Englsh Premer League (EPL) Soccer Matches Predcton usng An Adaptve Neuro-Fuzzy Inference System (ANFIS) for Amadn, F. I 1 and Ob, J.C. 2 Department of Computer Scence, Unversty of Benn, Benn Cty. Ngera. frankamadn@unben.edu 1 ; trpplejo2k2@yahoo.com 2 ABSTRACT Predcton of Englsh Premershp League (EPL) matches has been on the heart and mnds of researcher over the pass decades, but none has suffcently ntroduced and Adaptve Neuro-Fuzzy Inference System (ANFIS) approach for these predcton whch has served as the focal am of ths research paper usng seven premer league teams and nne lngustc values. Matrc Laboratory (MATLAB) 7.0 served as the tool of mplementaton hghlghtng varous vews. The ANFIS tranng was successful completed at epoch 2 and havng an error of 1.41237e-006. The model was further used to predct the outcome of 7 matches wth a successful rate of 71%. Keywords: ANFIS, Premershp, Soccer, Predcaton, Layers 1 Introducton It s no doubt that the most vewed sport n the world s soccer havng above 10 bllon fan all over the world (Tony, 2014). The Englsh league s the most watched soccer league all over the world havng more than 2 bllon fans (Jonathan, 2014 and Tony, 2014). It comprses of 20 teams and each team plays 38 match n a season whch spans ten months. A team plays 19 matches at home (at the cty n whch the club orgnates) and 19 match away (Jonathan, 2014). A wn for any match regardless of home or away s 3 ponts a draw s 1 pont whle a loss earn no pont. At the end of each season the 3 teams at the lower end (bottom) of the league are relegated to a lower dvson (Tony, 2014). The outcome of any match s a wn, a draw or a loss (Jonathan, 2014 and Tony, 2014). To calculate the number of games played n a season usng the hand shakng lemma we represent each team as a node and a matched played as an edge. There are two parallel edges between each node (one for home match and the other for away match). So, the number of game played = (38*20) / 2 =380 matches. Snce the edge contrbute twce to the degree of the graph. 2 Revew of Related Lterature In predctng the outcome of a soccer match, varous approaches have been used some of whch nclude Statstcal method, Probablstc method, Bayesan network, Multlayer perceptrons. Yue (2003) used multlayer perceptron model to predct the outcome of a soccer match. The neural network had 13 nputs, 3 hdden layers and 1 output layer. The network was feed wth the most recent 5 matches of team A and team B. The model was used to predct the outcome of 9 matches and 4 out of the nne matches gave accurate predcton. Based on the effcency of the result, the model was re- DOI: 10.14738/tmla.32.1027 Publcaton Date: 28 th Aprl, 2015 URL: http://dx.do.org/10.14738/tmla.32.1027
T r a n s a c t o n s o n M a c h n e L e a r n n g a n d A r t f c a l I n t e l l g e n c e V o l u m e 3, I s s u e 2, A p r l 2 0 1 5 mplemented wth two addtonal hdden layers (a layer for the home team wth a weght of 1 and the other for the poston of the team on the table of rankng) whch was utlzed n predctng nne matches, wth an 80% accuracy Adtya et al (2013) used a Mult Nomnal Logc Regresson (MNLR) and Support Vector Machnes (SVM) to predct the outcome of a match utlzng 3 fundamental approaches. In ther frst approach Mult nomnal Logstc was enacted for the tranng phase n whch performance optmzaton metrcs derved from current matches were consdered, rather than takng the average of prevous matches and durng testng they predcted the outcome between two teams usng the number of matches past played. In the second approach, they traned n the same way they later test the data and nstead of usng the feature vector as the performance metrc vector correspondng to the current match, they used Key Performance Parameters (KPP). The thrd approach tred to fnd a global set of parameter whch was ndependent of the competng teams. Ian and Phl (2013), forecasted nternatonal; soccer matches result usng bvarate dscrete dstrbuton. They collected a total of 8,735 nternatonal soccer results from two man sources. The data for the perod 1993-2001 was obtaned from the archve of Internatonal Soccer Results (ISR) and the data for the perod 2001 to 2004 were obtaned from the Record Sport Soccer Statstcs Foundaton (RSSSF) archve. Data on the Federaton of Internatonal Football Assocaton (FIFA) world rankngs were collected from the FIFA webste for each month durng the years from 1993 to 2004. The model was based on copula functons. The copula regresson model forecasts 41.8% of the results correctly. From the revew of related lterature An Adaptve Neuro-Fuzzy Inference System (ANFIS) approach has not been adopted prevously for EPL matches predcton whch s servng as the focal pont of our research. 3 The ANFIS Model for Predctng the Outcome of Englsh Premershp League (EPL) Soccer Match The Adaptve Neuro Fuzzy Inference System (ANFIS) s one of the many hybrds of neural and fuzzy system. ANFIS combnes the learnng capablty of the neural network and the explanatory power of the fuzzy system. The ANFIS archtecture uses the sugeno type nference system Jang (1991). An example of the sugeno nference s gven n equaton 1: If x s A and y s B, then f1 = p1x + q1y + r1 (1) Where x and y s the nput varable and A and B s the fuzzy set of lngustc varables and q, p and r, are consequent parameters. ANFIS ARCHITECTURE Fgure 1: ANFIS ARCHITECTURE C o p y r g h t S o c e t y f o r S c e n c e a n d E d u c a t o n U n t e d K n g d o m 35
Amadn, F. I and Ob, J.C.; Englsh Premer League (EPL) Soccer Matches Predcton usng An Adaptve Neuro-Fuzzy Inference System (ANFIS) for. Transactons on Machne Learnng and Artfcal Intellgence, Volume 3 No 2 Aprl (2015); pp: 34-40 The ANFIS archtecture n Fgure 1 comprses of vared layers whch ncludes: a. Layer 1 (Input Layer): ths s the frst layer t s called the nput layer. Each node generates the membershp grades of a lngustc label (Jang, 1993). An example of a membershp functon s the generalzed bell functon s gven n equaton 2: 1 A ( x) x c b [ ( ) 2 (2) 1 ] 2 a Where {a, b, c} s the parameter set and x stands for the ndvdual value. As the values of the parameters change, the shape of the bell-shaped functon vares. Parameters n that layer are called premse parameters. b. Layer 2 (Fuzzfcaton layer): The second layer of the Adaptve Neuro Fuzzy Inference System (ANFIS) model s fuzzfcaton layer t s also called the membershp functon layer. In ths layer the output of the frst layer s mapped to a fuzzy set usng bell-shaped membershp functon (Jang, 1997 and Nauck et al., 1997). The Bell membershp functon provdes smooth and non-lnear functons that can be used by the learnng systems. Each node calculates the frng strength of each rule usng the mn or prod operator show n equaton 3. In general, any other fuzzy AND operaton can be used. O2, w A ( x) B ( x) 1, 2 (3) c. Layer 3 (Rule Layer): The thrd layer s the rule layer. Each neuron n ths layer corresponds to a sngle frst-order Sugeno fuzzy rule recevng sgnal from the membershp functon layer and computes the truth value of the rule (Jang, 1993 and 1997. The nodes calculate the ratos of the rule s frng strength to the sum of all the rules frng strength usng the equaton 4. The result s a normalsed frng strength. w O 3, w 1, 2 w w (4) 1 2 d. Layer 4 (Normalzaton layer): The fourth layer s the normalzaton layer. Each neuron n ths layer receves sgnals from all rule neurons n the thrd layer, and calculates the normalzed frng strength of a gven rule. The nodes compute a parameter functon on the layer 3 output usng equaton 5. Parameters n ths layer are called consequent parameters. O4, w f w ( p x q y r ) (5) e. Layer 5 (Defuzzfcaton layer): The ffth layer s the defuzzfcaton layer. Each neuron n ths layer s connected to the respectve normalzaton neuron n the fourth layer (Jang, 1997 and Nagnevtsky, 2002). It s a sngle node that aggregates the overall output as the summaton of all ncomng sgnals usng equaton 6 O5,1 overall output wf (6) URL:http://dx.do.org/10.14738/tmla.32.1027 36
T r a n s a c t o n s o n M a c h n e L e a r n n g a n d A r t f c a l I n t e l l g e n c e V o l u m e 3, I s s u e 2, A p r l 2 0 1 5 3.1 Generatng Dataset In generatng the dataset we reled on 5 factors whch then consttuted the ANFIS parameters whch was then used to predct the outcome of the match, they are: 2 of the last most recent match played by team A 2 of the last most recent match played by team B The pont of both teams n the table of rankng Ther popularty Home advantage. The frst 2 parameters (2 of the last most recent match played by team have 9 lngustc varable (WW, WD, WL, DW, DD, DL, LW, LD, LL) whle the pont of both teams and the popularty of the teams have 3 parameters (hgha, same, lowa) and the home advantage have 2 lngustc varable (homea and awaya). 3.2 Varable Used In the Model Table 1, shows, sx lngustc varables and sx lngustc values assocated wth the Anfs proposed archtecture for predctng the EPL results and matches Table 1: Fuzzy Lngustc Varables and Values Poston Club Last Two Match Played Pont 1 Chelsea WD 33 2 Manchester Cty WW 25 3 Southampton WW 22 4 Manchester Unted WW 21 5 West ham Unted DW 20 6 Arsenal LW 20 4 Stmulatons and Experment The stmulaton was carred out usng MATLAB Fuzzy logc toolbox 2007 and the model was used to predct the outcome of 7 matches. The varous smulaton modules are specfed from Fgure 2, 3, 4 and 5 respectvely Fgure 2: Tranng Error C o p y r g h t S o c e t y f o r S c e n c e a n d E d u c a t o n U n t e d K n g d o m 37
Amadn, F. I and Ob, J.C.; Englsh Premer League (EPL) Soccer Matches Predcton usng An Adaptve Neuro-Fuzzy Inference System (ANFIS) for. Transactons on Machne Learnng and Artfcal Intellgence, Volume 3 No 2 Aprl (2015); pp: 34-40 Fgure 3: Surface Vew Predcton 1 Fgure 4: Surface Vew Predcton 2 Fgure 5: Surface Vew Predcton The ANFIS tranng was completed at epoch 2 and havng an error of 1.41237e-006. The model was further used to predct the outcome of 7 matches and 5 outcomes out of the matches were accurately predcted. URL:http://dx.do.org/10.14738/tmla.32.1027 38
T r a n s a c t o n s o n M a c h n e L e a r n n g a n d A r t f c a l I n t e l l g e n c e V o l u m e 3, I s s u e 2, A p r l 2 0 1 5 4.1 Predcton Results The EPL predcton matches are specfed clearly on Table 2, hghlghtng both actual result and predcton results Table 2: Englsh Premer League (EPL) Predcton Matches Home Team Away Team Actual Result Predcton Manchester Stoke Manchester Manchester Chelsea Tottenham Draw Chelsea Sunderland Man Cty Man Cty Man Cty Everton Hall Cty Draw Draw Arsenal Southampton Arsenal Southampton Lester Cty Lverpool Lverpool Lverpool Swansea QPR Swansea Swansea 5 Concluson The ANFIS model was able to make an accurate predcton of 5 out of 7 matches whch s promsng but ths mples that there mght be more factors whch were not ncluded n our model that determne the outcome of a soccer match. So, further study s encouraged to ncrease the accuracy of predcton of a soccer match sung more applcable varables. REFERENCES [1] Adtya S. T., Adtya P. and Vkesh K. (2013) Game ON! Predctng Englsh Premer League Match Outcomes retreved from gameon.com [2] Ian M. and Phl S (2013), Forecastng nternatonal soccer match results usng bvarate dscrete dstrbutons Centre for Operatonal Research and Appled Statstcs, Salford Busness School, Unversty of Salford, Salford, Manchester UK. [3] Jang, R (1991). "Fuzzy Modelng Usng Generalzed Neural Networks and Kalman Flter Algorthm". Proceedngs of the 9th Natonal Conference on Artfcal Intellgence, Anahem, CA, USA, pp. 762 767. Retreved on October 15th 2014 from www.rrolecom/artcle/00098.pdf [4] Jang, J. (1993). "ANFIS: adaptve-network-based fuzzy nference system". IEEE Transactons on Systems, Man and Cybernetcs Volume23 ssue3. do:10.1109/21.256541. [5] Jang, S (1997) Neuro-Fuzzy and Soft Computng Prentce Hall, Pp 335 368, ISBN 0-13- 261066-3 [6] Jonathan T. (2014), 2014-15 Englsh Premer League and MLS TV rtrved onlne from http://www.phlly.com/phlly/blogs/thegoalkeeper/nbc-sports-2014-premer-league-tvschedule-for-august-through-november.html#sd6wr3mqe4ehodh.99 [7] Nauck, D., Klawon F. and R. Kruse, (1997), Foundatons of Neuro-Fuzzy Systems, J. Wley & Sons pages 312 C o p y r g h t S o c e t y f o r S c e n c e a n d E d u c a t o n U n t e d K n g d o m 39
Amadn, F. I and Ob, J.C.; Englsh Premer League (EPL) Soccer Matches Predcton usng An Adaptve Neuro-Fuzzy Inference System (ANFIS) for. Transactons on Machne Learnng and Artfcal Intellgence, Volume 3 No 2 Aprl (2015); pp: 34-40 [8] Negnevtsky, M., (2002) Artfcal Intellgence: A Gude to Intellgent Systems, 2d ed. Harlow, England: Addson Wesley, pp. 90-343. [9] Tony M. (2014), 20 Englsh Premershp Teams http://www.busnessnsder.com/newpremer-league-kts-2014-8?op=1 [10] Yue W. M. (2003) Predcton on Soccer Matches usng Mult-Layer Perceptron ID: 903-051- 7735 URL:http://dx.do.org/10.14738/tmla.32.1027 40