Study on the Prediction of Real estate Price Index based on HHGA-RBF Neural Network Algorithm

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1 pp Study on the Predcton of Real estate Prce Index based on HHGA-RBF eural etor Algorthm Huan Ma 1 Mng Chen 1 and Jane Zhang 1 1 Softare Engneerng College Zhengzhou Unversty of Lght Industry Zhengzhou Chna songge @163.com Abstract The tradtonal error of the bac-propagaton algorthm multlayer feed-forard netor (BP neural netor) there are the flas of a slo convergence of forecast gettng local mnmum solutons easly and forecast accuracy rate s not hgh. Ths paper proposes a ne approach hch s the combnaton of herarchcal genetc algorthm and least squares method to optmze the RBF neural netor such that e can predct the real estate prce of the Real estate Prce Index. And hch overcomes the shortcomngs of tradtonal Fourer analyss has good localzed characterstcs n the tme doman and frequency doman and has mportant value. In sgnal processng mage processng voce analyss and other felds. The herarchcal genetc algorthm s usually used to optmze the topology of the RBF neural netor the radal bass functon center and dth. Alternatvely the least squares method could play an mportant role n decdng the eghts of the output layer. The expermental result shos that the feasblty of RBF neural netor hch could be optmzed by the hybrd herarchcal genetc algorthm to predct real estate closng prce and the superorty of ths approach n the aspect of predcton accuracy verfed n comparng th the other to methods. Keyords: Real estate Prce Index predcton RBF neural netor herarchcal genetc algorthm least squares method 1. Introducton The real estate s a product of the maret economy. The real estate prce s determned by ts value but nfluenced by economc poltcal and socal many factors. By observng the movement of Real estate prce ndex people can grasp of the macro economc stuaton of the real estate maret and the changes n the maret or from the mcro level people also can tae an analyss accordng ts nvestment trend and the realzaton of these roles based on the analyss and forecast of real estate prce ndex. In recent years th the real estate maret contnued to heat up problems about the rs of the real estate ndustry have become ncreasngly promnent. Usng scentfc methods to reflect the changes n real estate prces and presentng a correct nformaton gude to the man maret has become very urgent. Generally speang there exst many ays to predct real estate prces. For tradtonal forecastng methods e adopt the applcaton of regresson analyss tme seres analyss and Marov model. Hoever tradtonal forecastng methods are mostly based on statstcal analyss of long-term large sample and t requres hgh regularty of the data dstrbuton and ntegrty of data. Exstng research ndcates that ntellgent forecastng models outperform tradtonal models especally n short-term forecastng [1]. In recent years artfcal ntellgence technques of genetc algorthms artfcal neural netor and supportng vector machne methods are appled to short-term predcton of the real estate maret by many scholars. ISS: IJUESST Copyrght c 2015 SERSC

2 For example Eram Guresen et al. evaluated the effectveness of neural netor models hch ere non to be dynamc and effectve n real estate -maret predcton [2]. A sngle model could only reflect the pece of nformaton of real estate prces hch s dffcult to dg the hdden varaton of prce of real estate data. Furthermore there are obvous lmtatons hen usng a sngle model such as the slo convergence speed and poor generalzaton. Hoever the combned model could utlze the nformaton provded by varous models to a large extenson hch ould mprove the predcton accuracy especally n economc management and statstcal research a number of predcton approaches have become an mportant ay to mprove forecast accuracy. For example Armano et al. optmzed A th GA to forecast real estate ndces [3]. Md. Raful Hassan et al. proposed a fuson model by combnng the Hdden Marov Model (HMM) Artfcal eural etors (A) and Genetc Algorthms (GA) to predct real estate prce [4]. Lee proposed a predcton model based on a hybrd feature selecton method and SVM to predct the trend of real estate maret [5]. We Shen et al. used the artfcal fsh sarm algorthm (AFSA) to optmze RBF to forecast real estate ndces [6]. Lng-Jng Kao et al. proposed a methodology hch as the ntegraton of nonlnear ndependent component analyss and support vector regresson for real estate prce forecastng [7]. Yaup Kara et al. developed to effcent models th dfferent approaches: artfcal neural netor and support vector machne. Moreover they compared the performance of to models n predctng the drecton of movement n the daly Istanbul Real estate Exchange (ISE) atonal 100 Index [8]. Therefore n order to mprove the accuracy of predcton ths paper presents a nd of method combned the hybrd herarchcal algorthms and RBF neural netor and bulds the fuson model to predct the closng prce of the Real estate Prce Index (SCI). 2. RBF eural etor Radal Bass Functon (RBF) neural netor s a feed-forard netor th good performance and t can decde the approprate netor topology based on dfferent ssues th a hgh approxmaton precson a small-scale of netor tranng fast learnng speed and non-exstence of local mnma problems. The structure of RBF neural netor conssts of three layers: the nput layer hdden layer and output layer. The structure of topology s shoed n Fgure 1. The nput layer The hdden layer x 1 The output layer x 2 x 3 y 1 y 2 x 4 Fgure 1. RBF eural etor Structure These nodes of nput layer are only responsble for passng the nput sgnals to the hdden layer hch ncludng a group of non-lnear radal bass functon. Gaussan functon s generally used as radal bass functon processng the nput sgnal receved th nonlnear transformaton and then transmttng the processed sgnal to the output layer. Gaussan functon formula s gven by 110 Copyrght c 2015 SERSC

3 X C e x p 1 2 L 2 2 (1) n Where φ s the output of the hdden layer X R s the nput of neural netor C s the center of Gaussan functon σ s the dth of Gaussan functon. L s the number of nodes n the hdden layer. The output layer processes sgnals hch have been processed by the hdden layer th lnear eghted combnaton. Eventually the predcted value that s obtaned through the RBF neural netor processng s one-dmensonal vector y : y 1 2 L L (2) 1 Where s the connecton eght beteen the th output of hdden layer and the th neuron of output layer. 3. The Predcton Model of RBF eutral etor Optmzed by HHGA Herarchcal Genetc Algorthm (HGA) s a novel genetc algorthm ntroduced n recent years. For the case of determnng the number of hdden nodes tradtonal genetc algorthm optmzes the based functon s center and dth of hdden layer of RBF neutral netor. The HGA s a learnng algorthm proposed for RBF neural netor features regardng the RBF netor topology center and varance of the hdden layer of bass functon and the connecton eght from the hdden layer to the output layer are optmzed smultaneously together. In the HGA each chromosome conssts of control genes usng bnary codng genes and parameter genes usng real-coded genes hch s ntroduced accordng to the herarchcal structure of bologcal chromosome. Control genes use bnary codng bnary 1 ndcates that ts correspondng parameter gene s actvated hence the node of hdden layer occurs. 0 ndcates that ts correspondng parameter gene s n dormant or nactve state hch mples the node of hdden layer does not exst. Each control gene corresponds to a set of parameter genes n sequence. A set of parameter genes contan the center C and dth σ of radal bass functon of a hdden layer and the eght of the output layer. The herarchcal chromosome structure of RBF neutral netor hch s optmzed by HGA s gven belo C 1 σ 1 1 C 2 σ 2 2 C n σ n n Fgure 2. The Herarchcal Chromosome Structure of RBF eutral etor Optmzed by HGA Hoever n the process of learnng the convergent speed of algorthm s qute slo. Snce the output layer of RBF neural netor s a lnear neuron hence f t s n the case that determnng the center C and dth σ the eght of output layer can be calculated by the least squares method to mprove effcency of the netor's tranng. The herarchcal chromosome structure of RBF neutral netor hch s optmzed by Hybrd Herarchy Genetc Algorthm (HHGA) that s the combnaton of HGA and the least squares method s presented belo. Copyrght c 2015 SERSC 111

4 1 0 1 C1 σ1 C2 σ2 Cn σn Fgure 3. The Herarchcal Chromosome Structure of RBF eutral etor Optmzed by HHGA Chromosome Codng Each chromosome uses the hybrd encodng combnng bnary codng th real codng. The control gene usng bnary codng s n the upper layer 1 ndcates the number of hdden layer nodes. Usng real-coded parameter gene s n the loer layer ncludng parameters of hdden layer: the center C and dth σ of radal bass functon. Populaton Intalzaton The sze of populaton has an nfluence on the convergence of genetc algorthm. Hoever small populaton sze s dffcult to obtan the desred results. But f the populaton sze s too large t s easy to mae the calculaton more complcated. As much experence shon hen the sze of populaton generally ranges from 20 to 160 the convergence of algorthm ould be better. The populaton sze n ths paper s 40. In HHGA ntalng populaton s to ntalze control parameter genes. The command of genetc algorthm tool box s appled for ntalzaton of control genes. The ntalzaton of parameter genes has to parts the frst part s based on the tranng sample data the center C of radal bass functon correspondng to the parameter gene s obtaned by fuzzy C-means clusterng method and the other part s that the dth σ s determned by the mnmum Eucldean dstance of varous data. Populaton P 1 s nformed after ts ntalzaton. Ftness Functon The purpose of tranng RBF neural netor s to mae the netor structure smple th meetng the demand of certan precson namely hch requres composte ndcators hch are approxmaton error accuracy and netor complexty of RBF neural netor are mnmum respectvely. The obectve functon of RBF neural netor approxmaton error precson s represented by error sum of squares beteen netor output and expected output F S S E y y (3) Where y s the expected output value y ' s the real output value. etor complexty s determned by the number of nodes n c n the hdden layer. F n (4) 2 c In order to mae HHGA effectvely tran RBF neural netor ths paper uses the ftness functon of Aae nformaton crteron to reflect both the ftness of these to obectves. 1 lg 2 f y y 4 n d c 1 (5) 112 Copyrght c 2015 SERSC

5 Where s the number of samples n c s the number of hdden layer nodes; y s the expected output value; y ' s the output value of tranng RBF neural netor. The value of d s 5000 to ensure that f> 0. Accordng to the formula hen the squared error s smaller and the number of hdden layer nodes s smaller then the value of f s lager. 4. Genetc Manpulaton Selecton and Reproducton The selecton operaton of HHGA s analogous to tradtonal genetc algorthms. If the ftness of an ndvdual s larger the greater probablty of selected. Ths ndvdual selecton s used for the expectaton value method. The expected value of the ndvdual determnes hether ndvduals of populaton could be dvded nto the next generaton to optmze the probablty of ndvdual s coped drectly proportonal to f the number of ndvduals beng coped s the value of ndvdual expectaton v. The expected value of the ndvdual used as the follong formula. v f (6) f f / Where f s the ndvdual ftness f avg s the average ftness. f sum s the total ftness of the populaton s the sze of the populaton. After selecton and reproducton operaton the ntated populaton P 1 becomes P 2. Crossover and Mutaton The mutaton operaton s prmarly used to mantan the dversty of populaton. Based on the populaton ftness the populaton P 2 s conducted crossover and mutaton operatons. Crossover operaton creates ne gene combnaton to form group P 3. The crossover of control genes and parameter genes use sngle-pont crossover. Due to the dfferent encodng beteen control genes and parameter genes of each chromosome the mutaton of parameter genes selects real-value mutaton. The mutaton of control genes uses smulated bnary mutaton selectng randomly to ndvduals x 1 and x 2 from the parent populaton then by lnear combnatons to produce ne offsprng. a vg su m f y a x 1 a x y a x 1 a x (7) Where a s a random number a [ 0 1]. Calculate Weghts of the etor Output In the desgn of RBF neural netor optmzed by HHGA the parameter nformaton of output layer neurons n genetc algorthm encodng s redundant. If addng redundant nformaton n the encodng the effcency of genetc algorthm ll be reduced. Therefore usng HGA to determne the center C and dth σ of radal bass functon n the hdden layer tang advantage of the least squares method to calculate the eghts of output layer can study the fnal optmzed RBF neural netor. 5. Experments and Analyss In order to verfy the RBF neural netor optmzed by HHGA hch s feasble and effectve n real estate predcton comparng the performance of the method proposed n Copyrght c 2015 SERSC 113

6 ths paper th the exstng approaches such as RBF neural netor and BP neural netor optmzed by GA th conductng the same experment. Ths expermental data are the Real estate Prce Index closng prce of 125 tradng days from July to December collected on the Shangha Real estate Exchange. The frst 107 data s taen as tranng sample and the remanng 18 data s presented as the testng sample from the 155 th day to 185 th day. In order to avod a great range of data havng a negatve mpact on the RBF neural netor tranng a real estate closng prce x s normalzed to nterval [0 1] by x m n x x (8) m a x x m n x Where x s the nput of neural netor max(x) and mn(x) are the maxmum and mnmum value of the sample data respectvely. Through the normalzaton of x then mputng the sample data are regarded as the tranng sample of the neural netor. After the netor tranng and smulaton of the sample conductng ant-normalzaton process to revert the real closng prce hen outputtng predcted results. * m ax m n m n Y x u x x x x (9) Where u(x ) s the output of neural netor. The Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) are taen as the standard to assess the predctons accuracy of the model. M A P E R M S E 1 y y (10) 1 1 y 1 y y (11) Where y ' s the predcted value y s the actual value s the number of samples. When the value of MAPE and RMSE s smaller the hgher forecastng accuracy of the model s possble. To avod the nfluence of random factors on the expermental results three methods are conducted three tmes. The follong s the result Tables. 6. Expermental Process Table 1. The MAPE Values of Three Models Experment HHGA-RBF GA-BP RBF Table 2. The RMSE Values of Three Models Experment HHGA-RBF GA-BP RBF Step 1: obtan eght value and sequence of factors. There are lots of subectve eghtng methods such as Guln method AHP method expert nvestment method analytc herarchy process (AHP).n ths paper e use relatve eght method. y 114 Copyrght c 2015 SERSC

7 r s the score of -th factor n the -th questonnare then the orgnal eght value of -th factor n -th nvestgaton equals: r n r 1 (12) In formula (1) n s the number of affected factors n -th nvestgaton. So for each n 1 1 nvestgaton. Weght value defned by dfferent experts th varable acnoledgement toards each nfluence factors may not be the same. n order to elmnate the devaton e average from all questonnare: ' m 1 m (13) We get the fnal eght value of each nfluence factor by relatve eght method. At the same tme the sequence about factors can be decded accordng to the eght value. Step 2: program th MATLAB buld BP netor brng n MIV. Gets the sequence of nfluence factors usng engneerng data to tran netor When usng BP netor e should frst provde a tranng set here each sample s determned by the nput mode and the desred output mode. Suppose there are q sample tranng set then the sample can be formalzed as a model of ( X Y q ) X s the - ( x x... x ) 1 2 th nput n Y ( y y... y ) 1 2 s ts output n and they correspond to n neurons of the nput layer and the output layer respectvely. When the actual output of the netor and the desred output are consstent the learnng process s over. Otherse the learnng algorthm ll mae the actual output close to the desred by adustng the connecton eghts of the netor accordng to the error beteen the to outputs. Defne 1 h as a connecton eght from the neurons h n the nput layer to the neurons n the hdden layer and defne 2 as a connecton eght from the neurons n the hdden layer to the neurons X Y n the output layer. Suppose for a ( ) the global error functon n the output layer s: m 1 2 E ( ) y y q 2 y Among them s the actual output of output layer neurons s the desred output. Then error of the hole tranng set s: q E E For the -th sample the eghted nput of output layer neurons s: n ety b * p (p s the number of neurons n the hdden layer) Then the actual output s: In formula (17) y f ( n e ty ) 2 (14) (15) (16) (17) Copyrght c 2015 SERSC 115

8 f ( u) 1 1 u e (18) Among them s means the number of teratons. Thus e can obtan the ran of the nfluence factors and the eght value. The results n the Table 1 and Table 2 sho that for the experment of predctng the closng prce of SCI the values of MPAE and RMSE of RBF neural netor optmzed by HHGA are mnmzed so the predcted accuracy s maxmzed. The follong s comparson charts beteen actual and predcted values of three methods: Fgure 4. HHGA-RBF Approach Fgure 5. GA-BP Approach 7. Concluson Fgure 6. RBF Approach A seres of uncertan factors n real estate maret have led to the dffculty of predctng real estate prce such as polcy economc envronment and nvestor psychology. From numerous approaches studyng neural netor to predct the real estate prce ths paper proposes and mplements the combnaton of HHGA and RBF neural netor to forecast the closng prce of SCI. In addton comparng th the predcton effect of usng RBF neural netor and BP neural netor optmzed by GA th the same experment the results confrms the predcton error s smaller usng RBF neural netor optmzed by HHGA and the predcton accuracy s superor to other to methods. 116 Copyrght c 2015 SERSC

9 References [1] T. O. Hll M. Connor and W. Remus eural netor models for tme seres forecasts Management Scence vol. 42 no. 7 (1996) pp [2] E. Guresen G. Kayautlu and T. U. Dam Usng artfcal neural netor models n real estate maret ndex predcton Expert Systems th Applcatons vol. 38 (2011) pp [3] G. Armano M. Marches and A. Murru A hybrd genetc-neural archtecture for real estate ndexes forecastng: Informaton Scences vol. 170 (2005) pp [4] R. Hassan B. ath and M. Krley A fuson model of HMM A and GA for real estate maret forecastng Expert Systems th Applcatons vol. 33 (2007) pp [5] M.-C. Lee Usng support vector machne th a hybrd feature selecton method to the real estate trend predcton Expert Systems th Applcatons vol. 36 no. 8 (2009) pp [6] W. Shen X. Guo and C. Wu Forecastng real estate ndces usng radal bass functon neural netors optmzed by artfcal fsh sarm algorthm Knoledge-Based Systems vol. 24 (2011) pp [7] L.-J. Kao C.-C. Chu and C.-J. Lu Integraton of nonlnear ndependent component analyss and support vector regresson for real estate prce forecastng eurocomputng vol. 99 (2013) pp [8] Y. Kara M. A. Boyacoglu and Ö. K. Bayan Predctng drecton of real estate prce ndex movement usng artfcal neural netors and support vector machnes The sample of the Istanbul Real estate Exchange Expert Systems th Applcatons vol. 38 (2011) pp Authors Huan Ma born n June 1981 Henan P R chna Current poston grades: Lecturer at Zhengzhou Unversty of Lght Industry Chna Unversty studes: Master degree n computer applcaton technology from Huazhong Unversty of Scence and Technology n Chna Scentfc nterest: Informaton processng algorthm desgn and analyss Mng Chen born n Aprl 1983 Henan P R chna Current poston grades: Lecturer at Zhengzhou Unversty of Lght Industry Chna Unversty studes: PhD degree from Beng Unversty of Posts and Telecommuncatons n Chna Scentfc nterest: bg data Jan-e Zhang born n Aprl1971HenanP R chna Current poston grades: Professor at Zhengzhou Unversty of Lght Industry Chna Unversty studes: PhD degree from The PLA Informaton Engneerng Unversty n Chna Scentfc nterest: broadband nformaton netor and netor securty Copyrght c 2015 SERSC 117

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