pp. 528-535, 1996. F.M. Davide, C. Di Natale, and A. D’Amico, "Self-organizing Multisensor Systems for Odour Classification: Internal Categorization, Adaptation, and Drift Rejection," Sensors and Actuators B 18-19, pp. 244-250, 1994. S. Marco, A. Pardo, A. Ortega and J. Samitier, "Gas Identification with Tin Oxide Sensor Array and Self-Organizing Maps: Adaptive Correction of Sensor Drifts," in Proc. IEEE Instrumentation and Measurement Technology Conference, Orrawa, Canada, May 19-21, 1997, pp. 904-907. 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 57 - Texas A&M University References (3) C. Distante, P. Siciliano and K.C. Persaud, "Dynamic Cluster Recognition with Multiple SelfOrganising Maps," Pattern Analysis and Applications 5, pp. 306-315, 2002. J. W. Gardner, E. L. Hines and C. Pang, "Detection of vapours and odours from a multisensor array using pattern recognition: self-organizing Adaptive Resonance Techniques,” Measurement + Control 29, pp. 172-178, 1996. Y. Freund and Y. Mansour, “Learning under persistent drift,” in Proc. European Conference on Computational Learning Theory, 1997, pp. 109-118. 2nd Workshop Ricardo Gutierrez-Osuna Signal processing methods for drift compensation - 58 - Texas A&M University 2nd NOSE II Workshop Linköping, 18 - 21 May 2003 Questions 2nd NOSE II Workshop Linköping, 18 - 21 May 2003 Thank you