INTELLECT SENSING OF NEURAL NETWORK THAT TRAINED TO CLASSIFY COMPLEX SIGNALS. Reznik A. Galinskaya A.
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1 Internatonal Journal "Informaton heores & Applcatons" Vol INELLEC SENSING OF NEURAL NEWORK HA RAINED O CLASSIFY COMPLEX SIGNALS Reznk A. Galnskaya A. Abstract: An expermental comparson of nformaton features used by neural network s performed. he sensng method was used. Suboptmal classfer agreeable to the gaussan model of the tranng data was used as a probe. Neural nets wth archtectures of perceptron and feedforward net wth one hdden layer were used. he experments were carred out wth spatal ultrasonc data, whch are used for car s passenger safety system neural controller learnng. In ths paper we show that a neural network doesn t fully make use of gaussan components, whch are frst two moment coeffcents of probablty dstrbuton. On the contrary, the network can fnd more complcated regulartes nsde data vectors and thus shows better results than suboptmal classfer. he parallel connecton of suboptmal classfer mproves work of modular neural network whereas ts connecton to the network nput mproves the specalzaton effect durng tranng. 1. ask descrpton Experence shows that learnng speed and decson s accuracy of complex tasks can be mproved usng dfferent methods of neural networks combnaton n the multmodular systems [Sharkey. 1996], [Sharkey et al, 1997]. Great amount of papers s dedcated to understandng the potental capabltes and practcal applcaton of modular neural networks. Most of these papers descrbe homogeneous multmodular structures based on feedforward neural networks. Methods of nput data preprocessng and dfferent types decson fuson modules are dscussed [Gacnto et al, 2001], [Crepet et al, 2000]. Multmodular archtectures based on dfferent neural network types are nvestgated [Crepet et al, 2000], [ang et al], [Happel et al, 1994]. Most of researches nclne to common concluson that multmodular neural networks act lke a number of experts, whch consder task from dfferent postons. Due to such organzaton decsons based on local reactons of ndvdual neural ensembles are more nfallble. Unfortunately, smple mechancal transfer of collectve human expert behavor to the neural ensembles, level of complexty (and ntellect) of whch could be compared may be only wth worm s neural system, hardly approprate. Of course, neural network s able to learn and take self-dependent decsons, and so we can consder that t has artfcal ntellect that characterzed by outer world models presence. But such nterpretaton cannot be used for understandng nner procedure of formng and co-ordnaton of neural modules decsons. In our nvestgaton we used sensng method for clarfyng factors that defne behavor of traned neural network. For ths purpose statstcally optmal recever solvng the same problem that neural network was used. We proceed from that neural network durng tranng tends to statstcally optmal behavor for defned tranng set and errors crtera. Havng statstcal dstrbuton for tranng data t s possble to create statstcally optmal devce that satsfes defned crtera of work qualty and estmates the characterstcs of traned network s behavor. Combnng such optmal devce wth neural net n modular structure t s possble to nvestgate ther nteracton durng tranng and decson-makng. Nature of nformaton features of ntal data, whch neural network uses for makng decson, can be understood by varyng dfferent combnaton methods. Unfortunately, t s necessarly to have consstent estmates for every combnaton of tranng set elements values to create statstcally optmal devce. It s almost mpossble for bg data sets. But f data vectors elements have weak statstcal dependence we can assume that the condtons of central lmt theorem are met. In ths case the gaussan model of dstrbuton for tranng set can be a good approxmaton. hs model consders frst two moments of dstrbuton: average and covaraton. It s easy to obtan the estmatons for ther values. Havng such estmatons we can create suboptmal recever that reflect the man features of tranng data set. he goal of ths work s expermental nvestgaton of descrbed approach to the analyss of real neural net behavour. Comparson of behavour of suboptmal classfer and neural net was carred out wth spatal ultrasound sgnals used n car s passenger safety system. Analysng these sgnals neural net should estmate level of safety for passenger poston and block ar-bag deployment f passenger can be damaged. All
2 174 Internatonal Journal "Informaton heores & Applcatons" Vol.10 experments were carred out wth a help of MNN CAD software [Kussul et al, 2002] usng data provded by Automotve echnologes Internatonal (AI Inc. Danvlle, New-Jersey, USA). 2. Descrpton of nvestgated neural archtectures Fve base classfer models were used durng experments: 1. Feed-forward neural network wth one hdden layer; 2. Smple perceptron; 3. Lnear suboptmal classfer; 4. Quadratc suboptmal classfer; 5. Combnaton of lnear and quadratc suboptmal classfers. Experments were carred out wth a help of MNN CAD [Kussul et al, 2002] software that allows creatng multmodular structures usng dfferent types of neural networks and addtonal modules. Fgure 1 shows the archtecture of one of the used methods of modules combnaton. It s composed of feedforward neural net (module B3) and suboptmal classfer (B4). Fuson module (B5) conssts of one neuron. Module B1 s used for nput vector normalzaton, module B2 forms target vectors of all modules durng tranng. Fg. 1. Multmodular classfer archtecture (Var2) We examned 12 dfferent varants of classfer ncludng 5 base models, combnaton of feedforward network wth perceptron and 6 types of hybrd modular network that combned feedforward net wth suboptmal classfer. wo ways of constructon of such hybrd network were used. In the frst net s varant (Var1) suboptmal classfers were connected to addtonal nput of neural network that s addtonal component of nput vector was created. In the second structure type (Var2) we used addtonal fuson neuron wth output of neural network and normalzed suboptmal classfer s output as ts nputs. In both varants neural network was traned after connecton of suboptmal classfer that s ts reacton took part n the neural network s decson formng. 3. Structure of suboptmal classfer In our task tranng data set conssts of vectors X for two classes 0 and 1. We consder that data s dstrbuted normally. Frequency dstrbuton of probablty for th class s: 1 1 W ( X ) = exp ( X A ) Ψ ( X A ). N 2 2 (1) π Ψ Here ( ) Ψ s the covarance matrx for data of -th class; Ψ s the determnant of the matrx Ψ ;
3 Internatonal Journal "Informaton heores & Applcatons" Vol A s the average of dstrbuton of X; X. X s the transposed vector; N s the dmenson of the vectors A statstcally optmal soluton that provdes a mnmum rsk of error s based on a threshold estmate of the value (X) that defnes structure of optmal classfer [Mddleton, 1960] : ( X ) = lnw1 ( X ) lnw0 ( X ), (2) Decson of the stuaton ether 0 or 1 s made after results of comparson of value (X) wth the threshold that depends on the relatonshp between the costs of losses caused by errors to one or the other sde. After substtuton of expresson (1) to (2) obtan: 1 ( X ) = const + X ( A1 Ψ1 A0 Ψ0 ) X ( Ψ1 Ψ0 ) X (3) 2 1 const = ( ln Ψ0 ln Ψ1 + A0 Ψ0 A0 A1 Ψ1 A1 ). 2 he second and the thrd terms of the expresson that depend on X defne the lnear and the quadratc components of the classfer. he functon of the former can be represented by the followng sum: N S = u x, (4) l where = 1 u are components of the optmum flter vector: U = A1 Ψ1 A0 Ψ0. (5) he quadratc component functon of the classfer s: 1 ( Ψ Ψ ) X 1 Ss = X 0 1. (6) 2 Usng expressons (4)-(6) we can create suboptmal classfer wth sample estmates of dstrbuton average and covaraton matrces for tranng set. If the covaraton matrces values for both classes are smlar then optmal classfer conssts of only lnear part. Also t s possble that lnear component (5) s zero so optmal s the quadratc classfer (6). 4. Statstcal characterstcs of data set he data vectors used are sequences of 124 short nteger values of output sgnals of four ultrasound sensors. Data was dvded nto three groups: ran vectors; est vectors and Vald vectors, whch were used for tranng, testng durng tranng and network valdaton correspondngly. Each array conssts of 0 class vectors (safe passenger poston) and 1 class vectors (ar-bag deploy should be blocked) wth approxmately equal amount. Statstcal characterstcs of vectors obtaned on ran data set are shown on Fgure 2. On ths fgure dagonal elements of the matrces and the boundares of the sensor areas can be clearly seen. Dfferences of covaraton matrces (on the rght wndow) are the most pronounced classfcaton features of spatal sgnals. A, Fg. 2. Covarance matrces for classes 0 and 1 and ther dfference (on the rght).
4 176 Internatonal Journal "Informaton heores & Applcatons" Vol.10 he results of data analyss shown on Fg. 2 were used to suboptmal classfer s components calculaton (4-6). Fgure 3 shows values of lnear part U of flter. 5. Neural modules Before nvestgaton of modular network wth suboptmal classfer n t we chose the best archtecture of neural network. Best results were obtaned usng three-layer neural network wth 15 neurons n hdden layer. Sgmod actvaton functon and EDBD learnng algorthm [Reed et al, 1999] were used. Input data was normalzed n [0,1] dapason. Normalzaton was made ndependently for each nput usng tranng data set. Intal values for neural network module were defned by random values. Each experment was carred out 5 tmes and results were averaged. Perceptron module conssted of one neuron wth sgn actvaton functon and was traned usng Hebb learnng rule. Intal weghts for ths module were zero. Weght coeffcents obtaned durng tranng are shown on Fg. 3. he same fgure shows weghts of suboptmal lnear flter (5). Poston of extreme values s smlar for both charts. Suboptmal flter has strong extremes only n the range of nputs. In contrast to ths values of nput s weghts for perceptron dstrbuted more equally. Fg. 3. Weght coeffcents of perceptron and suboptmal lnear flter 6. Results of ndependent modules testng able 1 shows comparatve testng results for base classfer s models on ran and Vald data sets. able 1. Error rate for base modules. ype ran % Vald % SO/Lnear SO/Square SO/Ln. + Sq Perceptron Neural network able shows that feedforward neural network gves best results. Perceptron and suboptmal classfer (even wth both lnear and quadratc components) show much worse success rates. Suboptmal classfer shows better results than perceptron on tranng data set but much worse on valdaton set. So we can conclude that neural network durng tranng fnds more complex assocatve relatons than contaned n average values and mutual correlaton functons. o some extent the same suggestons can be appled to perceptron, decsons of
5 Internatonal Journal "Informaton heores & Applcatons" Vol whch are based on lnear transformaton of nput data. hs transformaton s smlar to that lnear suboptmal classfer uses. Fgure 4 shows hstograms of reactons of suboptmal classfer and perceptron for two data classes. Dagrams correspond (left to rght) to the nonlnear component, lnear component, full suboptmal classfer and postsynaps values of perceptron. Under each dagram there s the threshold value and the average number of correct decsons for each stuaton class. It can be seen that results for separate lnear and quadratc classfers are much worse than for full classfer. Dstrbuton of potental at the perceptron s nput s smlar to the dstrbuton of reacton of full suboptmal classfer. Class (threshold = 7) (threshold = - 5) (threshold = - 4) (threshold = 0) 0 / / / / / 5.82 otal % Fg. 4. Hstograms of reactons for suboptmal classfer and perceptron. Left to rght: lnear, quadratc, full suboptmal classfer, perceptron (ran data set). 7. Experments wth hybrd networks. he goal of experments was to understand the mportance of classfcaton features used by suboptmal classfer. We tested hybrd networks Var1 and Var2 wth lnear, quadratc and full suboptmal classfers. hus neural network before tranng had all useful nformaton that suboptmal classfer extracts from nput data. Also we nvestgated varant of hybrd network Var2 where already traned perceptron was used nstead of suboptmal classfer. ranng was carred out usng Save Best method untl 1.5M vectors tranng depth. Best result was saved. Each experment was carred out 5 tmes wth dfferent weght ntalzaton. In each seres of experments average and mnmum error rates were calculated. Expermental results are shown n able 2. Data n the last row of table for Var2 were obtaned whle autonomous testng of neural network wthn hybrd network Var2. Mode SO/ Lnear SO/ Square SO/ Ln. + Sq. Perceptron Neural network able 2. Expermental results for two types of hybrd network Var1 Var2 est mode Avg.% Mn% Avg.% Mn% ran est Vald ran est Vald ran est Vald ran est Vald ran est Vald
6 178 Internatonal Journal "Informaton heores & Applcatons" Vol.10 estng results on ran data set show that connecton of suboptmal classfer leads to decreasng of classfcaton errors for both types of hybrd network. Best results were obtaned usng both lnear and quadratc components of suboptmal classfer. But for est array there s no such mprovement and error rate on Vald data set even ncreased for Var2 network. estng of Var2 network on ths array gves opposte result error rate decreases almost on one thrd. Connecton of perceptron n Var2 network also decreases error rate for all data arrays. But success rate s worse than wth connecton of suboptmal classfer. Quanttatve estmaton of nformaton level of suboptmal classfer s decson can be obtaned by comparson of weghts values for the nputs of fuson neuron n Var2 network. able 3 shows these estmatons. We used such symbols: W NN weght value for neural network s output; W SO weght value for suboptmal classfer s output; k=w SO /(W NN +W SO ) nformaton level for correspondng component. Informaton level s about 15% for lnear component of suboptmal classfer, for quadratc t s much hgher more than 25%. Naturally hghest nformaton level was obtaned for sum of components more than 37%. Estmaton of nformaton level for perceptron appears enough unexpected less than 3%. 8. Concluson able 3. Estmaton of nformaton level for gaussan features n hybrd neural network Mode W NN W SO k = W SO / (W NN + W SO ) SO/ Ln SO/ Sq SO/ Ln. + Sq Perceptron Dstrbuton of used expermental materal s close enough to multdmensonal gaussan dstrbuton. So we could expect that neural network wll use manly the same classfcaton features that suboptmal classfer does. But neural network behavor shown s far from that. Neural network fnds complex assocatve relatons between data elements durng tranng. But t does not fully make use of more smple correlaton dependences used by suboptmal classfer. As t can be seen n able 2, t s obvous that connecton of suboptmal classfer always decreases error rate of neural network. Success rate mprovement s the most when suboptmal classfer s connected to fuson neuron (Var2). Improvement effect n ths case s the strongest for Vald data set. hs s a very mportant result. It shows that generalzaton ablty was mproved. Also we can conclude that decson-makng crtera used by neural network and suboptmal classfer are relatvely ndependent. If suboptmal classfer s connected to neural network nput (Var1) success rate ncreases only for ran data set. It shows that specalzaton effect becomes stronger due to suboptmal classfer s connecton. We found such effect for the frst tme and have no explanaton for t yet. We can only suppose that neural network s hdden layer blocks nformaton flow from suboptmal classfer to network s output. he nature of ths phenomenon s unclear but we can make practcal suggeston that the most nformatonal features should be connected closer to output of hybrd neural network. Low nformaton level of perceptron connected to fuson neuron appeared qute unexpected. Its weght s less than 3% that s much less than for lnear and quadratc suboptmal classfers (15% and 25%). hs s opposte to results shown n able 2. We can suppose that n ths case nformaton features formed by neural network have the same character that for perceptron but they are much more powerful. So perceptron contrbuton to the fnal decson s nsgnfcant. Acknowledgments he work s supported by INAS grant "Smart Sensors for Feld Screenng of Ar Pollutants". he authors wsh to thank Davd Breed and AI Inc. for the gvng data sets. Bblography [Sharkey, 1996] Amanda J.C. Sharkey, On combnng artfcal neural nets. - Connecton Scence V N. 3/4. - P
7 Internatonal Journal "Informaton heores & Applcatons" Vol [Sharkey et al, 1997] Amanda J.C. Sharkey, Noel J. Sharkey, Combnng dverse neural networks. - he Knowledge Engneerng Revew V. 12: 3. -P [Gacnto et al, 2001] Gorgo Gacnto, Fabo Rol, Desgn of effectve neural network ensembles for mage classfcaton purposes. - Image and Vson Computng. -Elsever Scence V P [Crepet et al, 2000] Agnes Crepet, Helen Paugam-Mosy, Emanuelle Reynaud, Dder Puzenat, A modular neural model for bndng several modaltes/ In Proc. of IC-AI'2000, Int. Conf. of Artfcal Intellgence. - Las Vegas, USA P [ang et al] Bn ang, Malcolm I. Heywood, Mchael Shepherd, Input Parttonng to Mxture of Experts [Happel et al, 1994] Bart L.M. Happel, Jakob M.J. Murre, he desgn and evoluton of modular neural network archtecture. - Neural Networks V. 7. P [Kussul et al, 2002] Kussul M., Rznyk A., Sadovaya E., Stchov A., Chen.Q. A vsual soluton to modular neural network system development // Proc. of the 2002 Internatonal Jont Conference on Neural Networks IJCNN'02. - Honolulu, HI, USA May. - Vol.1. - N749. [Mddleton, 1960] D. Mddleton, An Introducton to Statstcal Communcaton heory, V. 2., [Reed et al, 1999] R.D. Reed and R.J. Marks, Neural Smthng. MI Press P Author nformaton Reznk A., Galnskaya A. - Department of neural technologes, Insttute of Mathematcal Machnes and systems NAS Ukrane. neuro@mmsp.kev.ua APPLICAION OF HE SUFFICIENCY PRINCIPLE IN ACCELERAION OF NEURAL NEWORKS RAINING Krsslov V.A., Krsslov A.D., Oleshko D.N. Abstract: One of the problems n AI tasks solvng by neurocomputng methods s a consderable tranng tme. hs problem especally appears when t s needed to reach hgh qualty n forecast relablty or pattern recognton. Some formalsed ways for ncreasng of networks tranng speed wthout loosng of precson are proposed here. he offered approaches are based on the Suffcency Prncple, whch s formal representaton of the am of a concrete task and condtons (lmtatons) of ther solvng [1]. hs s development of the concept that ncludes the formal ams descrpton to the context of such AI tasks as classfcaton, pattern recognton, estmaton etc. Keywords: neural networks Introducton Nowadays developers have a lot of dfferent models of neural networks and algorthms of ther tranng [2, 3] for dsposal. hough the scentfc researches are permanently carred on n ths feld, the theory of neural networks s stll feebly formalsed. However, even now two stages of creaton of artfcal neural systems could be defned: structural and parametrc synthess. At the frst stage, developer has to do the followng: choose the model for the network, defne ts structure and choose the algorthm for ts tranng. he parametrc synthess ncludes tranng processes of the created network and verfcaton of the obtaned results. hen, dependng on verfcaton results, there can be a necessty of return to one of the stages of structural or parametrc synthess. hus, becomes obvous that creaton of the neural system s an teratve process. Feeble formalsaton of these stages results n necessty for the developer of the neural system to solve a number of problems. E.g., at the structural synthess stage, n case of solvng a non-standard task, t s necessary to spend a lot of tme for choosng the correspondng model for the network, choosng ts structure and tranng method. he problem of the parametrcal synthess s a consderable tranng tme. If real tasks are beng solved wthout any smplfcaton, then duraton of tranng process for created network could be too long. However, some tasks requre spendng as less tranng tme as t s possble, e.g., real-tme tasks. he am of the gven artcle s to offer possble methods to reduce the tranng tme for neural networks wth back propagaton tranng algorthm. As such methods are offered: control of procedures of modfcaton and
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