Daily Sales Forecasting for Grapes by Support Vector Machine *

Transcription

1 Daly Sales Forecastg for Grapes by Support Vector Mache * Qa We,2, Wesog Mu 3, L Su, Su Hua 4, ad Zhja Zhou,** College of Scece, Appled Mathematcs, Cha Agrcultural Uversty, Bejg, Cha, Departmet of Mathematcs ad Statstcs, Uversty of West Florda, Pesacola, Florda, College of Iformato ad Electrcal Egeerg, Cha Agrcultural Uversty, Bejg Cha Departmet of Statstcs, North Dakota State Uversty, Fargo, North Dakota, 5802 qw2@studets.uwf.edu, {slsally,zhjazh}@63.com, wsmu@cau.edu.c, su.hua@my.dsu.edu Abstract. I ths artcle, the quatty of grapes sold oe frut shop of a terlockg frut supermarket s forecasted by the method of support vector mache (SVM) based o defcet data. Sce SVMs have a lot advatages such as great geeralzato performace ad guaratyg global mmum for gve trag data, t s beleved that support vector regresso wll perform well for forecastg sales of grapes. I order to mprove forecastg precso (FP), ths artcle quatfes the factors affectg the sales forecast of grapes such as weather ad weeked or weekday, results are sutable for real stuatos. I ths artcle, we apply ε -SVR ad LS-SVR to forecast sales of three varetes of grapes. Moreover, the artfcal eural etwork (ANN) ad decso tree (DT) are used as cotrast ad umercal expermets show that forecastg systems wth SVMs s better tha ANN ad DT to forecast the daly sales of grapes overall. Keywords: support vector mache, artfcal eural etworks, grape sale forecastg, ε -SVR, LS-SVR. Itroducto Grapes are specal fruts that usually become rpe summer,.e., from July to September, ad are very popular amog frut customers. Because people are more ad more recogzg the utrtoal value of grapes, the sales of grapes have also dramatcally creased durg summer. Ulke the large cosumpto of grape products Europe ad Amerca, Chese cosumers prefer table grapes. However, * Ths paper s supported by the Cha Agrcultural Research System (CARS-30). ** Correspodg author. D. L ad Y. Che (Eds.): CCTA 203, Part II, IFIP AICT 420, pp , 204. IFIP Iteratoal Federato for Iformato Processg 204

2 352 Q. We et al. grapes are dffcult to store because they are pershable. For grape retalers,there are two causes for the loss of grapes: loss caused by storage because of a lack of refrgerato equpmet ad loss caused by customers who pck ad excse grapes accordg to ther prefereces. Therefore t s very mportat for grape retalers to make the rght decso orderg because a suffcet quatty of grapes wll ot meet the customer demad ad the shop ower wll obta less proft. O the other had, too may grapes may result a lack of freshess, thereby allowg the grapes be sold at dscouted prce, brgg a loss proft for retalers. As such, decso makers eed a accurate method that s based o mathematcs rather tha o ther experece, to determe the approprate order quatty of grapes. Sales forecastg s oe of the major tasks busess admstrato. Precse forecastg of demads ca ot oly decrease vetory costs but also mprove the qualty of customer servce ad ga compettve advatages. Recetly, some techques have bee mplemeted to develop some models of forecastg demad for agrcultural products wth the am of cotrollg vetory costs. However, for some fruts, especally grapes, the varous factors volved (e.g. clmate chages, holdays, ad ufxed preferece of cosumers) are so complcated ad chageable that forecast errors sgfcatly fluece vetory costs ad profts (Roy ad Samata 20). I ths paper, a ew algorthm wth hgher accuracy based o SVM s developed to forecast the demad for grapes, a method whch has rarely bee appled such a feld before. Because SVMs have greater geeralzato performace ad ca guaratee global mma for gve trag data, t s beleved that support vector regresso wll perform well forecastg grapes sales. The rest of ths artcle s orgazed as follows. The sales forecastg methods revew s gve detal Secto 2, ad models of SVM are preseted Secto 3. The the forecastg system framework based o the SVM s explored Secto 4. I Secto 5, the proposed model s preseted, ad umercal examples are used to vestgate the forecastg performace of the model. The cocluso, cotrbutos of ths artcle, lmtatos of the research, ad some future research drectos are provded Secto 6. 2 Selecto of Forecastg Method Durg the last few decades, may sales forecastg models such as tme seres, regresso aalyss, decso tree ANN ad SVM have bee developed the feld of pershable product. However ot all these methods are sutable for grapes sales forecastg. Next, we wll brefly troduce the tradtoal forecastg models ad the SVM sales forecastg model. 2. Tradtoal Method for Forecastg The tradtoal methods for forecastg models are mostly based o statstc methods. These methods rage from the movg average ad expoetal smoothg to lear ad olear regresso. Noetheless all these models have defceces ad caot solve the problem of ths artcle. ARMA model of tme seres s a method that uses the law of varato of the past varable to forecast future varato of the varable; however, ths

3 Daly Sales Forecastg for Grapes by Support Vector Mache 353 method caot reflect what factors affect the quatty of sale. The regresso aalyss method s used to reflect the relatoshp betwee the quatty of sale ad oe or more depedet varables, but ths method s always based o a large umber of data to solve the problem. As such t s ot feasble to adopt regresso aalyss to forecast daly sales of grapes. Recetly, ANN has receved much atteto solvg the problem of demad forecastg because of ts competet performace forecastg ad patter recogto. May studes have attempted to apply the ANN model to tme seres forecastg. However, ANN models adopt the steepest descet algorthm to fd optmal solutos, but they are uable to make sure that the error fucto of the eural etworks coverges to a global optmal soluto. Moreover, a crtcal ssue cocerg eural etworks s the over-fttg problem. 2.2 SVM for Forecastg The SVM has recetly bee proposed as a ew kd of learg etwork based o the statstcal learg theores: the Huber robust regresso theory ad the Wolfe dual programmg theory. SVM acheve good performaces terms of hgher accuracy, better geeralzato ad the global optmal soluto (S.R.Gu 998; Vapk 2000; Doumpos 2004). Orgally, SVMs were developed for patter recogto ad classfcato problems(cortes ad Vapk 995). Tag Hao (2007) used SVM mechacal falure dagoss ad proposed the combato of prcpal compoet aalyss (PCA) ad SVM to mprove the dagoss rate dramatcally. Wu Jag (2007) appled SVM computer-aded detecto of cacer dseases ad provded a referece of dagosg cacer. I recet years, SVM has bee used regresso problems, whch makg forecastg by SVM possble. May scholars use SVM to forecast varous subjects. For example, Wu Q (2008) forecasted the car sales by SVM based o the Gaussa loss fucto. Du Xaofag (20) used SVM, combed wth fuzzy theory, to forecast the demad of pershable farm products. Therefore, SVM s deed a effectve forecastg method as t eeds oly a small amout of data to forecast sales. Ths method apples partcularly to the sales forecastg of grape, whch lacks hstorcal data. At preset, there s o such research that apples the SVM method forecastg the sales of grapes, thus we use SVMs to forecast the sales of grape ths paper. 3 SVMs Forecastg Model It s well kow that SVMs were developed by Cortes & Vapk (995) for bary classfcato ad that they ca also be appled regresso problems by troducg a alteratve loss fucto. Oe character of SVMs s t s a algorthm that ca oly deal wth lear problem. Whe the system s o-lear, the put vector x, s mapped to a hgh-dmesoal feature space z, va a o-lear mappg, ad the coductg lear regresso ths space. The er product of ths mappg s called kerel fucto. I ths artcle, the kerel fucto used s Radal bass fucto (RBF):

4 354 Q. We et al. (, ) exp { / } 2 2 j j K x x = x - x δ. The stadard support vector regresso model gve by followg equato: ( ) ( φ ( )) y = f x = w x + b (3.) where φ ( x) s the hgh-dmesoal feature space, whch s o-learly mapped from the put space x. The coeffcets w ad b are estmated by mmzg rsk fucto R( C ): 2 Mmzg R ( C) w C L ( d, y ) where costat 0 = 2 + = C > s pealty factor ad L ( d, y ) ε ε s loss fucto. 3. ε -SVR Model I regresso, the qualty of estmato s measured by the loss fucto. There are four possble loss fuctos that ca be used: quadratc loss fucto, Laplaca loss fucto, Huber s loss fucto ad ε sestve loss fucto. The ε -SVM model selects ε sestve loss fucto as ts error measuremet. 0 d y < ε L ε ( dy, ) = d y ε otherwse Based o ε -sestve loss fucto, the decso fucto of ε -SVR model (S.R.Gu, 988) s Where (, j) f ( x) = * ( α α ) K( x, x) + b ( α * α ) (, ) ε α ( 0, ) ( α * α ) (, ) ε * α ( 0, ) yj K x xj + C = b = yj K x xj C = K x x s RBF kerel fucto. 3.2 LS-SVR Model The LS-SVR model selects quadratc loss fucto as ts loss fucto. The formula of quadratc loss fucto s: 2 q(, ) = ( ). = L d y d y Combe the above loss fucto ad RBF kerel fucto wth the equato (3.), we get the LS-SVR decso fucto (S.R.Gu, 988): ( ) α (, ) y = f x = K x x + b =

5 Daly Sales Forecastg for Grapes by Support Vector Mache 355 α C where b = d α jk( xj, x) ad (, j) j= K x x s RBF kerel fucto. 4 Forecastg System Based o SVM 4. Selecto of SVM Toolbox For the momet, there are some toolboxes we ca utlze such as LS-SVM toolbox ad LIBSVM toolbox of MATLAB. Frstly, LIBSVM s a lbrary for Support Vector Maches (SVMs) ad developed by Chh-Je L. Ths package has bee actvely developed by researchers sce the year 2000 to help users to apply SVM easly. Also there has a easer edto at preset for the user who does ot kow aythg about SVM. Ths edto makes everythg automatc--from data scalg to parameter selecto (Chh-Chug Chag, 20). Those are the reasos why we select LIBSVM tool ths paper. Secodly, The LS-SVM toolbox s maly used wth the commercal Matlab package. The Matlab toolbox s compled ad tested for dfferet computer archtectures cludg Lux ad Wdows. LS-SVM lab s terface for Matlab cossts of a basc verso for begers (K. Pelckmas,2003). 4.2 Forecastg Framework The forecastg system framework s showed the fgure. At frst, we eed deal wth data two ways: Oe s data ormalzato processg ( order to avod data overflow) cludg smooth the hstorcal sale data ( order to elmate sgular values ad ose). Aother s to process dyamc formato, such as weather data, week data, etc., whch s correspodg to the hstorcal sale data, as metoed Secto 5.2. After that the set of date wll separate to two parts, oe s called trag set ad the other oe s called testg set. Subsequetly, the trag set putted to SVM model s traed ad leart for adjustg the parameters to the optmal values. The future request s forecasted by the system after the mache completes learg. I addto, we obta the best parameters C (pealty factor) ad γ (a parameter of kerel fucto) by grd-search o C ad γ wth cross-valdato. At last, forecastg s performed ad the values Fg.. Framework of forecastg

6 356 Q. We et al. are obtaed after test set s putted to the traed SVM model. All these process wll be doe by the SVM toolboxes. What must be metoed s we perform sgle-pot forecast every tme, other word, there s oly oe value output every terato process. Whe the sale of a certa day s forecasted, we wll put the real value of that day to the trag set to reew the hstory data. 5 The Sale Forecastg of Grape 5. About Data The data we used s obtaed from a frut supermarket called Fu Ma Ja. The data cover the tme from the begg of July 20 up to the ed of September year 202 sce grape rpe o the large scale durg ths perod. There are three kds of grape sold ths market ad they are XaoMFeg, JuFeg ad MeGuXag. We use all of them to test the effcecy of SVM forecastg model ths paper. The data of weather s collected from Webste. 5.2 Idex of Varables Forecastg for sale of grape s a complcated procedure that volves multply varables, ad could be treated as regresso fucto y = f ( x) = ( w φ ( x) ) + b. The output value of the regresso fucto s sale quatty y, ad the put varable x cota may relevat factors, whch cotrol the sale, such as hstorcal sales, weather formato, holdays formato, etc. The objectve of ths model s to fd a mappg that has a hgh geeralzato performace from factors x to sale quatty y. Accordg to hstorcal sales, weather data, holday s data, etc., we form 8 styles of trag samples. Iput varable of grape sale forecastg model are show as: X = ( Sd, Sd 7, Wd, Wd, Pd, Pd, Td, Td ) where S Sales quatty at the day before the forecastg day d S Sales quatty at the day 7 days before the forecastg day d W d 7 Wd P d Pd T d d Type of date at the forecastg day (workday or weeked) Type of date at the day before forecastg day (workday or weeked) Sale prce of grape at the forecastg day Sale prce of grape at the day before forecastg day The weather codto of the forecastg day T The weather codto of the day before forecastg day Sce the data s type of weather codto ad holday are ot umercal value, we quatfy them as follow:

7 Daly Sales Forecastg for Grapes by Support Vector Mache 357 () Quatfed value of weather codto Table. Quatfed value of weather codto Weather value suy cloudy 0.9 overcast 0.8 Lght ra 0.7 moderate ra 0.5 Showery ra 0.4 dowpour 0.2 (2) Quatfed value of type of workg day date W d 0 moday, tuesday, wedesay, thursday, frday = saturday, suday 5.3 Crtera of Forecastg System I order to verfy the valdty of the predcto performace of SVM method, we use the day absolute error as statstcal metrcs as we oly forecast oe day s sale every tme. Defto of crtera s llustrated the followg expresso: d () f( x) DAE= 00% d () Where d() ad f( x ) represet actual sales ad the forecastg values respectvely. 5.4 The Result of Forecastg ad Aalyss The result s showed the followg fgures ad tables. The curves of fgure 2, 3 ad 4 show the comparso amog real data, ε-svr forecastg value, LS-SVR forecastg value ad ANN ad DT forecastg values. It s revealed from those fgures that SVRs forecastg value are closer to real data tha ANN ad DT forecastg values. From table 2, 3 ad 4, we fd that the SVRs have smaller average relatve error ad maxmum relatve error. Eve though we fd the decso tree performs faster tha other methods, that s ot a decsve advatage wth respect to forecastg grapes sale, sce we just have small amout of data. As a cocluso, the forecastg systems of SVRs, though does ot that satsfy the sale quatty, outperform the ANN ad DT method.

8 358 Q. We et al. All the pots that have relatve large forecastg error fall to followg two categores. Oe s forecastg value s greater tha the sale quatty. I ths case, we foud that there s o stock of grapes the store at most of those stuatos,.e., the demad quatty s greater tha sale quatty. Therefore, wth our method, we ca ot oly satsfy the customer demad, but also crease proft of the store ower at those pots. Aother case s forecastg value s less tha sale quatty. There are some specal actvtes that eed large amout of grapes may happe at those pot. I ths case, the customers always place order at least oe day advace, our method wll ot brg loss to the store ower at some pots. What s more, those stuatos rarely happe. Overall, the SVM methods we used are great ways to help store ower to ga hgher proft. Fg. 2. The result of sale forecastg for XaoMFeg Table 2. Comparso of real data ad forecastg result for XaoMFeg method Average relatve error Maxmum relatve error Tme spet(s) ε-svr LS-SVR ANN DR Fg. 3. The result of sale forecastg for JuFeg

9 Daly Sales Forecastg for Grapes by Support Vector Mache 359 Table 3. Comparso of real data ad forecastg result for JuFeg Method Average relatve error Maxmum relatve error Tme spet(s) ε-svr LS-SVR ANN DR Fg. 4. The result of sale forecastg for Meguxag Table 4. Comparso of real data ad forecastg result for Meguxag Method Average relatve error Maxmum relatve error Tme spet(s) ε-svr LS-SVR ANN DR Coclusos Forecastg s the foudato of frut supermarket to make order pla ad vetory cotrol, whle grapes sale has ts ow characterstcs such as mult-dmeso, small sample ad olearty. It s dffcult for the decso maker to forecast the sale accurately by ther experece. I ths artcle, the ε -SVR ad LS-SVR are used to forecast daly grapes sale, ad the result s acceptable. Thus we provde a advaced tellget forecastg techque for decso maker.

10 360 Q. We et al. Ths artcle also has sgfcat cotrbuto applcatos. For example, the forecastg techque we created ca be appled the maagemet of frut market more successfully. By applyg ths techque, the correct quatty of fruts wth rght qualty the approprate tme wll be obtaed ad the shortages or over-stockg wll be avoded properly. However, there stll have some lmtatos our model. For example, we do ot take to accout the substtutg frut of the grape that may affects the grapes sale. Further study wll focus o mprovg the algorthm accuracy whle more practcal factors are volved, so that more realstc sale forecastg result ca be obtaed the future. Refereces. Smola, A.: Regresso estmato wth support vector learg maches. Master s thess, Techsche Uversty at Muche (996) 2. Chakraborty, K., Mehrotra, K., Moha, C.: Forecastg the behavor of multvarate tme seres usg eural etworks. Neural Networks 5(6), (992) 3. Chag, C.-C., L, C.-J.: LIBSVM: A lbrary for support vector maches. ACM Trasactos o Itellget Systems ad Techology 2, 27: 27:27 (20), 4. Cortes, C., Vapk, V.: Support vector etworks. Mache Learg 20, (995) 5. Doumpos, M.: A Expermetal Comparso of Some Effcet Approaches for Trag Support Vector Maches. Operatoal Research 4(), (2004) 6. Tag, H., Qu, L.: Fault dagoss of ege based o support vector mache. Joural of X a Jaotog Uversty 9, (2007) ( Chese) 7. Wu, J., Dog, T.: SVM appled to modelg of cacer date. Scece Techology ad Egeerg 20(7), (2007) 8. Pelckmas, K., Suykes, J.A.K.: LS-SVMlab Toolbox User s Gude. Katholeke Uverstet Leuve. ESAT-SCD-SISTA Techcal Report, (2003) 9. Wu, Q., Ya, H.-S., Yag, H.-B.: A Forecastg Model Based Support Vector Mache ad Partcle Swarm Optmzato. Power Electrocs ad Itellget Trasportato System (2008) 0. Roy, A., Samata, G.P.: Ivetory Model wth Two Rates of Producto for Deteroratg Items wth Permssble Delay Paymet. Iteratoal Joural of Systems Scece 42, (20). Gu, S.R.: Support Vector Maches for Classfcato ad Regresso. ISIS Techcal Report, Uversty of Southampto, Departmet of Electrocs ad Computer Scece (998) 2. Vapk, V.N.: The Nature of Statstcal Learg Theory, 2d ed. Sprger, New York (2000) 3. Du, X.F., Leug, S.C.H.: Demad forecastg of pershable farm products usg support vector mache. Iteratoal Joural of Systems Scece, 2 (20) 4. Xu, X.-H., Zhag, H.: Forecastg Demad of Short Lfe Cycle Products by SVM. I: Iteratoal Coferece o Maagemet Scece & Egeerg, vol. 9, pp. 0 2 (2008)