The Design of WBPCLS for Computer Science Courses 439 Table 3. Student A selected courses Course name Course conception items Network programming { network,software,method } {ACE} Network management & security { network,hardware,management } {ABG} Distributing System { network,system,management } {AFG} Software Engineering { software,method,management } {CEG} Systems Analysis & Design { software,database,method,system } {CDEF} Multimedia System Design { software,system } {CF} Database Management { network,database,management } {ADG} E-Commerce {software,database,method,system, management} {CDEFG} Programming { software,system } {CF} Table 4. Student A course conception favor vector favor vector reliability A->G 0.833333333 C->E 0.75 C->F 0.833333333 the student A’s records shown in the Table 3, in which the item A , B , C , D , E , F , G represent ‘Network’, ‘hardware’, ‘software’, ‘database’ , ‘method’ , ‘system’ and ‘management’, respectively. The finally course conception favor vector is formed (Table 4). 3. To comparison and recommendation When the student wants to search for the course that belongs to someone course con- ception, we first turn the course conception favor vector into favor rule vector, then compare it with the course vector (Table 5), calculate comparison value v using con- trast formula(1), and finally recommend courses according to the descending order of v value. For example, when student A wants to search for the course with course concept C (software): according to C-> E , C-> F which come from student A course conception favor vector, we may deduce out that student A possibly likes the course with the course conception including ‘software’, ‘method’ , ‘system’ (C , E , F).The course conception favor vector is turned into favor rule vector [0010110] (possibility favor course’s vector value sets 1 , the others sets 0), and then the favor rule vector is compared with the course vector by using characteristic contrast for- mula, the results were shown in table 5. 1 1 (1 | |) n ii i vxy n = =−− ∑ (1) 440 Z. Li and X. Zhao The bigger the v value is, the better the corresponding course is (Table 5), based on which if student A wants to search for the course with the course conception ‘soft- ware’, the system will recommend three courses, e.g. ‘multimedia introduction’, ‘programming’ and ‘data structure’. Table 5. Student A comparison favor rule vector with course vector Course name Course conception Items Course vector V-value Management Information System {software,database,method, system,management } {CDEFG} [0011111] V=4/7 =0.57 Computer Architecture {hardware,method } {BE} [0100100] V=4/7 =0.57 Multimedia Introduction { software,system } {CF} [0010010] V=6/7 =0.85 Programming { software,system } {CF} [0010010] V=6/7 =0.85 Database Management System Introduction {Network, hardware, software, database, method , system, management} {ABCDEFG} [1111111] V=3/7 =0.43 Data structure {software,system} {CF} [0010010] V=6/7 =0.85 5 The Optimal Collaborative Partner Discovery "The optimal collaborative partner discovery” means that when the learner who is learning in the personal way encounters the difficulty, an optimal learning partner, who can help him solve the problem, may be found out from all online learners currently. Once the learner has logged in, the system is able to get his personal characteristics from the learner model according to his ID, the personal characteristics of all current online learners have buildup a fuzzy matrix. The algorithm of "the optimal collabora- tive partner discovery" will run around this matrix mainly. Besides, for Seeking of the optimal collaborative partner, the system or the teacher need to define the standard of “the optimal collaborative partner”, and the weights of characteristics which were included in standard beforehand. For example, the standard can be defined by expression forms (the knowledge grade similar/the studying style complementary = 0.6/0.4). It means that the learner should seek the person whose knowledge grade is similar and studying style is com- plementary with him, and “the knowledge grade similar” is more important than “the studying style complementary”. The main idea of “the optimal learning partner discovery” algorithm is: by analyz- ing the feature model of help-seeker, the algorithm produces a "visual learner ",puts this "visual learner" in current online learners and then mines out the class whose The Design of WBPCLS for Computer Science Courses 441 members are similar with the "visual learner" using clustering method. Finally, ac- cording to the weights in standard, it figures out matching values for each member who will be compared with the “visual learner” and recommends the optimal partner according to the descending order of matching value. The steps are: 1. a "visual learner" is created, then a new characteristics matrix U= (u ij ) is gener- ated by putting it’s characteristics into the matrix that is composed of present online learner’s characteristics. Creating "visual learner" includes three aspects: (1) the character characteristic value of "visual learner" was set as “be ready to help others very much” or “be ready to help others”. (2) the value of characteristic that demands to be similar in the standard of “the optimal collaborative partner" is equal to the corresponding characteristic value of help-seeker. (3) the value of characteristic that demands to be complementary in the standard of “the optimal collaborative partner” was set to the result of full mark minus charac- teristic value of help-seeker. 2. standardization If needed, the original data can be standardized using formula (2), (3), (4), (5). Af- ter above translation, for each variable, the average is 0, the standard deviation is 1, and the value range belong to 0~1. 1 1 n kik i uu n = = ∑ (2) 2 1 1 () n k kik i suu n = =− ∑ (3) ' k ik ik k uu u s − = (4) '' '' 1 '' 1 1 min{ } max{ } min{ } ik ik in ik ik ik in in uu u uu ≤≤ ≤≤ ≤≤ − = − (5) 3. the fuzzy similarity matrix calculation For the matrix above-mentioned X = { X 1 ,X 2 , …,X n } , X i =(x i1 , x i2 ,…, x in ), calcu- late the fuzzy similarity matrix R = (r ij ), r ij =μ (X i , X j ).The r ij is called similarity coef- ficient. In our system , the formula (6) be used for r ij calculation. 442 Z. Li and X. Zhao 1 1, 1 , { m ik jk k ij ij xy i j M r = = ≠ = ∑ (6) For example, 10 online learners x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 , x 9 , x 10 . Their char- acteristics are described in the Table 6. Assuming that the learner that currently need helps is x 10 , need to seek a "the optimal collaborative partner " in current online learners. Here, the standard defined By : the studying style is complementary, but other characteristics are similar, and each characteristic weight in standard is 0.3, 0.1 , 0.4 , 0.2, respectively. Table 6. Learner’s characteristic ID value characteristic Character 685 56 68893 knowledge grade 5 8 5 7 6 8631 6 studying style 333 26 7253 7 collaborative ability 8 2 7 8 2 8965 8 x 9 x 10 x 5 x 6 x 7 x 8 x 1 x 2 x 3 x 4 Referring to the Table 6, we can generate the matrix U as shown in expression(7). 6855668893 5857686316 3332672537 8278289658 U ⎛⎞ ⎜⎟ ⎜⎟ = ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ (7) For U, its fuzzy similarity matrix R is as shown in (8). 4. clustering For the matrix R, choose the threshold for the similarity coefficient λ. then the class A, to which the help-seeker belongs, can be attained. In our system, for the choosing of λ-value , we test the clustering results while assigned the different value to λ which can be also given by the expert who is experienced in professional area. When λ=0.88 be selected, the class A=( x 1 , x 3 , x 4 , x 7 , x 10 ). 5. comparison and recommendation For class A, the algorithm calculates the inner products M using weight vector in the standard and characteristic vector of the members in the class A except for help- seeker. The system recommends the “the optimal collaborative partner”, according to the descending order of inner product. The Design of WBPCLS for Computer Science Courses 443 1.00 0.82 0.90 0.88 0.82 0.86 0.88 0.85 0.85 0.91 0.82 1.00 0.82 0.82 0.83 0.82 0.82 0.82 0.82 0.82 0.90 0.82 1.00 0.88 0.82 0.86 0.88 0.85 0.85 0.90 0.88 0.82 0.88 1.00 0.82 0.86 0.89 0.85 0.85 0.88 0.82 0.83 0.82 0.82 1.00 0.82 0.82 0.82 0.82 0. R = 82 0.86 0.82 0.86 0.82 0.82 1.00 0.86 0.85 0.85 0.86 0.88 0.82 0.88 0.89 0.82 0.86 1.00 0.85 0.85 0.88 0.85 0.82 0.85 0.85 0.82 0.85 0.85 1.00 0.85 0.85 0.85 0.82 0.85 0.85 0.82 0.85 0.85 0.85 1.00 0.85 0.91 0.82 0.90 0.88 0.82 0.86 0.88 0.85 0.85 1.00 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ (8) For A=( x 1 , x 3 , x 4 , x 7 , x 10 ),and standard weight vector (0.3, 0.1 , 0.4 , 0.2) ,the M value can be decided, which is as shown in(9). 6 5 3 8 0.3 5.1 4 5 3 7 0.1 4.2 5 7 2 8 0.4 4.6 8 6 2 9 0.2 5.6 M ⎛⎞⎛⎞⎛⎞ ⎜⎟⎜⎟⎜⎟ ⎜⎟⎜⎟⎜⎟ =•= ⎜⎟⎜⎟⎜⎟ ⎜⎟⎜⎟⎜⎟ ⎜⎟⎜⎟⎜⎟ ⎝⎠⎝⎠⎝⎠ (9) According to the results calculated above, the recommendation order (“x 7 , x 1 ,x 4 , x 3 ”) can be estimated. 6 The Optimal Group Formation The collaborative learning mode is adopted usually when all learners are confronted with a definite and identical studying task. But in almost all current online learning systems, the learner is randomly grouped. In order to improve the learning effective- ness, the grouping method based on the learner’s characteristics was adopted in our system. The main idea is: according to grouping standard, “the optimal group formation” first generates a matrix that consists of the characteristics that need to be similar among the members in same group from the earner's characteristics model, then attain requested K groups using clustering method depend on the similar characteristics. And then pick out a learner from each group as representative and assigned the other learners one by one to the existing group according to the grouping standard of some characteristics similar and some complementary. In our system, we calculate the group average distance d based on these similar characteristics, and calculate the group average variance σ based on these complemen- tary characteristics. It’s obvious that the group more matches the grouping standard, if the d value is smaller and theσvalue is bigger. Therefore, we take the result of d minus σ(d-σ) as grouping estimation value. The group whose d-σ is the smallest is our desired one. . WBPCLS for Computer Science Courses 441 members are similar with the "visual learner" using clustering method. Finally, ac- cording to the weights in standard, it figures out matching values. grouped. In order to improve the learning effective- ness, the grouping method based on the learner’s characteristics was adopted in our system. The main idea is: according to grouping standard,. The collaborative learning mode is adopted usually when all learners are confronted with a definite and identical studying task. But in almost all current online learning systems, the learner