A Novel Spatial Interpolation Method Based on the Integrated RBF Neural Network

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1 Avalable onlne at Proceda Envronmental Scences 10 (2011 ) rd Internatonal Conference on Envronmental Scence and Informaton Applcaton Technology (ESIAT 2011) A Novel Spatal Interpolaton Method Based on the Integrated RBF Neural Network Scong Lu, Yufeng Zhang*, Panhua Ma, Bng Lu, Hong Su Department of Electronc Engneerng, Informaton School, Yunnan Unversty,Kunmng,Yunnan, P.R.Chna Abstract Wth the development of the GIS and computer technology, t s necessary to use samplng data for spatal analyss n ther researches. However, the emergence of spatal data nterpolaton algorthms makes t possble for us to get contnuous spatal data that satsfy certan accurate requrement. These tradtonal methods are sufferng some lmtatons, such as strong subjectvty, numerous assumptons, poor adaptve varaton, etc. Ths paper presents a noval approach by usng the establshment of ntegrated radal bass functon (RBF) neural network for mprovng the spatal nterpolaton performance. Based on the expermental results on the lead element content n the sol n Kunmng and ts extensonal areas through spatal nterpolaton by RBF network, t can be concluded that the proposed approach provde the more detal spatal dstrbuton than that by usng the tradtonal methods Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Selecton and/or peer-revew under responsblty of Conference ESIAT2011 Organzaton Commttee. KeyWords: ntegrated RBF network; Krgng method; spatal nterpolaton analyss 1. Introducton Wth the development of the GIS and computer technology, researchers are less satsfed wth only usng samplng data for spatal analyss. The reason s that spatal nformaton s omsson besdes the gven samplng ponts. It s dffcult to get the desred spatal dstrbuton results by only usng the tradtonal spatal nterpolaton methods from dscrete samplng data for spatal trend predcton. Thus, the focus s on how to get the contnuous space data. The emergence of spatal data nterpolaton algorthms ncreases the possblty of gettng contnuous spatal data whch satsfes certan accurate requrement. In the current perod, the most used nterpolaton methods are Krgng nterpolaton algorthm, the nverse dstance weght nterpolaton algorthms, etc. However, these methods have the followng lmtatons: strong subjectvty, numerous assumptons, poor adaptve varaton, etc. The neural network has a strong nonlnear fttng ablty, and ts outputs automatcally match the system nputs accordngly. It can map arbtrary complcated nonlnear relaton. It s easy to be learned, and be recognzed by computer. The neural network has strong robustness, memory capacty, nonlnear mappng capacty and strong self-learnng ablty as well. However, sngle neural network generalzaton ablty s lmted. In 1990, Hansen and Salamon proposed neural network ntegraton *Correspondng Author Tel.: E-mal address: yfengzhang@yahoo.com Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Selecton and/or peer-revew under responsblty of Conference ESIAT2011 Organzaton Commttee. do: /j.proenv

2 Scong Lu et al. / Proceda Envronmental Scences 10 ( 2011 ) method, and they proved that neural network generalzaton ablty could be mproved sgnfcantly by smply tranng multple neural networks and combnng ther results. Ths method s easy to use and has dstnct effect; therefore t s consdered as an effectve engneerng neural computatonal technology. Commonly used neural network s the BP (Back Propagaton) neural network or RBF (Radal Bass Functon) neural network. BP neural network can learn and store a lot of nput/output model mappng relatonshp wthout revealng before the mathematcal equatons whch descrbe the mappng relatonshp. It adjusts network weghts and network threshold constantly by reversng transmsson error to ensure mnmum network error quadratc sum. But ts convergence speed s slow and t requres longer tranng tme because of the fxed learnng rate. For complex problems, BP algorthm takes excessve amount of tme. Compared wth BP network, RBF (radal bass functon) neural network has hgher convergence rate, t can determne correspondng network topology structure accordng to the specfc ssues and self-study, organzaton, adaptve functon. The output layer s drectly connected to ts hdden layer. The transfer functon of the RBF neural network hdden n layer unt s symmetrcal RBF (such as Gaussan functon). RBF network has approxmaton to nonlnear contnuous functon, and t can learn at hgh speed and undertake a wde range of data fuson and hgh-speed processng data n parallel. Therefore, ths paper adopts the ntegrated neural network, whch s made up by RBF neural network, to mprove the accuracy through the space data nterpolaton for lead s content n the sol and eventually make a comparson wth Krgng nterpolaton method. 2. Materals In ths research, Kunmng and ts geologcal surroundngs were chosen as research area whch s located n the md-eastern Yunnan-Guzhou Plateau. It belongs to low lattude mountan plateau and has monsoon clmate. The ground slopes from north to south, most between 1500 and 2800 meters above sea level whle the maxmum alttude s 4247 meters, the mnmum alttude s 746 meters, and average alttude s 1894 meters. The Kunmng cty, whch s located n the north of Danch lake basn. Surrounded by mountans, has a good spatal envronment. The annual average temperature s 14.5, wth the hghest temperature s 19.7, the lowest s 7.5. The annual average precptaton s 1,035 mllmeters, relatve humdty s 74% and t snows rarely. The area of land s square klometers, ncludng hlly and mountanous area for square klometers, whch accounts for 84% of the total area; flat area for 2011 square klometers whch accounts for about 12.9% and lake area for 337 square klometers, accountng for approxmately 2.16% of the total area. The whole Kunmng cty s red loam area manly wth three knds of sol: red loam, purple sol and rce sol, whch are ft for plantng gran crops, such as paddy, wheat, beans, corn, economc crops, such as rape, tobacco, vegetables and flower, and economc fruts, such as peaches and pears, oranges. In addton, there are mllon hectares of forest area n the cty. 3. Samplng plan All data n ths paper are from the frst project of "Sol Polluton Investgaton n Yunnan Provnce". Accordng to "The Natonal Survey of Sol Polluton Condton of Techncal Regulatons Statonng and Codng Rules", there are 1718 regonal stes on the Yunnan Provncal map, whch s under 1: dgtal. The number of the cultvated land stes s 956 about 55.6% of the total number; forest and grassland stes(except prmtve forests) are 550, accountng for 32.0%; nature reserve ponts are 204, occupyng 11.9%; constructon land stes s 8, accountng for 0.5%. Ths paper selects 354 stes as the samplng spots n Kunmng and 557 stes n the surroundng area. To test the nterpolaton precson of nterpolaton methods, ths expermentaton classfes the sample ponts. The prncples are followng:

3 570 Scong Lu et al. / Proceda Envronmental Scences 10 ( 2011 ) plan a, the number of the tranng samples are ncreased from 10 ponts to 330 ponts, wth 100 ponts for test usng. Plan b, the sample ponts for tranng s 4/5 of the total, and the test sample ponts are 1/5 of the sample ponts. All the tranng samples and test samples are random varables. 4. Methods 4.1. Krgng nterpolaton Krgng method s a method that s based on varogram spatal analyss and the value comes from lmted area regonalzed varables and the optmal estmaton for unbased. Krgng method states that spatal varables are regonalzed varables. It s spatal varaton as well as self-smlarty, whch requres spatal varable to have structure and randomcty to meet some assumptons, such as the two-order smooth hypothess, and the egenvalue hypothess. ntegrated RBF neural network nterpolaton method, etc Integrated RBF neural network nterpolaton The neurons of RBF neural network use radal bass transfer functon, wth two structural layers. The frst layer s mpled n radal bass functon layer, and the second layer s output lnear layer. The mappng relatonshp of surface s stored n network connecton weghts and threshold whch make RBF neural network wth strong fault tolerance and functonal approxmaton ablty. RBF neural network has two groups of parameters: 1) hdden layer node center, the wdth and the number of hdden nodes; and 2) hdden layer to the output layer weght. As shown n fgure 1 below: Fg.1. The RBF neural network model

4 Scong Lu et al. / Proceda Envronmental Scences 10 ( 2011 ) Ths experment adopted Baggng technology due to better mplement and more stable, researchers can use mean algorthm or weghtng method to make the fnal concluson. In some occasons whch do not call for hgh accuracy, researchers could get the fnal result by usng mean algorthm. Compared wth mean algorthm, weght algorthm can obtan output value n a hgher precson. Ths paper uses the weght algorthm to acqure the fnal data. Each chld neural network weghts calculaton process as follows: Assume that chld neural networks have fnshed tranng. Ther results rmse (=1 pn), take thers bottom: w 1/ rmse W w / w, and W 1 (1) Therefore, the calculaton formula of ntegrated neural network s result s: R W * r (2) th Where R s ntegraton neural network s output; w s the ndvdual neural network s weght; r s th the ndvdual neural network s output. As shown n fgure 2 below: Fg.2. The Integrated RBF neural network dagram In ths paper, the development platform s Matlab, Verson s 2009a, whch s acheved by usng neural network programmng tool kt Interpolaton performance evaluaton The root mean square error (RMSE) defned n (3) s used as an ndex for evaluaton of the nterpolaton performance. The calculaton formula s defned as: RMSE n 1 2 ( z z) / N (3)

5 572 Scong Lu et al. / Proceda Envronmental Scences 10 ( 2011 ) Where z s predcton value of Krgng method or Integrated RBF neural network method; z s real value; N s the sample number of test samples. The smaller the rmse value s, the hgher the nterpolaton accuracy s and the smaller the error s. 5. Results and dscusson 5.1. Lead element descrptve analyss A basc statstcal characterstc manly reflects the spatal varaton of lead element n sol n dfferent plans. The partal degrees reflect double tal characterstcs of normal dstrbuton. The kurtoss reflects sample space s centralzed level. The coeffcent of varablty reflects the sample space degree of dsperson. Analyss result under dfferent scheme shows n Table 1 below: Table 1. Statstcal characterstcs of element Lead n dfferent projects Project Samples Max value Mn value average Coeffcent of varaton kurtoss Partal degrees value A % B % Accordng to Table 1, t concludes that the ampltude of lead element n both two projects vares dramatcally. The coeffcent of varaton s 94.65% n project a, but t s 57.62% n project b. The data n Table 1 shows that: lead element spatal varaton degree n study area s hgh. And there are many random factors to nfluence lead element spatal dstrbuton, whch lead to the complex spatal dstrbuton. In both projects, the lead element samples appear skewness dstrbuton. If researchers use land statstcal method to analyse these samples, they need to undertake logarthmc converson to make t close to normal dstrbuton Interpolaton result analyss Usng ntegrated RBF neural network and Krgng method separately, dfferent projects tranng to tran, and then use test sample to test. Interpolaton precson analyss s as shown n Fg.3.(left) and Fg.3.(rght) below. In Fg.3.(left), X axs s for numbers of test samples, and Y axs s for error values. In Fg.3.(rght), X axs s for the dstance from Kunmng cty; Y axs s for error values.

6 Scong Lu et al. / Proceda Envronmental Scences 10 ( 2011 ) Fg.3. (left) The error curves of project (a); (rght) The error curves of project (b) Project a: the number of tranng samples s from 10 ponts to 330 ponts, the nterval of 10 ponts. Hollow crcle n the fgure represents the predctve value of Krgng method. Cross n the fgure represents the predctve value of Integrated RBF neural network. The number of test samples s 100 ponts. All data are selected random. Fg.3.(left) shows that Krgng method error s hgh and the performance s nstable. The maxmum error of Krgng method s 7 tmes hgher than the error of ntegrated RBF neural network. Compared to Krgng method, ntegrated RBF neural network error s much lower and ts performance s more stable. Project b: Takng Kunmng as the center and extendng around t, step length s 50KM, max dstance s 250KM.Tran set number s 4/5 of the total. Test set number s 1/5 of the total. All data are selected random. Hollow crcle n the fgure represents the predctve value of Krgng method. Cross n the fgure represents the predctve value of Integrated RBF neural network. Fg.3.(rght) shows that the error of Krgng method s becomng hgher when dstance ncreases. Compared to Krgng method, the error of Integrated RBF neural network grow slowly and nterpolaton accuracy s sgnfcantly better than Krgng method. Wth the ncrease of dstance, the error of Krgng method s becomng hgher. Compared to Krgng method, the error of Integrated RBF neural network grow slowly and nterpolaton accuracy s sgnfcantly better than Krgng method. Usng the same resoluton to dsplay the data got by two nterpolated methods, researcher gets Fg 4 (left) and (rght). Accordng to these two fgures, t s concluded that ntegrated neural network nterpolaton fgure shows more detals than Krgng method nterpolaton fgure. The Krgng method nterpolaton fgure has a strong tendency to smooth, but lead element n the sol has strong spatal varablty and complex spatal dstrbute. Therefore, the result of ntegrated neural network s more reasonable.

7 574 Scong Lu et al. / Proceda Envronmental Scences 10 ( 2011 ) Fg.4. (left) The results by usng Krgng; (rght) The results by usng neural network nterpolaton Concluson The expermental analyss shows that the predcton ablty of Krgng method s weak when the lead element n the samples has strong volatlty and spatal varaton degree. There are many constrant condtons when Krgng method has been used, and the predcton accuracy s low. Compared to Krgng method, Integrated RBF neural network has strong nonlnear functon fttng ablty, and there s no specal requrement of data. The predcton performance of ntegrated RBF neural network s more stable, and the predcton accuracy s better. Therefore the ntegrated RBF neural network s an effectve alternatves to tradtonal spatal nterpolaton method. Acknowledgment Ths work was supported by the Natonal Natural Scence Foundaton of Chna under Grant and the Yunnan Natural Scence Foundaton under Grant 2009CD016.

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