Research on Course Recommendation Based on Rough Set Xueli Ren1, a *and Yubiao Dai1, b

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1 6th Internatonal Conference on Sensor Network and Computer Enneern (ICSNCE 2016) Research on Course Recommendaton Based on Rouh Set Xuel Ren1, a *and Yubao Da1, b 1 School of Informaton Enneern Qujn Normal Unversty Qujn, Chna a olveleave@126.com, babaoda@163.com Keywords: Course recommend; Smlarty; Rouh set; Cosne; MAE Abstract. A credt system s the nexorable trend of hher educaton development. Course selecton s the bass and core. Therefore, t s necessary to establsh a reasonable course recommendaton system. A method to recommend the course s used to ude students to choose the rht course based on a lare number of rades n the educatonal manaement system, and the K nearest nehbors are chosen to estmate score based on smlartes between the student and the others. Reducn the attrbute of datasets s one of the core contents n rouh set theory. Remove the attrbutes that are not as mportant or redundant n knowlede property to mprove the effcency. The method s appled to the predcton of student rades usn 3 dfferent methods to dscrete scores, the results show that the equal frequency alorthm s better than the others methods. Introducton Wth the contnuous expanson of collees and unverstes, hher educaton has been transformed from outstandn mode nto the qualty and the mass mode, the scale of the school contnues to expand, the students have a lare dfference n the level and the startn pont, therefore the mplementaton of the credt system n collees and unverstes meet not only the requrements of the tmes, but also the needs of hher educaton development and law of personnel trann [1-3]. It s the most mportant how to ude the students to choose courses whch are sutable for both the professon and ther own. The smlartes between students are computed n the paper, and then the scores are estmated to recommend these courses. The rouh set s used to mproved effcency. Smlarty Computn and Rouh Set Smlarty Computn. The common methods to compute smlarty are Eucldean Dstance, Cosne Smlarty, Adjusted Cosne and Pearson correlaton [4-7]. Rouh Set. Rouh set frst descrbed by Polsh computer scentst Zdzsław Pawlak to deal wth mprecse or vaue concepts. In recent years we wtnessed a rapd rowth of nterest n rouh set theory and ts applcatons, worldwde. Here, the basc notaton s ntroduced only from rouh set approach used n the paper [8-11]. An nformaton system s denoted as S=(U, A, V, f) where U={ U1,U2,U3,,U u } denotes the set of all objects n the system, A={a1,a2,a3,,a A } s the set of all attrbutes. C s the set of condtonal attrbutes and D s the set of decson attrbutes. C and D are mutually exclusve and C D = A, C D=φ, then S s vewed as a decson table. V= Va where a A Va s the rane of the attrbute a; f; U A V s an nformaton functon, f q A, x U, then f(x, q) Va s the attrbute value of the object n U. f(x, q) denotes the value of attrbute q A n object x U. f(x, q) defnes an equvalence relaton over U. Wth respect to a ven q, the functon parttons the unverse nto a set of parwse dsjont subsets of U: Rq x : x U f(x,q ) f(x 0,q ) x 0 U (1) Assume a subset of the set of attrbutes, P A. Two objects x and y n U are ndscernble wth respect to P f and on f(x,q ) f(y,q ) q P The authors - Publshed by Atlants Press. 370

2 IND(P) denotes the ndscernblty relaton for all P A. U / nd( P ) s used to denote the partton of U ven IND(P) and s calculated by formula 2. q P : U / IND( ) (2) U / IND( P ) q Where A B X Y : X A, Y B, X Y The lower and upper approxmaton of a set P U (ven an equvalence relaton IND(P) )s defned as: PY X : X U / IND( P ), X Y (3) PY X : X U / IND( P ), X Y (4) Rouh Sets nvolve the approxmaton of tradtonal sets usn a par of other sets, named the Neatve or Postve Reon. The postve reon contans all objects n U that can be classfed n attrbutes Q usn the nformaton n attrbutes P. The neatve reon s the set of objects that cannot be classfed ths way. Pawlak defnes the deree of dependency of a set Q of decson attrbutes on a set of condtonal attrbutes P s defned as: ( Q ) p POS ( Q ) p U (5) Where s the cardnalty of a set; ves a measure of the contradctons n the selected subset of the dataset. If = 0, there s no dependence; f 0 < < 1, there s a partal dependence. If = 1, there s complete dependence. It s now possble to defne the snfcance of an attrbute. Ths s done by calculatn the chane of dependency when removn the attrbute from the set of consdered condtonal attrbutes. Gven P, Q and an attrbute x P: p( Q, x) P( Q ) P { x }( Q ) The hher the chane n dependency, the more snfcant x s. Our Method Accordn to the whole course rades of students, the model to predct the scores of the follow-up courses s establshed based on smlarty, and whch provdes a useful udance for the students to select courses and learnn. The processes are shown n F. 1. (6) Fure 1. The process of score estmaton Data Pretreatment. Mssn value n data tables should be processed frstly before computn. The technques of mssn value mputaton are: lstwse deleton, mean mputaton and some types 371

3 of hot-deck mputaton [12-13]. The lstwse deleton s used to deal wth mssn value n the paper. Attrbute Dscrete. Rouh set theory analytcal requrements that data s n the form of cateores, therefore, data must be dscrete at frst. Dscrete results may reduce the accuracy of the raw data, but t wll mprove ts eneral.dscrete n nature s that the ssue of spatal condtons consttute property s dvded usn the selected breakponts, dvdn the n-dmensonal space nto a fnte number of reons, so that the same decson values n each reon of the object. These methods are commonly used: equal wdth alorthm, equal frequency alorthm, Nave Scaler methods and so on. The equal wdth alorthm s the smplest dscretzaton method, whch dvdes the numercal rane nto ntervals accordn to number k by user specfed, and each nterval s equal to (max- mn) / K. The equal frequency alorthm dvdes the numercal rane nto k ntervals where the number of each nterval s the same. There are non-quanttatve values n the set of attrbutes of rade table, such as Boolean, numerc, so the dfferent methods are appled to dscrete these values. If the score s for numerc, then the two methods are used n the paper. The equal wdth alorthm: Dvde the rade nto 4 ntervals that are dscrete by formula 7, the method dscrete data usn the same standard that don t reflect the dfferences n each course. The other method s proposed n the paper whch dscrete rades of each course by formula , 25 25, 50 50, 75 75, 100 max mn 1 mn, mn 4 max mn max mn 2 mn, mn max mn max mn 3 mn 2, mn max mn 4 mn 3,max 4 Where max s the hhest score and mn s the lowest score. The equal frequency alorthm: two steps are used to dscrete. Frstly, the rades of each course are sorted from small to lare; then dscrete rades to 4 ntervals. If s for fuzzy value, then the fuzzy value s converted to number start from 1 based on the level from low to hh. Attrbute Reducton. Reducn the attrbute of datasets s one of the core contents n rouh set theory. Remove the attrbutes that are not as mportant or redundant n knowlede property. The process s realzed by alorthm n the paper [10]. sm ( s, ) Smlarty Computn. The smlarty a s s computed by cosne. Score Estmaton. Frstly, the K nearest students are chosen based on smlarty;then the score s estmated by the method n [3]. (7) (8) Experment An experment s done to show the method feasble. Score Estmaton Based on Smlarty. As an example, some rades of students n a class n specalzed n computer for 1 year are taken. Ths decson table s constructed where courses are columns and students are rows; and then mssn scores n rade table are processed. The scores are dscrete separately based on the two equal wdth alorthms and the equal frequency alorthm n the prevous paper. The attrbute reducton sets are {C2, C4, C5, C6, C10, C11, C12, C13}, {C2, C4, 372

C5, C6, C12}and {C1, C4, C5, C6, C8}.The smlarty s computed by cosne, then the 10 nearest nehborhoods are chosen based on smlarty to estmate score, and the result s shown n F. 2. Result Evaluaton.

4 C5, C6, C12}and {C1, C4, C5, C6, C8}.The smlarty s computed by cosne, then the 10 nearest nehborhoods are chosen based on smlarty to estmate score, and the result s shown n F. 2. Result Evaluaton. The mean absolute error (MAE) s a quantty used to measure how close forecasts or predctons are to the eventual outcomes [14].The MAEs of the 4 methods are shown n F. 3., and t shows the equal frequency alorthm s better than the others methods. Concluson Fure 2. The results of scores estmated Fure 3. The MAEs of 4 methods On the bass of the data of students' achevement n educatonal admnstraton manaement system, the nearest nehborhoods are chosen based on smlarty to estmate score. Rouh set s used to redact attrbutes to mprove the effcency of score estmaton, 3 knds of methods to dscrete attrbute are used, and the results show the method wth reducton s better than the method wthout reducton, the equal frequency alorthm s better than the others methods. References [1] Lu Huhu. The practce and enlhtenment of the total qualty manaement of Unted States[J].Journal of Jamus Collee of Educaton : [2] Q Youran,Pan Zhehen, Luo Jn.The Mathematcal Model of the Unversty Course Recommendaton System[J].Acta Scentarum Naturalum Unverstats ankaenss :50-52 [3] Ren xuel,da yubao.course Selecton of Students Based on Collaboratve Fltern[C].emcs2016 [4] Zhou Ljuan, Xu Mnshen, Zhan Yanyan.Model of recommended courses based on collaboratve fltern[j].applcatonr esearch ofcomputers : [5] Calculaton of smlarty [EB/OL] [6] Eucldean dstance[eb/ol], [7] Pearson Correlaton Coeffcents[EB/OL], [8] Pawlak Z. Rouh Set Theory and Its Applcaton to Dat a Analyss[J].Cybernet cs an d Sy stems, 1998, 9(5): [9] DING Jan-je. Research of Software Project Rsk Manaement Based on Rouh Set Theory. Computer Scence, 2010:

5 [10] Rouh set. SS5TDtB_L724vpFZ5eLHbyyK3QrkTSUIr2o0-uVEXDruHSY5F1S5EJ-B4TNCW, [11] Dn Hao,Dn Sh-fe, Hu Lhua.Research Proress of At trbute Reducton Based on Rouh Sets[J].COMPUTER ENGINEERING & SCIENCE.2010:93-94 [12] Zhan Shchao. Mssn Value Imputaton Based on Data Clustern [EB/OL]. [13] Anonymous. Imputaton (statstcs) [EB/OL] [14] Mean absolute error [EB/OL]. KKeZ_D9SQBGn5mLatbS

Subspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points;

Subspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points; Subspace clusterng Clusterng Fundamental to all clusterng technques s the choce of dstance measure between data ponts; D q ( ) ( ) 2 x x = x x, j k = 1 k jk Squared Eucldean dstance Assumpton: All features