BAYESIAN NETWORK AND ITS APPLICATION IN MAIZE DISEASES DIAGNOSIS

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1 BAYESIAN NETWORK AND ITS APPLICATION IN MAIZE DISEASES DIAGNOSIS Gufe Che, 2, Helog Yu,2,* Computer Scece ad Techology Isttute, Jl Uversty, Chagchu 3002, Cha 2 Iformato Techology Isttute, Jl Agrcultural Uversty, ChagChu 308, Cha * Correspodg author, Address: Iformato Techology Isttute, Jl Agrcultural Uversty, 2888 Cheg Street, ChagChu, 308, P. R. Cha, Tel: , Fax: , Emal: yuhelog@yahoo.com.c Abstract: Key words: Bayesa etwork s a powerful tool to represet ad deal wth ucerta kowledge. Ths paper maly troduces some techologes ad methods of modelg Bayesa etwork, whch are used the buldg Maze Dseases Dagoss system. I the costructo of Bayesa etwork, osy-or model ad trasformato from certaty factor to probablty are used. The maze dsease dagoss system based o BN s bult by Netca (a BN software package). The practce proves that BN s a effectve tool for maze dsease dagoss. Bayesa Network; maze; dsease; dagoss. INTRODUCTION There exsts a lot of ucertaty pheomeo ad problem. Ucertaty agrculture s more extesve ad complex. So, order to create a effectve tellget system, ucerta kowledge must be dealt wth. From represetato of ucertaty kowledge, there are two methods of dealg wth ucertaty. Oe s rule-based method, ad the other s modelbased method. The advatage of rule-based method s that ts computato s coveet, ad ts dsadvatage s that ts sytax s ot systemc. The advatage ad dsadvatage of model-based method are cotrary to the rulebased method.

2 Bayesa Network ad Its Applcato Maze Dseases Dagoss 927 From measuremet of ucertaty, the methods of dealg wth ucertaty are fuzzy theory ad probablty theory. Fuzzy theory maly deals wth vagueess, ad probablty theory maly deals wth radomess. Therefore, Bayesa etwork the artcle s a model-based probablty method. For the ucertaty agrculture, there are some good model ad applcato, but maly rule-based. Ths method s adapted to kowledge represeted by rule. However, ucertaty agrculture s varous. It s ot adequate for rule to represet ths ucertaty. I order to solve t, Bayesa etwork s troduced. It wdes kowledge represetato that creases the relablty of expert system. Bayesa etwork s a combato of probablty theory ad graph theory. Study of Bayesa etwork orgates from the 980 s. Sce 990 s, ts study ad applcato have strred great cocer. Compared wth rule based method, the sytax of Bayesa etwork s clearer, whch ca reaso dual drecto ad ca be costructed ad debugged rapdly. The dsadvatage of Bayesa etwork s that the computato complexty s hgh. Ths paper maly troduces the applcato of Bayesa etwork maze dsease dagoss system. As far as the computg complexty s cocered, the Bayesa etwork costructo, osy or techology are adapted to smplfy etwork structure ad codto probablty table. O rug the system, we fd that the result s coformed to doma expert. It proves that t s effectve to use Bayesa etwork to represet ad deal wth ucerta kowledge agrculture. 2. BAYESIAN NETWORK 2. Bayesa Network Sytax BN= (Structure, CPT) () Structure cota odes ad arcs Nodes: radom varable.! Nodes ca be cotuous or dscrete.! Nodes ca have two states or more.! Nodes ca be determstc or odetermstc. Arcs: relatoshps betwee odes.! Arcs represet causal relatoshps of odes.! Arc betwee x ad y represets that x has drect causal fluece oly. (2) CPT: Codto Probablty Table! Each ode has codto probablty whch s stored a table(cpt).

3 928 Gufe Che, Helog Yu! Value table s parets( )), parets( ) s the set of paret odes of.! Root ode s partcular, as t has o paret ode ad has oly pror probablty: parets ( ) = Φ, so parets( ))= ). 2.2 BN Sematcs! Local sematc: represet codtoal depedece the et! Global sematc: represet global probablty dstrbuto... ) = Parets( )) = We ca coclude that Bayesa Network s combato of etwork structure ad CPT, or global probablty dstrbuto s combato of codtoal depedece ad local probablty. 3. BN BUILDING Before beg deduced, Bayesa etwork must be costructed. As we kow, Bayesa etwork has two parts: structure ad CPT, so the process of costructg Bayesa etwork s to costruct structure ad CPT(Davd J.Spegelhalter,993). There are three methods to costruct Bayesa etwork: maual costructo, mache learg ad combato of them. Ths artcle maly troduces maual method, whch costructs Bayesa etwork by doma expert elctato(e.charles, J.Kah, etc,997). 3. Elcato of BN Structure I ths process, varables ad relatoshps betwee them should be determed. Frst, select varable set. It s mportat to lmt the umber of varables. So, t s ecessary to choose mportat varables whch are! Query varables: or object varables, they are outputs of et ad what we wat to kow.! Evdece varables: or observato varables, they are puts of et ad used to reaso states of query varables.! Cotext varables: or mddle varables, they are used to coect query varables ad evdece varables.! Cotrollable varables: or adjustable varables, they are used to cotrol ad adjust et. If objects are mutex, they ca be states of a varable, else beg varous

4 Bayesa Network ad Its Applcato Maze Dseases Dagoss 929 varables. Arc cause ->effect represet cause s oe of cause for effect. There are two cases:! Mult-causes, oe effect.! Oe cause, mult-effects. Accordg to the formula P (... ) =,..., ) 2,..., )... 2 ) ), we ca fd that the = ( Parets( ) ) = rght sequece of addg odes s:! Add root odes.! Add odes that be flueced drectly by root odes.! Repeat the above two steps utl leaf odes are added. 3.2 Elctato of Codto Probablty Table There are three kds of probablty, amely objectve probablty, frequet probablty ad subjectve probablty, whch orgate from data, doma experts ad lterature. I ths process, the state of each varable ad qualtatve probablty should be determed. Ths ca be obtaed by doma expert ad lterature. I order to decrease the sze of etwork, state umber should be lmted. I the meawhle, states should be mutex. Geerally, probablty gve by doma expert s qualtatve, so the trasformato from qualtatve probablty to quattatve probablty s ecessary (Table ). Table. The trasformato from qualtatve probablty to quattatve probablty Qualtatve Probablty Quattatve Probablty always 0.99 geerally 0.85 ofe 0.78 usually 0.73 Not ofe 0.50 sometme 0.20 occasoally 0.5 Usually ot 0.0 seldom 0.30

5 930 Gufe Che, Helog Yu 3.3 Two methods used buldg maze dsease dagoss system 3.3. Nosy-or Techology Ths model has three assumptos:! Parets ad chld are Boolea varables.! Ihbto of oe paret s depedet of the hbtos of ay other parets.! All possble causes are lsted. I practce ths costrat s ot a ssue because a leak ode ca be added (a leak ode s a addtoal paret of a Nosy-or ode). Now, we ca have a defto of osy-or:! A chld ode s false oly f ts true parets are hbted.! The probablty of such hbto s the product of the hbto probabltes for each paret.! So the probablty that the chld ode s true s mus the product of the hbto probabltes for the true parets. For Fg., we ca get ths formula: F H, H 2,... H ) = ( p ) = Geerally, for ode havg k paret odes, f use Nosy-or, t eeds k (k) parameters, f ot, t eeds ( 2 ) parameters. Obvously, BN s smplfed Trasformato from Certaty Factor to Probablty of BN H =reaso F=result I the maze dsease dagoss, the kowledge gve by doma expert s rule-based, ad measuremet for the belef s certaty factor, that s:

6 Bayesa Network ad Its Applcato Maze Dseases Dagoss 93 IF A THEN B CF(B A) Defto of certaty factor (CF): f > CF ( = 0f = f < p( However, the Bayesa etwork, ucertaty s measured by probablty. So, order to costruct Bayesa etwork, t eeds to trasform CF to probablty(f.tra. 996; Kev B.Korb, A E.Ncholso, 2006;Nev Lawe Zhag, 996). From above formula, we ca obta: CF( B A)( ) + fcf( B A) 0 P ( B A) =. ( CF( B A) + ) fcf( B A) < 0 So, order to get probablty, t eeds to kow, whch s pror probablty of ode B. ca be obtaed from doma expert, lterature, or assume = IMPLEMENTATION OF MAIZE DISEASE DIGNOSIS SYSTEM BASED ON BAYESIAN NETWORK Costruco of a Bayesa etwork for a doma problem eeds commucato ad cooperato of Bayesa etwork expert, doma expert ad BN software tool(p.j.f Lucas, 2005). There are two types of odes the Maze Dsease Dagoss System whch are dsease odes ad symptom odes. The dsease odes are Boolea varables, whch cota states: happe ad uhappe [P.J.F Lucas,200; Radm Jrousck,997], whle Symptom odes may cota multple states. Ths BN s a two-layer etwork, whch the upper layer s composed of dsease odes ad the lower layer s composed of symptom odes. Obvously the arc drecto s from dsease odes to symptom odes. Fg.2 s a part of BN structure for maze dsease dagoss. I ths structure there are four dsease odes ad four symptom odes, whch correspods to four dseases ad four symptoms. The four dseases are maze dwarf mosac, maze sheath blght, maze orther blght ad bpolarsmayds.

7 932 Gufe Che, Helog Yu Fg.2: A part of BN structure Wth the Nosy-or techology ad probablty trasformg from CF to probablty, ode s CPT s acheved. We ca fd the ferece results from Fg.3, whch are the posteror probablty of dsease whe plat shape s ormal, speckle posto s lama ad speckle shape s others. Fg.3: ferece results of the BN 5. CONCLUSIONS BN s a strog tool for represetg ad dealg wth ucerta kowledge. There exsts a lot of ucertaty kowledge maze dsease dagoss. So t s atural to use BN to buld maze dsease dagoss system. Whle buldg BN, Nosy-or model ad trasformato from CF to probablty are used to decreasg etwork scale ad smplfy the etwork structure. I rug the maze dsease dagoss system, we fd that the reasog result s coformed wth the soluto gve by doma expert, as proves that t s effectve to use Bayesa etwork to represet ad deal wth ucerta kowledge dsease dagoss. Obvously, BN ca be used the dagoss of maze pestcde, whch wll be doe the ear future.

8 Bayesa Network ad Its Applcato Maze Dseases Dagoss 933 ACKNOWLEDGEMENTS Ths artcle s supported ad fuded by Cha Natoal 863 Plas Projects (Cotract Number: 2006AA0A309). REFERENCES Davd J.Spegelhalter.993.Bayesa Aalyss Expert Systems, Statstcal Scece, Volume 8, Issue 3: E.Charles,J.Kah, etc.997.costructo of a Bayesa etwork for mammographc dagoss of breast cacer, Comut.Bol.Med: F.tra. 996.A bayesa etwork for predctg yeld respose of wter wheat to fugcde programs, Computers ad electrocs agrculture: -2. Kev B.Korb, A E.Ncholso Bayesa Artfcal Itellgece, CRC Press: Nev Lawe Zhag, 996.Explotg causal depedece Bayesa etwork ferece, Joural of artfcal tellgece: P.J.F Lucas, 2005.Bayesa etwork modelg through qualtatve patters. Artfcal Itellgece: P.J.F Lucas.200.Certaty-Factor-Lke structures Bayesa belef etworks, Kowledgebased systems: Radm Jrousck.997.costructg probablstc models, Iteratoal joural of medcal formatcs 45: 9-8.