SOM SOM(Self-Organizing Maps) SOM SOM SOM SOM SOM SOM i

20 SOM Development of Syllabus Vsualization System using Spherical Self-Organizing Maps 1090366 2009 3 5

SOM SOM(Self-Organizing Maps) SOM SOM SOM SOM SOM SOM i

Abstract Development of Syllabus Vsualization System using Spherical Self-Organizing Maps Hiroshi HAMADA In recent years, syllabi have been introduced into most of universities. Syllabus is a booklet that shows course outline, and it is used for making students study plan. Syllabus has information to show relations between subjects. It is important that students understand the information of syllabus for the purpose of making systematic study plan. However, syllabi have problem what is that syllabi are difficult to understand the subjects relations. To solve the problem, syllabus visualization was proposed to easy to understand the subjects relations. A study of syllabus visualization using Self-Organizing Maps(SOM) was proposed as a past study. SOM makes node on a map learning data, and data is classified by their similarity. In the past study, the result of SOM was visualized by 2D map. However, the method of the past study has a problem that the result of visualizing become distorted at edge of map. In this paper, to solve the problem in the past study, we proposed syllabus visualizing system using spherical SOM. Moreover, to evaluate the validity of the system, we send out questionnaires to teachers and students. As a result, we confirmed that the system is easier to understand the subjects relations than the past study. key words Syllabus, Syllabus Visualization, SOM, Spherical SOM ii

1 1 2 2 2.1................................. 2 2.2.............................. 2 2.3................................ 4 2.3.1 SOM................... 4 2.3.2 SOM............. 5 3 7 3.1 SOM............................ 7 3.2 SOM.................................. 10 3.3................................. 11 3.4.............................. 12 3.5............................. 14 3.6............................ 14 4 15 4.1................................ 15 4.2................................ 15 4.3 SOM.............................. 15 4.4............................ 16 4.5............... 18 4.6................................... 19 4.7........................... 19 iii

5 23 5.1................................... 23 5.2................................... 26 5.3................................ 28 6 30 31 32 iv

2.1............ 3 2.2........................ 5 3.1 SOM................................. 8 3.2...................... 10 3.3.................................... 12 3.4 1.............................. 12 3.5 2.............................. 12 4.1.................................... 16 4.2.................. 17 4.3.................... 18 4.4............................. 20 4.5......................... 21 4.6................................ 21 4.7............................... 22 5.1 1 2.......................... 24 5.2....................... 24 5.3......................... 24 5.4 3......................... 25 5.5 3........................ 25 5.6 4............................. 25 v

3.1.............................. 13 4.1............................. 17 5.1................... 26 5.2 1 2............................ 26 5.3 3............................... 27 5.4 4............................... 27 vi

1 Web [1] SOM(Self-Organizing Maps) SOM SOM SOM SOM SOM 1

2 2.1 2.2 2

2.2 2.1 2.1 3

2.3 8 8 8 8 2.3 2.3.1 SOM [1] SOM Self-Organizing Maps [2] SOM 2.2 2.2 4

2.3 2.2 2.3.2 SOM SOM SOM 5

2.3 SOM SOM SOM 6

3 SOM SOM [1] 3.1 SOM SOM Teuvo Kohonen [2] SOM SOM 2 N in = ( m 1 m 2 m L ) m 11 m 12 m 1N m 21 m 22 m 2N N out =...... m M1 m M2 m MN m k n w k = (w k1, w k2,, w kn ) 7

3.1 SOM 3.1 SOM 3.1 SOM SOM λ R M N λ 1000 R 2 1 M N 1. N in N out 2. m m x 3. 8

3.1 SOM v m ij w ij 2 dist(v, v ) = v v 2 = n (v i v i) 2 (3.1) dist(x, w ij ) m ij 4. m m xy x w xy (3.2) 0 t λ 1 v (t) v t w (t+1) xy = (1 T ) w (t) xy + T x (3.2) i=1 (3.2) T α(t) h(m, m xy ) (3.3) T = α(t) h(m, m xy ) (3.3) α(t) α(t) = 1 t λ (3.4) w (t) xy v α(t) 0 1 (3.2) x h(m, m xy ) ( dist(m, m h(m, m ) ( ) ) m m 2 ) = exp = exp ( ) 2 α(t) R σ 2 (3.5) h(m, m xy ) m xy m 1 0 σ 0 < σ < R 9

3.2 SOM 0 (3.2) m R (3.5) 3.2 h(m, m ) 1 3.2 5. t λ 2 6. 3.2 SOM SOM SOM H.Ritter [7] 10

3.3 2.3.2 SOM 3.3 SOM SOM 1 1. 2. 3. 4. 5. 2 3.3 3.4 3.5 3 3 3 642 11

3.4 3.3 3.4 1 3.5 2 20 3.4 [1] 3.1 [4] 5 12

3.4 3.1,,,,,,,,,,, ( ), ( ), ( ), ( ), ( ), ( ), ( ), ( ),,,,,, ( ), ( ), ( ), ( ),, ( ), ( ), ( ), ( ),,,, ( ), ( ), ( ), ( ),,,, 13

3.5 3.5 [6] 3.6 1 14

4 4.1 SOM Java SOM Java3D[5] 4.2 SOM 4.1 4.1 4.3 SOM SOM 3.3 SOM 15

4.4 4.1 4.4 [6] 4.1 4.2 4.2 16

4.4 4.1 4.3 4.2 17

4.5 4.3 4.5 SOM SOM SOM 18

4.6 6 4.6 4.4 4.5 4.7 2 4.6 3 XY Z 3 (x,y,z) λ λ = tan 1 y x 3 φ φ = tan 1 z x 2 + y 2 19

4.7 4.4 20

4.7 4.5 4.6 21

4.7 4.7 φ λ R x = cos φ(rλ) y = Rλ 1 x = λ y = φ 4.7 1 22

5 5.1 3 3 5.1 4.6 23

5.1 評価方法 図 5.1 図 5.2 問 1 問 2 のウィンドウ 論理回路理論 に注目した画面 24 図 5.3 画像処理 に注目した画面

5.1 5.4 3 5.5 3 5.6 4 25

5.2 5.1 1 5.1 1 2 2 5.2 5.3 1 2 3 5.4 5.5 3 3 4 5.1 5.6 1 2 4 1 2 3 4 5 1 2 3 4 5 1 2 1 1 2 2 4 5.2 7 5 12 5.2 5.3 5.4 5.2 1 2 1 2 3 4 5 1 0(0) 0(0) 0(0) 10(4) 2(1) 2 0(0) 0(0) 2(1) 4(2) 6(2) 26

5.2 5.3 3 1( 5.4) 2( 5.5) 6(3) 6(2) 5.4 4 1( 5.1 ) 2( 5.6 ) 8(3) 4(2) 3 2 5.6 5.3 27

5.3 5.3 1 1 3 2 3 4 1 3 28

5.3 2 4 Web Web 29

6 SOM SOM SOM SOM 3 SOM 30

2 1 4 3 3 31

[1] 19 2007 [2] Teuvo Kohonen 2005 [3] SOM NC2004-23 pp.67 72 2004 [4],http://www.ieice.org/jpn/index.html. [5] Java3D,http://java.sun.com/javase/technologies/desktop/java3d/index.jsp. [6] 19 2007. [7] H.Ritter,Self-Organizing Maps on non-euclidean Spaces,in Kohonen Maps,ed.E.Oja and S.Kaski,pp.95-110,Elsever,New York,1999. 32