Hacia un Modelo de Red Inmunológica Artificial Basado en Kernels. Towards a Kernel Based Model for Artificial Immune Networks

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1 Haca un Modeo de Red Inmunoógca Artfca Basado en Kernes Towards a Kerne Based Mode for Artfca Immune Networs Juan C. Gaeano, Ing. 1, Fabo A. Gonzáez, PhD. 1 Integent Systems Research Lab, Natona Unversty of Coomba Branch Bogota Bongenum Research Lab, Natona Unversty of Coomba Branch Bogota {cgaeanoh, fagonzaezo}@una.edu.co Recbdo para revsón 8 de Novembre de 007, aceptado 14 de Febrero de 008, versón fna 8 de Febrero de 008 Resumen En este artícuo se presenta una adaptacón de un modeo de red nmunoógca artfca a a estratega de os métodos de erne. Esta adaptacón proporcona a área de os sstemas nmunoógcos artfcaes, por prmera vez, agunas de as ventaas de os métodos de erne, taes como a habdad para ser apcados sobre datos no vectoraes y a transformacón a espacos de ata dmensonadad por medo de amado erne trc. Agunos exper mentos premnares fueron evados a cabo con e fn de obtener agunas uces sobre e comportamento de modeo propuesto. Paabras Cave sstemas ntegentes, agr upamento basado en smtud, redes nmunoógcas artfcaes, métodos de er ne. Abstract Ths paper presents an adaptaton to the strategy of erne meth ods of a we n own ar tfca mmune n etwor. Ths adaptaton brngs to artfca mmune systems, for the frst tme, some of the advantages of erne methods, such as the abty to dea wth non vector data and the mappng to hgh dmensona spaces thr ough the erne tr c. Pr emnar y exper ments were carred out n order to get some nsghts of the behavor of the proposed mode. Keywords ntegent syst ems, smar ty based cust er n g, artfca mmune networs, er ne methods. I. INTRO DUCTION achne earnng oos for fndng and recognzng patterns M n data comng from a source of nterest []. The patterns extracted from such data may be used for obtanng nowedge of the data source or to mae predctons []. Machne earnng technques can be cassfed nto, at east, two approaches: the feature based approach and the smartybased approach [13]. The former consders a process to represent the obects as feature vectors as a prevous step to earnng []; the atter, uses ony a (ds)smarty measure between obects as the nput for the earnng process [13]. There are some domans where the obects have a compex structure, whch maes dffcut to perform the feature extracton process [13]. Exampes of ths nd of domans are mages, sequences, graphs, and text documents. In those cases, the appcaton of the smarty based approach appears to be more sutabe. Kerne methods s a machne earnng strategy that maes agorthm desgn ndependent from the representaton of the data [5]. Such ndependence requres that agorthms receve as nput a par wse measure nstead of feature vectors. From ths pont of vew we can consder the strategy of erne methods as a smarty based approach. Bo nspred computng (aso nown as natura computng) s the fed of machne earnng (and computer scence) that deveops probem sovng technques by mmcng a natura system. Some exampes of ths nd of technques are Genetc Agorthms that tae nspraton from speces evouton [9], Artfca Neura Networs that tae nspraton from bran functon [4], and Artfca Immune Systems (AIS) that tae nspraton from the mmune system behavor [6]. Most of those agorthms foow the feature based approach snce the frst step n settng them up s a representaton process where doman obects are usuay coded as attrbute vectors, wth each component representng some mportant feature of the obect. There s not much research on the deveopment of bo nspred agorthms that foow the smarty based approach, except for the erne versons of the sef organzng map (erne SOM) [16], [1], [1] and the erne partce swarm optmzaton (erne PSO) [1]. In ths paper, the probem of expressng an artfca mmune networ (AIN) mode as a erne method s taced. Specfcay, a nown AIN mode, anet [7], s modfed n such a way that t does not receve as nput the vector representaton of antgens, but the nter antgen dstances. Revsta Avances en Sstemas e Informátca, Vo.5 No. 1, Edcón Especa, Medeín, Mayo de 008, ISSN III Congreso Coombano de Computacón 3CCC 008

2 66 Revsta Avances en Sstemas e Informátca, Vo.5 No. 1, Edcón Especa, Medeín, Mayo de 008, ISSN III Congreso Coombano de Computacón 3CCC 008 Ths paper s organzed as foows: Secton II presents a revew of the artfca mmune networ mode for custerng and the strategy of erne methods for pattern anayss. Secton III presents an AIN mode for custerng based on the erne methods strategy. Secton IV presents the resuts of some premnary experments, and fnay, Secton V concudes the paper and proposes some deas for future wor. II. BACK GRO UND A. Artfca Immune Networs The natura mmune system (NIS) s the man defense of the body aganst pathogen organsms, caed antgens []. The NIS exhbts some nterestng propertes from a computatona pont of vew, such as pattern recognton, autonomy, dstrbutvty, earnng and memory [6]. Thus the fed of artfca mmune systems (AIS) wors on the defnton of modes nspred by prncpes and theores of the NIS n order to be apped to probem sovng [6]. The mmune earnng s the abty of the NIS for adaptng tsef to the changes n the antgenc envronment [6]. When an antgen enters the body for the frst tme, the NIS uses adaptaton mechansms to create ces (B ces) and moecues (antbodes) abe to dea wth such antgen. Addtonay, the NIS uses a memory mechansm for eepng an nterna mage of the antgen, so that t can dea wth t faster and more effectvey f the same antgen (or a smar one) nvades the body agan []. From the pont of vew of the mmune networ theory, mmune earnng and memory can be expaned as foows: the producton of a gven antbody (ected by an externa antgen) stmuates/ suppresses the producton of other antbodes that stmuate/ suppress the producton of other antbodes and so on []. The man hypothess of ths theory states that mmune memory s mantaned by B ces nteractng wth each other even n the absence of foregn antgens []. These nteractons between ces/moecues are va shape matchng (recognton). The way an antgen (or an antbody) can stmuate/suppress the producton of antbodes s based on the strength of the recognton, whch s caed affnty []. An artfca mmune networ (AIN) s an AIS that uses concepts from the mmune networ theory [6], many the nteractons between B ces (stmuaton and suppresson) and the ce conng and mutaton processes [8]. In the ast years dfferent AIN modes have been proposed to sove probems such as pattern recognton n DNA sequences [10], data anayss [0], [15], [7], [6], [7], web mnng [18], [19], mutmoda functon optmzaton [5], robot contro [11], [17], autonomous navgaton [14], [17] and e ma cassfcaton [4]. Most of AIN modes are based n the shape space concept ntroduced by Pereson [8]. Ths concept represents antbodes and antgens as ponts n a n dmensona space, where each dmenson s reated to a feature nvoved n the recognton process []. An antbody recognzes those antgens n ts scope, whch s defned by a hypersphere wth certan recognton radus and center n the antbody []. From ths pont of vew, AIN can be abeed as a feature based approach. Most of AIN modes assume a feature based representaton of the doman obects to be used n the earnng process. Ths maes dffcut to appy such modes n domans wth compex structure. Then, a representaton ndependent AIN mode woud aow to extend the appcaton doman of AIN. The erne methods approach gves a sutabe strategy to acheve such mode. B. Kerne Methods Kerne methods are descrbed as a unfed approach based on statstca methods for pattern anayss [5]. The approach assumes that transformng the nput data to a proper feature space coud mae the pattern dentfcaton process easer [5]. Such transformaton corresponds to the representaton process mentoned above. However, the transformaton s defned mpcty by a erne functon, whch s reated to the specfc data type and the nd of patterns that s expected to fnd n the data set [5]. Fg. 1. A schematc representaton of the erne methods approach The erne methods strategy can be represented as n Fg. 1. Data are mapped to a feature space through a erne functon κ, whch computes dot products between obects n the new space. The erne matrx Kcontans the evauaton of the erne functon for each par of obects and acts as nput of a earnng agorthm Athat s desgned to fnd patterns n the feature space based on such matrx [5]. One nterestng and usefu property of the erne functon s that t can compute the dot product from the orgna obects. Ths property s caed the erne trc [3]. Then, the earnng agorthm s desgned so that t does not need the coordnates of the obects n the new space, but ony the erne matrx [5]. Kerne methods can be apped to any data type,.e., nput data do not need to be represented as feature vectors [5]. It s because constrants to consder a functon as a erne functon are stated n terms of the erne matrx. Therefore, any par wse measure (e.g. smarty) abe to produce a par wse matrx that

3 Haca un Modeo de Red Inmunoógca Artfca Basado en Kernes Gaeano, Gonzáez 67 satsfes those constrants can be consdered as a erne functon [5]. Hence, erne methods can be abeed as a smarty based approach. Kerne methods have the advantage of separatng the earnng agorthm from the data representaton [5]. Ths aows research on pattern anayss to be defned n two drectons: one for defnng erne functons for specfc data types, and other for budng earnng agorthms to fnd specfc pattern types. The defnton of a erne method mpes the expresson of computatons n terms of dot products [5]. Ths can be acheved drecty as the case of support vector machnes or by modfyng a nown mode as the case of the erne means, whch s the erne verson of the means agorthm [5]. C. Kerne Methods on Bo nspred Agorthms There s not much research on the deveopment of bo nspred agorthms that foow the erne method strategy. Here, we revew the erne versons of the sef organzng map (SOM) and the erne verson of the partce swarm optmzaton agorthm (PSO). 1) KM Kerne SOM: In [16] MacDonad and Fyfe present a erne verson of the Kohonen's sef organzng map (SOM). The authors revew the erne means (KM), whch s the base for ths ernezed SOM (KSOM). In that mode, each mean m u s a near combnaton of nput data n the feature space, whch s expressed as x, where { } [ 1 N ] m µ γ µ ( x ) s the set of nput sampes, s the mappng from the nput space to the feature space, nduced by a erne functon, and γ μ s the weght of the th smpe for the mean m μ. Coeffcents γ μ are n [0, 1] and the sum over a the coeffcents representng a mean equas the number of ponts assgned to the custer that mean represents. Thus, n KM KSOM, neuron weghts are near combnatons of nput data n the feature space, and the weght updatng mechansm s the same as n the orgna SOM, even usng the same neghborhood functon. As revewed n [1], n ths mode neuron weghts are defned n the feature space but not n the nput space. ) GD Kerne SOM: Ths erne verson of SOM, revewed n [1], s presented n [1] by Pan et a. and n [3] by Andras. The mode s based on gradent descent (GD) and the probem s to mnmze the mean square error of an nput and the correspondng prototype n the mapped space. 3) EF Kerne SOM: In [1] Lau et a. present a revew of the KM KSOM the GD KSOM. They show that SOM can be performed competey n feature spaces and that both versons of KSOM are equvaent to a unfyng KSOM based on energy functons, a of ths eepng n mnd cassfcaton tass. Authors derve a KSOM based on a energy functon (EF) to be mnmzed. It s foowed from a defnton of the orgna SOM as mnmzer of such functon. They then show the updatng rues of KM SOM and GD SOM are partcuar cases of the updatng rue n the EF SOM, that can be used dependng on weghts are or are not defned n the feature space. 4) Kerne PSO: In [1] Abraham et a. present a erne verson of the Partce Swarm Optmzaton (PSO) agorthm to perform automatc custerng,.e., wthout pror nowedge about the rght number of custers. The modfed verson s acheved by defnng a custerng ndex, caed CS measure, n terms of nner products and sovng the custerng probem as an optmzaton probem where CS measure shoud be mnmzed, whch mpes an optma partton has been reached. In the process, each partce represents a partton of the nput data set and therefore, the souton s the gobay best partce at the end of the process. III. A PROPOSAL FOR A KERNEL ARTIFICIAL IMMUNE NETWORK (KAIN) Fg. shows a genera tranng agorthm for AIN, whch s taen from [8]. The agorthm receves as nput a set A A of antgens, whch are gong to be presented to the networ, where A s the set of a possbe antgens. The agorthm returns an artfca mmune networ composed of a set B B of B ces and connectons between them, where B s the set of a possbe B ces. The set B s the set of B ces of an AIN at a gven tme. The frst step, ntazaton, s to create an nta set of B ces. After ths, an teratve process s performed startng by presentng the set of antgens to the networ, whch means that for each antgen and each B ce the stmuaton s cacuated ( f A B A R ). Such stmuaton s based on an stmuato n : affnty measure between antgens and B ces ( f affnty : B A B A R ) that measures the smarty/ compementarty between eements n the shape space. In the next step B ces are aowed to nteract wth each other, ths s done by cacuatng the stmuaton and suppresson effects between them ( f B B B R stmuato n : and f B : B B sup presson R ). Smar to antgen/b ce stmuaton, B ce/b ce stmuaton (and suppresson) coud be cacuated as a functon of B ce/b ce affnty. Tota stmuaton of B ces s then cacuated by summng up the effects caused by antgen and networ nteractons ( F : B R ). Based on tota stmuaton, some B ces are seected and some copes ( f conng : B Ν ) of each seected B ce are created and mutated ( mutate : B B ). Some modes nterpret ths rate as the probabty of a B ce to be seected for sufferng mutaton; other modes nterpret t as the

4 68 Revsta Avances en Sstemas e Informátca, Vo.5 No. 1, Edcón Especa, Medeín, Mayo de 008, ISSN III Congreso Coombano de Computacón 3CCC 008 Fg.. A Genera Artfca Immune Networ agorthm proporton of the B ce feds that w be changed. In the meta dynamcs step, some useess B ces are removed from the networ, new B ces are created randomy and ncorporated nto the networ, and ns among a B ces are reorganzed. Fnay, when the stoppng crteron s met, the current networ s returned. A. A Modfed Verson of the GAIN Agorthm To modfy the GAIN agorthm so that t foows the strategy of erne methods, t shoud be notced that a cruca step s the mutaton operator, snce t s usuay mpemented as a few varaton n the coordnates of a feature vector. For ths purpose we propose to defne a new representaton for B ces. 1) Representaton and Mutaton of B Ces: Here, we foow a smar approach to that of Kerne SOM. Generay, n most AIN modes, antgens correspond to nput sampes and antbodes may be assmated to custer centrods (neura weghts). Therefore, n KAIN B ces (antbodes) are represented as near combnatons of antgens n the feature space. In a more forma way, a B ce s represented as b ( a ) where b B s a B ce, a A s an antgen, s a γ mappng from the nput space to a feature space and s a weght. We can constran the near combnaton to be convex n order to mae the B ce be surrounded by the antgens t recognzes. In genera, a may be any antgen presented to the networ,.e. A A, however we can restrct A to ncude ony those antgens whch have nteracted wth (stmuated) b. Notce that those A are not necessary dsont. From the boogca pont of vew, ths representaton maes sense because when an antgen enters the body, the mmune system creates some B ces n order to neutraze such antgen. The B ces more ey to survve are those wth hgh affnty wth the stmuatng antgen, n that way, those B ces are nterna mages of such antgen. As a B ce s stmuated by those antgens cose enough n the shape space,.e., the affnty between the B ce and each of those stmuatng antgens s greater than a certan threshod, the shape of a B ce s defned for the set of antgens t recognzes, as more than one B ce can recognze the same antgen, the sets A are not necessary dsont. A a, a B Notce that gven a set of antgens { } [ 1, m ] ce b s totay determned by the coeffcents γ. Ths

5 Haca un Modeo de Red Inmunoógca Artfca Basado en Kernes Gaeano, Gonzáez 69 means that a B ce b can be represented as the vector of weghts (γ 1..., γ m ). Based on ths representaton t s easy to adapt a genetc agorthm mutaton scheme for rea vaued chromosomes. For nstance, a Gaussan mutaton scheme as descrbed n [9] mutate b ( ) mutate ( γ 1,..., γ m ) ( γ,..., γ ) + (,..., ) 1 m where each Δ ~ N(0, σ) and σ s a parameter that contros the expected sze of Δ. Notce that a normazaton step s requred after addng the vector Δ n order to eep the convexty property. The mpementaton of ths operator s straghtforward, however the cruca step s the mpementaton of mutaton n such a representaton. ) B ce antgen and B ce B ce affnty: As t was mentoned n Secton II, affnty s a centra concept n AIN modes. Snce B ces are represented as a near combnaton of antgens, the B ce antgen and the B ce B ce affnty may be defned n terms of antgen antgen affnty. Notce that n the natura mmune system there s not such a concept as antgen antgen affnty; ths s aso the case n most AIN. However, most of the AIN represent B ces and antgens n the same way, thus the B ce antgen affnty measure may be naturay extended to an antgen antgen affnty measure. For ths paper, we use the antgen antgen affnty gven by f affnty A where ( ) ( ) A ( ( ) ( ) a, exp a D a a Gven that D A 1 m D σ x x, x, the expresson above turns nto ( a ) ( a ), ( a ) ( a ) ( a ), ( a ) + ( a ), ( a ) ( a ), ( a ) whch can be expressed usng the erne functon A ( a, a ) + κ ( a, a ) κ ( a a ) D κ, κ as In a smar way, the B ce antgen affnty w gven by where D BA a f affnty D σ BA ( ( )) a b, exp a γ b ( a ) κ ( a, a ) + κ ( a, a ) κ ( a, a ) + and fnay, the B ce B ce affnty can be expressed as where f D affnty B B D σ ( ) b, b exp b, b + and usng the fact that b, b b b b b, b b the expresson above turns nto D B b, b b, b ( a ), γ ( a ) γ κ γ γ κ γ ( a ), ( a ) κ ( a, a ) ( a, a ) ( a, a ) κ + + ( a, a ) 3) New B ce generaton: As the representaton of B ces n feature space requres a set of antgens for each B ce, the ntazaton step can be performed by randomy seectng a set A 0 Awhere each antgen represents a B ce,.e., f the th antgen s seected, the correspondng B ce w be b ( ) a and 1 for. γ where γ 0 for a IV. PRELIMINARY EXPERIMENTS Some smpe experments were carred out n order to test the sutabty of the proposed mode for detectng custers n data. In ths wor resuts w be vadated by vsua evauaton of B ces ocatons. For ths purpose a synthetc dmensona data set consstng of 5 custers was used. Ths data set s a verson of the one used n [7], t conssts of 50 ponts, each custer contanng 10 ponts. Fg. 3 shows a pot of ths data set. The mpementaton we used s an adaptaton of the anet agorthm [7] consderng the defntons presented n Secton III. One maor modfcaton was ntroduced n the affnty measure, whe anet agorthm uses 1 D as the affnty measure, where D represents the Eucdean dstance between patterns, the proposed agorthm uses D exp as the affnty measure. σ +

6 70 Revsta Avances en Sstemas e Informátca, Vo.5 No. 1, Edcón Especa, Medeín, Mayo de 008, ISSN III Congreso Coombano de Computacón 3CCC 008 A. Expermenta Setup In ths setup experments were carred out varyng the nput data: the frst one usng custers and 3 (ponts n the upper eft hand and ower rght hand), and the second one usng the whoe data set. Tabe I shows an expanaton of each parameter aong wth the vaues used n ths setup. For these experments, the dentty erne κ ( x, y ) x, y was used, whch means that no transformaton of the nput space s made. Ths has the purpose of the vsua vadaton of the agorthm's performance. B. Expermenta Resuts Fg. 4 and Fg. 5 show the output of the agorthm for the experments performed. Antgens are represented as crces and B ces are represented as crosses. Notce that n both experments, B ces are ocated n the antgen regons, and regons free from antgens reman empty. Ths suggests that the agorthm s abe detect custers. Another property that can be seen s that the number of B ces s ow compared to the number of antgens. Notce that ths agorthm does not perform data compresson, as the orgna anet does, because each antgen presented to the networ s ncuded n a near combnaton that defnes a B ce. Tang nto account these resuts, we can say that t performs we n spaces where custers appear to be we separated. As the mode has been presented as a erne method, we coud tae advantages from the erne trc n order to transform spaces of nput data wth dfferent custer structures nto spaces where they appear to be we separated. V. CO NCL USI O N In ths paper a erne based mode for artfca mmune networs was ntroduced. A ey concept for ths mode s the representaton of antbodes as near combnatons of antgens, whch aows the defnton of a mutaton mechansm wthout assumng a vector representaton of antbodes. The mode assumes an affnty measure between antgens, whch s an dea present n the current modes and supported by the shapespace concept, but not expcty mentoned. Expermenta resuts on synthetc data gave a good nsght of the abty of the proposed mode for detectng custers. Some ssues were mentoned regardng the modfed verson of the anet mode, whch suggest some tass for future wor, namey to test the use of the erne trc wth dfferent nds of custer structures, to ncude the dea of "antbody saturaton", whch means that a B ce can be defned by a mted number of antgens, and to appy the mode to a non vector data set. ACKNOWLEDGMENT Authors than to members of the Integent Research Lab. and Bongenum Research Lab. for ther support n ths proect. REFERENCES [1] Ath Abraham, Swagatam Das, and Amt Konar. Kerne based automatc custerng usng modfed partce swarm optmzaton agorthm. 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Gaeano, A. Veoza Suan, and F. A. Gonzáez. A comparatve anayss of artfca mmune networ modes. In H. Beyer, edtor, Proceedngs of GECCO 005, pages ACM Press, 005. [9] Davd E. Godberg. Genetc Agorthms n Search, Optmzaton and Machne Learnng. Addson Wesey, [10] J. E. Hunt and D. E. Cooe. Learnng usng an artfca mmune system. Journa of Networ and Computer Appcatons, 19:189 1, [11] A. Ishguro and Y. Uchawa. A gat acquston of sxegged robot usng mmune networs. In Proceedngs of the Internatona Conference on Integent Robotcs and Systems (IROS?94), voume, pages , Munch, Germany, [1] Kng Wa Lau, Huun Yn, and Smon Hubbard. Kerne seforgansng maps for cassfcaton. Neurocomputng, 69: , 005. [13] R. S. Ledey and C. Y. Suen. Pattern recognton, the ourna of the pattern recognton socety, October 006. [14] G. C. Luh and W. W. Lu. Reactve mmune networ based mobe robot navgaton. In G. NcosaV. CuteoP. J. Bentey. Tmms, edtor, Proceedng of the Thrd Conference ICARIS, pages Sprnger, 004. [15] Nea. M. Meta stabe memory n an artfca mmune networ. In P. Bentey J. Tmms and E. Hart, edtors, Proceedngs of the Second Internatona Conference ICARIS, pages , Ednburg, UK, September 003. Sprnger. [16] D. MacDonad and C. Fyfe. The erne sef organsng map. In Proc. 4th nt. conf. on nowedge based ntegence engneerng systems and apped technooges, pages , 000. [17] R. Mchean and F. J. Von Zuben. Decentrazed contro system for autonomous navgaton based on an evoved artfca mmune networ. In Proceedngs of the IEEE Congress on Evoutonary Computaton, voume, Honouu, HI, May 00. IEEE. [18] O. Nasraou, C. Cardona, C. Roas, and F. Gonzáez. Tecnostreams: Tracng evovng custers n nosy data streams wth a scaabe mmune system earnng mode. In Thrd IEEE Internatona

7 Haca un Modeo de Red Inmunoógca Artfca Basado en Kernes Gaeano, Gonzáez 71 Conference on Data Mnng,Mebourne, FL, November 003. IEEE. [19] O. Nasraou, F. Gonzáez, and D. Dasgupta. The fuzzy artfca mmune system: Motvatons, basc concepts and appcaton to custerng and web profng. In IEEE Internatona Conference on Fuzzy Systems, pages , Hawa, HI, May 00. IEEE. [0] M. Nea. An artfca mmune system for contnuous anayss of tme varyng data. In J. Tmms and P. J. Bentey, edtors, Proceedngs of the 1st Internatona Conference on Artfca Immune Systems (ICARIS), voume 1, pages 76 85, Unversty of Kent at Canterbury, September 00. Unversty of Kent at Canterbury Prntng Unt. [1] Z. S. Pan, S. C. Chen, and D. Q. Zhang. A erne base SOM cassfer n nput space. Acta Eectron. Sn., 3:7 31, 004. n Chnese. [] A. S. Pereson and G. Wesbuch. Immunoogy for physcsts. Revews of Modern Physcs, 69(4): , October [3] Bernhard Schopf and Aexander J. Smoa. Learnng wth Kernes: Support Vector Machnes, Reguarzaton, Optmzaton and Beyond. The MIT Press, December 001. [4] A. Secer, A.and Fretas and J. Tmms. Asec: An artfca mmune system for e ma cassfcaton. In H. Abbass T. Kay Chen R. McKay D. Essam R. Sarer, R. Reynods and T. Gedeon, edtors, Proceedngs of the Congress on Evoutonary Computaton, page 131? 139, Canberra. Austraa, December 003. IEEE. [5] J. Shawe Tayor and N. Crstann. Kerne Methods for Pattern Anayss. Cambrdge Unversty Press., 004. [6] J. Tmms, Nea M., and J. Hunt. An artfca mmune system for data anayss. BoSystems, 55: , 000. [7] J. Tmms and M. Nea. A resource mted artfca mmune system for data anayss. Knowedge Based Systems, 14:11 130, 001. J uan Caros Gaeano. Earned hs bacheor's degree n computer scence and engneerng from the Natona Unversty of Coomba at Bogota, and he s currenty a master student n computer scence and engneerng at the same unversty. Fabo A. Gonzáez. Earned hs bacheor's degree n computer scence and engneerng, and hs master's degree n mathematcs from the Natona Unversty of Coomba at Bogota. He aso earned a master's degree and a PhD degree n computer scence from the Unversty of Memphs, USA. He s currenty an Assocate Professor of the Systems and Computer Engneerng Department at the Nacona Unversty of Coomba.

8 7 Revsta Avances en Sstemas e Informátca, Vo.5 No. 1, Edcón Especa, Medeín, Mayo de 008, ISSN III Congreso Coombano de Computacón 3CCC 008