DATA FORECASTING USING SUPERVISED LEARNING

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1 Inernaional Journal of Pure and Applied Mahemaics Volume 115 No , 9-14 ISSN: (prined version); ISSN: (on-line version) url: hp:// ijpam.eu DATA FORECASTING USING SUPERVISED LEARNING Tharangni H Sivaji 1, Simran Kaur Deol 2, and K Senhil Kumar 3 1,2,3 Deparmen of Compuer Science and Engineering, SRM Universiy, Kaankulahur, Chennai, Tamil Nadu, INDIA 1 harangni@gmail.com, 2 simrandeol05@gmail.com, 3 senhilkumar.k@kr.srmuniv.ac.in Absrac: Sales of legacy video game sysems has gone hrough various rends over he pas few years. Wih echnologies being compressed o smaller devices i is highly crucial o esimae he curren and fuure sales of legacy sysems. Daa forecasing is used o predic fuure values of ime series daa according o he hisorical rends observed using saisical procedures. Various facors such as sales from numerous counries, year of release, genre, gaming plaform ec affec he model. Supervised learning mehods were incorporaed ha esimaed how he sequence of observaions would coninue ino he fuure. Regression models were used o correlae beween he predicor variables. Numerous plos were formulaed o esablish relaionships amongs he daa for beer analysis. Time series forecasing such as ARIMA analysis has been used o exrapolae rends, sales paerns and populariy. Keywords: Video game sales, ime series analysis, daa forecasing, supervised learning, regression, ARIMA model. 1. Inroducion Forecasing involves predicing he fuure based on pas and presen daa by analysing he rends observed [1]. A common example is esimaing he GDP or populaion or alcohol consumpion of any counry a some specified fuure dae. Daa Forecasing uses he exac echnique bu can be classified in erms of qualiaive and quaniaive forecasing[7]. In his case, analysis has been done using quaniaive analysis as daa presen is in he form of numerical informaion. Figure 1. Differen Machine Learning Algorihms Wih he ongoing boom in he gaming indusry,i has become even more imporan o analyse and esimae he sales and demands so as o minimise he loss associaed wih excessive manufacuring. Daa forecasing esimaes he fuure producion requiremens using machine learning echniques on he daa se. Graphical represenaion of hese algorihms can be seen in Figure 1. The basic algorihm ha can be used in such scenarios is regression. In a saisical model, regression can be used o esimae he relaionship beween variables[7]. The variable whose value is o be prediced is dependen variable and he one whose value is known is independen variable. Figure 2. Linear Regression Linear regression is a form of supervised learning which predics resuls wih coninuous oupu. The aim of linear regression is o esablish a relaionship (linear) beween he predicor ( x ) and he oucome ( y ) only when he value of predicor variable(s) is known. When x holds a single value, i represens a simple regression whereas when i has muliple values sored as a marix hen i represens muliple regression. The generalised mahemaical equaion for linear regressions is: ˆ = ˆ ˆ x (1) y 0 1 In he above equaions x holds he predicor value which requires o be forecas for each inpu of x o obain he respecive forecas ŷ. 0 is he y -inercep and 1 is he slope for he model and ogeher hey are called as he regression coefficiens (Figure 2). is he error erm, he par which he regression model is unable o explain. Afer calculaions are done using he observed values of x from he daa, he resuling value of ŷ is a "fied value". ŷ is no a genuine forecas since he acual value of y for ha predicor value x was used o rain he model. ŷ is a "genuine forecas" only when he value of 9

2 Inernaional Journal of Pure and Applied Mahemaics x is a new value from he esing se. The mos imporan model ha is used in he analysis is Time Series model[2, 5]. Time Series comes ino acion if he provided daa se is changing wih ime.the daa is observed sequenially over a period of ime. Wih his an esimae is made a how he sequence will coninue in he fuure. Time series forecasing uses informaion only of he variable which needs o be forecased wihou making an aemp o discover facors affecing i[4]. ARIMA models, exponenial smoohing and srucural models are differen ime series models used for forecasing. While exponenial smoohing and ARIMA analysis are he wo mos popular approaches owards ime series forecasing, hey boh have complemenary approaches for he problem. ARIMA models funcion o expound he auocorrelaions in daa whereas exponenial smoohing characerises [3] hrough analysis of rends and seasonaliy in daa. Thus, ARIMA models provide an easier approach owards ime series forecasing. ARIMA sands for Auo Regressive Inegraed Moving Average. In his model, inegraion is he reverse of differencing. The complee equaion of he model is: y = c y y e e 1 1 p p 1 1 q q (2) where y is he series which has been differenced eiher once or more han once. Lagged values of y () and lagged errors e () are he predicors on he righ hand side. is he co-efficien of lag variable y () and q p is he co-efficien of lag error e (). This is ofen referred o as ARIMA ( p, d, q) model, where, p = order of he auo regressive par; d = degree of firs differencing involved; q = order of he moving average par Saionariy and inveribiliy condiions applied o boh he AR (Auo Regressive) and MA (Moving Average) models apply o he generalised ARIMA model as well [2]. 2. Objecive The aim of his analysis is o provide informaion abou deermining he fuure producion (sales) of legacy video game sysems. This will be obained hrough supervised learning mehods concenraing on forecasing echniques such as regression and ime series analysis. Annual predicions of he video game sales along wih predicing he populariy of various plaforms and genres are performed on he daase. Wih he inegraion of linear regression mehods and ARIMA models, video game sales can be analyzed. 3. Approach Forecasing problems are generally solved by following he seps given below: Collecing he daa Undersanding he daa Training a model Evaluaing he model Improving he performance Figure 3. Overview of Daa Forecasing The deailed overview of analyzing he problem is given in Figure 3. The proposed approach given in Figure 3. can be divided ino four sages [6]. 1. The firs sage deals wih gahering and undersanding he daa for he proposed model. e 2. The daa is divided o raining daase and esing daase for evaluaing i agains he differen learning mehods. 3. The resuls from he previous sage are hen summarized o formulae he respecive equaions. 4. Finally, necessary graphs are ploed o forecas he predicions. These sages are furher explained in he following secions Daa Managemen The iniial sep of his sage involves preparing he daa ha includes informaion necessary for forecasing resuls. The daa for he proposed model was aken from kaggle amassing o an aggregae of enries. Figure 4. Video Game Sales Daa The daase conained informaion abou video game sales as represened in Figure 4. Ranking of game wih respec o global sales in millions of dollars, plaform in which he game was released (i.e PC, PS4 ec.), year in which he game was released, genre, publisher and he overall sales divided amongs differen counries such as Norh America, 10

3 Inernaional Journal of Pure and Applied Mahemaics Europe, Japan ec. Relaionship amongs he various aribues were sudied afer cleaning he daa o omi any incomplee or irrelevan enries for predicing he overall sales in he fuure. The hisogram in Figure 5 depics his relaionship. 6 Year Based on he plo obained furher resuls were produced denoing he inercep and slope ha are displayed in able 1. From his informaion we were able o generae an equaion for he model. Figure 5. Hisogram of he global sales of he games by year 3.2. Model Evaluaion One of he mos inegral seps ha follows daa undersanding is dividing he daa ino raining se and esing se. The significance of his sep is so ha he daases are rained o he respecive procedures such ha he underlying paerns or rends can be grasped. For he curren model, seveny five percen of he daase is randomly rained while he remaining weny five percen is used for esing. Addiionally in his sep, he model is esed sequenially agains wo supervised learning mehods, namely: Linear Regression and Time Series Analysis Daa Inerpreaion Linear regression is implemened o undersand he basic relaionship beween he variables. I can be observed from Figure 5 ha he revenue kep increasing gradually ill 2009 where i was a is peak. The maximum sale was noiced in 2008 and 2009 afer which he sales sared decreasing rapidly. Figure 6 depics a linear regression o he fi. Figure 7. Bes fi Line The esimaed regression line for he model of sales and years is given in equaion below (3): y ˆ = x (3) Using his equaion a line of bes fi was added o he graph for furher predicions (Figure 7) Daa Visualizaion This is he las sep in he proposed mehodology. The daa visualized in his sep depics he forecased daa in he model. Figure 8. Forecas from Linear Regression Model For he year x = 2019, he average revenue forecased in millions is ŷ = from he linear regression model presened in Figure 8. The corresponding 95% and 80% confidence inervals are [ , ] and [ , ] respecively. Figure 6. Linear Regression fi on he model Table 1. Summary of Linear Regression Coefficie ns Esimae Sd. Error value Pr( > ) (Inercep ) Figure 9. Trends observed 11

4 Inernaional Journal of Pure and Applied Mahemaics When using regression for predicion, we observed cerain rends emerging from he daa (Figure 9). Trends are observed when here is a long erm rise and fall in he daa. I can be eiher linear or non linear. Trends are ofen observed changing direcion when shifing from an increasing rend o decreasing or vice-versa[2, 7]. As a resul, we considered analyzing our daa as ime series daa while aiming o forecas he fuure. The analysis of revenue colleced over a cerain number of years was hen subjeced o ARIMA modelling in ime series analysis (Figure 10). Figure 10. ARIMA Forecas The observed model obained he bes resuls when subjeced o an ARIMA (1,0,0) forecas wih zero mean [4]. This implies ha he given model is an auo regressive AR(1) model. An AR( p ) model can be represened using he general ARIMA equaion (2) wih he only consrain being ha d,q = 0. The simplified equaion of an AR( p ) model is: y = c y y y e (4) p p where c is a consan and e is whie noise. AR( p ) model is similar o muliple regression bu wih lagged values of y as predicors. On furher analysis of he forecass obained in Figure 10 he following resuls were abulaed. Table 2. AR(1) Model Informaion Coefficiens ar1 mean value s.e An AR(1) equaion was formulaed afer analysis of equaion (4) wih he daa from able 2. The equaion for he curren model is: y = y 1 e (5) Using his equaion video game sales was forecased for he nex 5 years hrough a series of poins. These predicions are abulaed in able 3. Table 3. Forecass from AR(1) Model Poin Forecas Lo 80 Hi 80 Lo 95 Hi Resuls Accuracy Accuracy beween he rained and esed values was evaluaed using MAPE (Mean Absolue Percenage Error) as a meric for boh he models [5]. MAPE is defined as: observed forecased MAPE = Avg 100 (6) observed According o Lewis MAPE definiion [6], forecass are considered o have: high accuracy if MAPE value is less han 10%, good accuracy if MAPE value is in beween 10% and 20%, reasonable accuracy if he value of MAPE is wihin 20% and 50% and inaccurae if MAPE value is greaer han 50%. Table 4. Accuracy Measures of Regression Se RMSE MAE MPE MAPE Training se Tes se Table 4 represens he accuracy measures of he forecased values of he regression model. The conclusion drawn from his observaion is ha regression model is highly inaccurae since is MAPE value is approximaely 95%. Table 5. Accuracy Measures of AR(1) Se RMSE MAE MPE MAPE Training se Tes se On he conrary, he AR(1) model showcases (Table 5) o depic forecass of good accuracy wih MAPE value of approximaely 18.2%. 5. Conclusion 12

5 Inernaional Journal of Pure and Applied Mahemaics This work presens an approach for daa forecasing under supervised learning ha predics he overall sales of legacy video game sysems afer learning from he hisorical daa. I was shown in his sudy ha he general relaionship beween he various aribues of a daase can be derived using Linear Regression. However linear regression does no produce accurae predicions and he resuls show a lo of deviaions from he observed daa. Consequenly, i was mapped ha he video game sales daa is a ime series daa as cerain rends were observed ha are unique o ime series analysis. Therefore, we were able o winess more accurae forecass for he daa using ime series analysis which exemplified ARIMA models. I was observed ha he forecasing hrough ARIMA analysis coninued along wih he rend which he model originally perceived and also he prediced daa was almos accurae o he observed daa. 6. Fuure Work This is jus he beginning for he analysis of legacy video game sysems. The sales predicions can be inegraed wih core conceps of business inelligence for beer resuls. Addiionally, apar from sales predicion several oher analysis such as predicing he mos popular genre or plaform can also be performed using machine learning conceps. Moreover, he same algorihms can be used for differen daases o forecas he required aribues. Acknowledgmen The auhors would like o hank Gregory Smih for he immaculae daa provided and heir guide K. Senhil Kumar for his suppor. References [1] Armsrong, J S, Principles of Forecasing: A Handbook for Researchers and Praciioners. Kluwer Academic Publishers, [2] Brockwell, Peer J, and Richard A Davis, Inroducion o Time Series and Forecasing. 2nd ed. New York: Springer, [3] Sibei Xia, "Marke Forecasing of Super Srengh Fiber: Glass Fiber," Journal of Texile and Apparel Technology Managemen, Vol 9, Issue 2, pp. 1-6, [4] Hyndman, Rob J, and Yeasmin Khandakar, "Auomaic Time Series Forecasing: The Forecas Package for R," Journal of Saisical Sofware, Vol 27, Issue 3, pp. 1 22, [5] İrem İşlek and Şule Gündüz Öğüdücü, "A Reail Demand Forecasing Model Based on Daa Mining Techniques," IEEE Inernaional Symposium on Indusrial Elecronics (ISIE), ar. no , pp , [6] Alber Y. Chen,Tsung -Yu Lu and Mahew Huei-Ming Ma, "Demand Forecas Using Daa Analyics for he Preallocaion of Ambulances," IEEE Journal Of Biomedical And Healh Informaics, Vol 20, Issue 4, pp , [7] Rob J Hyndman and George Ahanasopoulos, Forecasing: principles and pracice, Universiy of Wesern Ausralia, [8] R. Sumahy, P. Kanchanadevi & Dr.A.Amuhan, Enhanced Public Inegriy Audiing On Cloud Daa Using Sha Algorihm, Inernaional Innovaive Research Journal of Engineering and Technology,Vol.2, pp.4-14, march

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