Increasing the separability of chemosensor array patterns with Hebbian/anti-Hebbian learningIntroductionContrast enhancement through Hebbian/anti-Hebbian learningContrast enhancement in the KIIIHebbian/anti-Hebbian learning in the KIII modelComparison with other methodsSynthetic binary problemSensor array-pattern validationDiscussionAcknowledgementsReferencesSensors and Actuators B 116 (2006) 29–35Increasing the separability of chemosensor array patterns withHebbian/anti-Hebbian learningA. Gutierrez-Galvez, R. Gutierrez-Osuna∗Department of Computer Science, Texas A&M University, College Station, TX 77843, United StatesReceived 11 July 2005; received in revised form 7 October 2005; accepted 30 November 2005Available online 18 April 2006AbstractThe olfactory bulb is able to enhance the contrast between odor representations through a combination of excitatory and inhibitory circuits.Inspired by this mechanism, we propose a new Hebbian/anti-Hebbian learning rule to increase the separability of sensor-array patterns in aneurodynamics model of the olfactory system: the KIII. In the proposed learning rule, a Hebbian term is used to build associations within odorsand an anti-Hebbian term is used to reduce correlated activity across odors. The KIII model with the new learning rule is characterized on syntheticdata and validated on experimental data from an array of temperature-modulated metal-oxide sensors. Our results show that the performance ofthe model is comparable to that obtained with Linear Discriminant Analysis (LDA). Furthermore, the model is able to increase pattern separabilityfor different concentrations of three odorants: allyl-alcohol, tert-butanol, and benzene, even though it is only trained with the gas sensor responseto the highest concentration.© 2006 Elsevier B.V. All rights reserved.Keywords: Contrast enhancement; Hebbian; Anti-Hebbian; KIII model; Gas sensor-array1. IntroductionThe olfactory system has been optimized over evolutionarytime to allow animals detect and interpret the information fromvolatile molecules in the environment. The striking similaritybetween the olfactory system across phyla seem to imply thatits architecture has been shaped to reflect basic properties ofolfactory stimuli [1]. This suggests that the underlying mecha-nisms of the olfactory system could be of practical use to processsignals from gas sensor arrays.Motivated by this idea, our long-term research objective is todevelop biologically inspired computational models for chem-ical sensor arrays. In this paper, we focus on the ability of theolfactory bulb to improve the separability of odor representa-tions. The olfactory bulb receives direct inputs from olfactoryreceptor neurons in the epithelium, and reshapes this informationthrough excitatory–inhibitory circuits, increasing the contrastacross odor representations [2]. This article presents a learning∗Corresponding author. Tel.: +1 9 798 452 942; fax: +1 9 798 478 578.E-mail addresses: [email protected], [email protected](R. Gutierrez-Osuna).rule to apply this computational function to gas sensor-array pat-terns. The proposed learning rule is validated on the KIII modelof Freeman et al. [3,4]. The KIII is a neurodynamics modelof the olfactory system that encodes odor information throughdynamic attractors. In recent years, computational models usingthis coding strategy have been shown to have resistance to noiseand higher storage capacity [5,6,7]. However, with a few excep-tions [8–10], the KIII model has gone largely unnoticed in themachine olfaction literature.2. Contrast enhancement throughHebbian/anti-Hebbian learningContrast enhancement in the olfactory bulb is performedthrough the inhibition of mitral cells by nearby granule interneu-rons [11]. This inhibition has the effect of reducing the moleculartuning range (i.e., the number volatile molecules detected) of amitral cell relative to that of olfactory receptor neurons, effec-tively orthogonalizing patterns across odors. It is well knownthat this computational function can be achieved by means ofanti-Hebbian learning [12]. The anti-Hebbian learning rule is theopposite of the Hebbian rule [13], and states that the strength ofthe connection between two neurons should decrease when both0925-4005/$ – see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.snb.2005.11.08130 A. Gutierrez-Galvez, R. Gutierrez-Osuna / Sensors and Actuators B 116 (2006) 29–35activate simultaneously:wkl=−xkxl(1)where xkand xlare the kth and lth inputs to the system. Theapplication of this rule to a laterally connected network leads toa decorrelation of the input channels in the system.We propose a learning rule that combines Hebbian andanti-Hebbian terms to achieve both robustness to sensor fail-ures and enhanced pattern separability, respectively. Assum-ing a pattern recognition problem with N odor patterns pi=[xi1xi2, ..., xiM]T;1≤ i ≤ N, and a recurrent network with Mfully laterally connected neurons, the strengths of the lateralconnections are computed with the following off-line expres-sion:w =Hebbian  Ni=1pi(pi)T−anti-Hebbian  Ni=1Nj=1j =ipi(pj)T(2)The first term in Eq. (2) is the Hebbian rule, which strengthensthe connection between neurons that are active within a pat-tern. The second term is the anti-Hebbian component, whichreduces the connection weights between neurons that are activefor multiple patterns, on the average reducing the overlap acrosspatterns. Negative mitral-to-mitral connections are avoided byforcing to zero all elements in Eq. (2) that become negative.3. Contrast enhancement in the KIIIThe proposed learning mechanism is implemented on theKIII, a neurodynamics model of the olfactory system developedby Freeman and colleagues over the last 30 years [3,4]. TheKIII reproduces electroencephalographic (EEG) recordings inthe olfactory system by modeling the oscillatory behavior ofneuron populations [4]. The topology of the model, shown inFig. 1, is based on the physiology of the mammalian olfactorysystem [3,14]. Each node in the KIII represents a population ofneurons, modeled by a second order differential equation, andeach edge models the interaction between two populations. TheFig. 1. The KIII model architecture. The KIII model is built after the basic architecture and building blocks of the olfactory system: R olfactory receptor neurons;P periglomerular cells; M mitral cells; G granule cells; E and I cells from