Determination of Housing Price in Taipei City Using Fuzzy Adaptive Networks

Transcription

1 Determnaton of Housng Prce n Tape Cty Usng Fuzzy Adaptve Networks We-Tes Lee, Jan-Jun Chen and Kuenta Chen*, Abstract The man purpose of ths research s to forecast pre-owned housng prces usng Fuzzy Adaptve Network (FAN). Fuzzy adaptve network (FAN) combnes fuzzy nference system wth neural networks and utlzes the strengths of both methods. It has the power of fuzzy nference and the learnng ablty from neural networks. Fuzzy varables are frst ntroduced to the area of predctng housng prces. The results are compared to back-propagaton neural network (BPNN) and adaptve network fuzzy nference system (ANFIS). Fuzzy varables used n ths study nclude lvablty, ambent condtons and expected development potental. Conclusons of ths research are: (1) the housng prces n the Tape Admnstratve Regon fall nto three clusters; (2) the overall predctons n the Nehu Dstrct are better than the Da-an Dstrct; (3) the predctons of FAN, BPNN and ANFIS are MAPE of 4.54%, 8.27% and 15.07%, respectvely. That s, FAN performs better than BPNN and ANFIS n predctng the housng prces of Tape cty. Keywords real estate prces, fuzzy adaptve network, back-propagaton neural network and adaptve network fuzzy nference system to forecast. I. INTRODUCTION ape Cty, as the captal of Tawan, s well-developed Tand ts constructons are farly of advanced. The ctzens have prvleges of very good lvng condtons and convenent traffc network, whch n return brngs up much hgher housng prces. Wth such a hgh prce, each purchase of a house s an mportant decson to make for a famly. The prce of a house s usually determned by both objectve condtons of the house and the subjectve preferences of the buyer. The objectve house condtons nclude sze of lvng area, parkng space, dstance to school or metro system or bus staton, and so on. On the other hand, the subjectve preferences vary by dfferent buyers. There are many subjectve factors affectng the prce of real estates, such as the dsgust facltes, convenence of lvng, and the neghborhood safety. Tradtonal predctng methods concentrated on the objectve condtons wth the attempt to provde an unbased reference prce for the buyers. However, the problem s that the prce a buyer s wllng to pay s n natural never unbased because of many personal reasons. Manuscrpt submtted on December 28, Ths work was supported by the Mng Ch Unversty of Technology. All authors are wth the Department of Industral Engneerng and Management, Mng Ch Unversty of Technology, Tape, Tawan. ( ; fax: ) The emal of we-tes Lee s fgh1110@hotmal.com, the emal of Jan-Jun Chen s sng0702@hotmal.com whle the e-mal of Kuenta Chen (correspondng author) s: kuenta@mal.mcut.edu.tw. To address ths problem, we propose to buld a model wth both fuzzy and crsp varables. The ntroducton of fuzzy subjectve factors s n hope of mprovng the accuracy of predcton to Tape s housng prces. In ths research, the prces of pre-owned houses are selected as the target, and the collected tradng records are from January 2009 to June. II. LITERATURE A. Varable Selecton The real estates are nherently permanent commodtes regardng poltcal, economc, supply and demand, global and local consderatons, envronmental condtons and many other factors. There are many drect and ndrect factors that can affect ther sales prce, whch makes t dffcult to predct. Some researches are conducted to the prce model buldng, but the uses of mpact varables are never the same. Ths study tres to collect varables used n the past artcles, and the result s shown n Table 1. Studyng the prevous research related to the real estates, we categorze the ndependent varables as objectve and subjectve factors. These varables are then dvded nto two categores: fuzzy varables and crsp varables. 1) fuzzy varables: we propose to use three fuzzy varables, namely the Lvablty, Ambent condtons, and the Expected development potental. 2) crsp varables: lmted to the data collecton dffculty, only part of crsp varables are avalable to us. These varables nclude the floor space, number of floor, total number of floors n the buldng, land stakeholders and housng age. Chang (Chang and Chang, 2005) ponted out that the back-propagaton neural network utlzes the Wdrow-Hoff learnng rule generalzed from the mult-layered wth nonlnear dfferental transfer functon of the network. Back-propagaton neural network archtecture can be dvded nto three layers, the nput layer, a hdden layer and output layer. The nput layer bascally does sample nput, hdden layer has a double curved lne transfer functon, and the output layer has a lnear transfer functon. Therefore, the output value of the network can be more than one non-consecutve ponts of any functon, whch explans problem of the non-lnear nput varables. A well-known study named Adaptve network fuzzy nference system (ANFIS), ntroduced by Zhang, has ts model archtecture combned by the fuzzy nference system and fuzzy nference system extenson developed by fuzzy theory. It collects the gven nput and output varables to generate a set of fuzzy rules and membershp functons

2 TABLE I Real estate-related varable selecton Author Research themes Select a varable Chn-Oh Chang Steven C. L. Farr(1993) Mok et al. (1995) LIN-SU-CHING (2002) Chen Hung-Chou (2002) Chen Hu-Cheh (2007) L (2007) A STUDY OF Real Estate Transacton Prce A Hedonc Prce Model for Prvate Propertes n Hong Kong The Elastcty of Consumpton and Investment for Housng Demand n Tawan A Research of Applyng Multcrtera Evaluaton wth Qualtatve and Quanttatve Data Model n Real Estate Apprasals A Study on the Factors Attrbutng to the Prces of Resdental Buldngs Usng Fuzzy Neural Network n Real Estate Prces Predcton Perod, locaton, use patterns, housng age, on the ground floor, where the floor area Away from the commercal center, floor, feld of vew, floor area, housng age, ftness actvtes, shoppng malls Floor number, housng age, resdental structure, resdental use patterns, ts own ktchen, household currently lvng satsfacton Regonal envronmental factors:frontage road wdth, traffc route dstrbuton and the adjacent buldng of the degree of Transportaton: Close to the center of the degree, nearly to the extent of the busness dstrct and close to the parkng level Indvdual characterstcs factors:degrees of vson near and far, housng patterns, lghtng, housng, age, mantenance facltes as well as the Publc than The tsubo Prce, floors, the face of the wdth of the road, the straght-lne dstance of the resdental buldng and park The characterstcs of the real estate, qualty, locaton, envronment, and resdents pay levels parameters. Fuzzy nference fuzzy system s the most mportant core mode, t can smulate human thnkng approach to solve the problem and thus acheve the ntended purpose. (Zhang, 1993) III. RESEARCH METHODS Ths study uses Matlab 2008a programmng software to code FAN model. Then FAN s compared wth BPNN and ANFIS predcton model. The core purpose of the study s commtted to mprove the qualty of the forecast of real estate prces. We collected real transacton data from the real estate transacton Quotes Bulletn Tape from January 2009 to June perod. Fuzzy adaptve network (FAN) s ntroduced by Cheng and Lee (1999). The proposed framework s formed by combnng the fuzzy nference sklls and neural network learnng ablty. The Fuzzy adaptve network s formed basng on past use of fuzzy adaptve networks n dfferent research felds. FAN uses lngust terms to represent how human spoken language to convey the message. The tranng ablty of FAN s obtaned from the error backpopagaton of the network. Some research have successfully appled FAN n dfferent felds (Jao et al, 2006; Chen et al, 2006). Fuzzy adaptve network s a network model of a total of fve-layer network archtecture (Fgure 1). The structure s smlar to adaptve network fuzzy nference system but dfferent n how the mnmal error s reached. The nodes n the archtecture are manly dvded nto two parts: crcles and square nodes. Crcle nodes are fxed nodes that perform certan transformaton functon, whle the square nodes can be traned. FAN calculates premse parameters as well as the soluton of fuzzy lnear programmng and feedback the error to push the front layers of the network through backpropagaton. The correcton of the premse parameters contnues tranng untl t reaches the desred mnmum allowable error or maxmum epochs to tran. Fuzzy nference system bascally conssts of three concepts: (1) the rule base: a set of fuzzy If-Then rules; (2) database: usng fuzzy rules to defne ts membershp functon; (3) the nference mechansm: based nference rules to perform the nference process condtons gven to draw reasonable output value. Varous fuzzy nference systems can buld a framework based on the If-Then rules and aggregaton process, whle the FAN s derved va Takag and Sugeno nference model, whch retans the sklls of fuzzy systems and neural network learnng ablty to provde an adaptve network system. The FAN has fve layers: The frst layer: Ths layer conssts of adaptve node contanng the premse parameters mean and standard devaton for the premse part of the fuzzy rules. Second layer: the nodes n the layer are fxed nodes denotng the attrbuton of dfferent semantc fuzzy rules (Fuzzy Rule). Multplyng s performed n order to calculate the ntensty value of each node and then output to the next network layer. Thrd layer: The network layer node are fxed nodes to calculate the weghts of the prevous lnks. Normalzaton s performed so that the output values of weghts are between0-1. Fourth layer: The network layer nodes are adaptve nodes. l Y s the nference part of fuzzy rules, and the nromalzed l weghts w are multpled. Ffth Layer: Summaton. Ths research apples Mean Absolute Percentage Error (MAPE) as the error measure. The smaller the MAPE s, the

3 better the model performs. To estmate the predcton error, the MAPE formula s as follows: P T MAPE 100 N T where P s predctve value, T s actual value, and N s total number of samples. In ths research, n addton of MAPE, we also calculated mean square error (MSE) as a bass to determne the predctve ablty of the network model. The MSE manly estmated the predcton accuracy of the network model. The smaller the MSE s, the smaller the degree of dsperson between the predcted value and the actual value s. The MSE calculaton can be expressed by the followng formula: N 2 y yˆ MSE 1 N where y s the actual value, ŷ s the predcton, and N s the Total number of samples. The referenced experts suggested usng road blocks n major dstrcts n Tape Cty when desgnng a questonnare for collectng nformaton of fuzzy varables. For example, the roads dvde a sngle admnstratve area nto several blocks for experts to grade the lvng functon of dfferent blocks, as well as the surroundng envronment condtons and the expected development potental. In ths way, scores are obtaned more effcently and t allows experts to judge the extent of the pros and cons of the dfferent blocks of the same admnstratve regon. Clusterng analyss s also performed n ths research. As there exsts twelve admnstratve regons n Tape Cty, they are dvded accordng to ther propertes. The blocks of smlar nature are combned nto the same cluster such that a hgh degree of heterogenety exsts between dfferent clusters. IV. RESULTS As shown n Table 3, the correlaton coeffcent matrx of all crsp varables used n ths research s calculated. It suggests that area of use and the tradng prce of the transacton has a lnear relatonshp, whle no sgnfcant lnear relatonshp exsts between other varables. A. Resdual analyss Total number of 1255 tradng recordng are consdered n ths research. Resdual analyss shows that the samples are not normally dstrbuted and there exsts some outlers. Therefore, outlers are dentfed and deleted form the samples for further analyss. B. BPNN forecast results In ths study, BPNN s set to use the Bayesan functon, one hdden layer, 10 neurons n hdden layer, and 3000 tranng epochs. The followng examples selected two dstrcts, Nehu Dstrct and Daan Dstrct, to demonstrate the prce predcton. The research results show that: (1) Nehu Dstrct, usng 117 samples for the tranng generates MAPE 16.34% as the tranng error, and the MSE of (mllon). For 13 testng samples, the predcted results n MAPE of 15.58% and MSE of 37,920.5 (mllon), as shown n Fgure 3. (2) Da-an Dstrct, usng 171 tranng samples, results n a tranng error of 15.82% MAPE, and 76, (mllon) MSE. For 20 testng samples, the MAPE s 14.56% and the MSE s , (mllon). The predctons are as shown n Fgure 2 and Fgure 3. C. ANFIS predcton results In ths research, the ANFIS s set to use Gaussan membershp functons, tranng 3000 teratons. The same two dstrcts, Nehu Dstrct and Daan Dstrct, are analyzed for comparson. The results show that: (1) Nehu Dstrct, MAPE s 7.14% and the MSE s 11, (mllon). For the 13 testng samples, the MAPE s 6.89% and the MSE s 13, (mllon), as shown n Fgure 3. (2) Daan Dstrct, the MAPE s 11.62% and the MSE s 39, (mllon). For the 20 testng samples, the MAPE s 9.65% and the MSE s 28, (mllon). The predctons are as shown n Fgure 4 and Fgure 5. D. FAN forecast results After screenng of the best changes n parameters of the Daan Dstrct and Nehu Dstrct, we found the best combnaton of parameters are the same for both two dstrcts wth confdence level = 0.6, fuzzy wdth e k = 0.1, and learnng rate L-rate = The mnmum allowable error s set to E = The results are as follows: 1) For the Nehu Dstrct, the tranng error converged wth (10K). The 13 testng samples result n MAPE of 3.79% and MSE of (mllon), whle the tranng error of MAPE s 3.70% and MSE s (mllon). The predctons are as shown n Fgure 6. 2) For Daan Dstrct, the tranng error converged wth (10K). Usng 20 test samples for predcton, the predcton results n MAPE of 5.28% and MSE of (mllon), whle the 171 tranng samples wth MAPE of 2.60% and the MSE of (mllon). Fgure 7 shows the predctons are very close to the target values.

4 Y Fg. 1. Adaptve Network Fuzzy Inference System Archtecture 4 TABLE II Correlaton coeffcent matrx Area of use Land stakeholders Floor Total number of Floor Land stakeholders Floor Total number of Floor Year of constructon Year of constructo n Turnover Total prce Turnover Total prce per pyeong Prce TABLE III Resdual analyss chart

5 Fg. 2. BPNN forecast results n the Nehu Dstrct Fg. 6. The target value and the predctve value of the 13 test samples n Nehu Dstrct Fg. 3. BPNN forecast results n the Daan Dstrct Fg. 7. The predcton of Daan Dstrct housng prces usng 20 test samples Fg. 4. ANFIS n Nehu forecast results Fg. 5. ANFIS forecast results n the Daan Dstrct E. Comparson Ths research uses three predctve models, namely FAN, BPNN, and ANFIS, to predct the housng prces. A total of sx varables were ncluded n these models, ncludng three crsp varables (area to use, land stakeholders, house age) and three fuzzy varables (lvng functons, the surroundng envronmental condtons, expected development potental). For demonstraton, Nehu Dstrct and Daan Dstrct are selected as examples. In comparson, we found that: 1) FAN model has the best performance among three methods when predctng both Dstrcts. Its MAPE decreased to 3.79% and mean square error (MSE ) to (mllon). In other words, the performance s FAN>ANFIS>BPNN. 2) The overall predctons n Nehu Dstrct are better than n Da-an Dstrct for all methods. As we know that the numbers of samples used for tranng are 117 and 171, respectvely, t suggests that the sze of 117 samples s good enough for tranng. TABLE IV Three forecastng models predct the effect of fnshng Dstrct Nehu Dstrct, Daan Dstrct Model predcted results forecast results MAPE MSE(Ten MAPE MSE(Ten % thousand) % thousand) FAN BPNN ANFIS

6 V. CONCLUSION In recent years, real estate prces n Tape are much hgher than many other ctes, a rsng trend of housng prces n Tape cty can be easly observed. More and more people and government agences become aware of ths problem. Wth ths hgh prce, t s mportant to obtan more nformaton for the buyers before they make the decsons. Thus an effcent decson support wll be desred and demanded. In ths study, a fuzzy adaptve network (FAN) s proposed to predct the real estate prces n Tape Cty through both crsp and fuzzy varables. The results are compared wth BPNN and ANFIS. The contrbuton of ths study and the results can be summarzed as the followng: 1) In ths study, the advantages of ncorporatng fuzzy varables n predcton of housng prces are demonstrated. In other words, both objectve varables and subjectve varables should be consdered. 2) For predcton, Tape's twelve Admnstratve Regon should be clustered before model constructon. 3) Sample sze of 117 for tranng usng FAN can provde satsfactory results. 4) In ths study, FAN performed better. 5) Predctons n Nehu Dstrct are better than n Da-an Dstrct usng FAN, ANFIS, or BPNN. ACKNOWLEDGEMENT Ths research s funded by Mng Ch Unversty of Technology, Tawan. REFERENCES [1]. LIN-SU-CHING (2002), "The Elastcty of Consumpton and Investment for Housng Demand n Tawan", The ROC Resdental Socety 11th Annual Conference Proceedngs,parer268 of paper277. [2]. Chn-Oh Chang Steven C. L. Farr(1993),"A STUDY OF Real Estate Transacton Prce", Chaoyang Unversty of Technology Archtecture and Urban Desgn, Vol. [3]. Hu-Cheh Chen (2007),"A Study on the Factors Attrbutng to the Prces of Resdental Buldngs", Chaoyang Unversty of Technology, Department of Fnance Thess. [4]. Chn-Oh Chang Steven C. L. Farr(1993),"A STUDY OF Real Estate Transacton Prce", Resdence of a page. [5]. Chen, K. T., and E. S. Lee (2006). Fuzzy Adaptve Networks n Credt Ratng and Loan Approval. [6]. L, Z. X. (2007). Usng Fuzzy Neural Network n Real Estate Prces Predcton. Proceedngs of the 26th Chnese Control Conference, Hunan, Chna. [7]. L, D. Y., W. Xu, H. Zhao, and R. Q. Chen (2009). A SVR Based Forecastng Approach for Real Estate Prce Predcton. Proceedngs of the Eghth Internatonal Conference on Machne Learnng and Cybernetcs, Baodng. [8]. Mok, H., P. Chan, and Y. S. Cho (1995). A Hedonc Prce Model for Prvate Propertes n Hong [9]. Jang, Jyh-Shng, (1993), ANFIS : Adaptve-Network-Based Fuzzy Inference System, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 23, NO. 3, MAYIJUNE 1993