ਛᄩᄢቇᄢቇ㒮ℂᎿቇ⎇ⓥ⑼ᖱႎᎿቇኾ᡹

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ਛᄩᄢቇᄢቇ㒮ℂᎿቇ⎇ⓥ⑼ᖱႎᎿቇኾ᡹

ୃ჻⺰ᢥ

ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢࠍ↪޿ߚ

⾈޿࿁ࠅⴕേߩಽᨆ㧦

᧲੩ㇺ⥄↱߇ਐࠍ੐଀ߣߒߡ

#P#PCN[UKUQH5JQR#TQWPF$GJCXKQT7UKPI$C[GUKCP 0GVYQTM%CUG5VWF[QH,K[WICQMCKP6QM[Q

ᑝᎹ ⾆ਭ

Takahisa Hirokawa

ቇ☋⇟ภ 08N8100030C

ᜰዉᢎຬ ↰ญ ᧲ ᢎ᝼

2010 ᐕ 3 ᦬

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i

᭎ⷐ

᧪ⴝ⠪ߩ⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺࡞ࠍ૞ࠆߎߣ߇ߢ߈ࠇ߫㧘ㇺᏒ㐿⊒߿⚻༡ᚢ⇛ߥߤ ߦᄢ޿ߦᵴ↪ߢ߈ࠆߣ⠨߃ࠄࠇࠆ㧚ߒ߆ߒ㧘ᦐᣣߦࠃࠅ᧪ⴝ⠪ߩᐕ㦂߿⡯ᬺߣ޿ߞߚၮ ᧄዻᕈ߇⇣ߥࠆߎߣ߿㧘᧪ⴝ⠪ߩၮᧄዻᕈߦࠃࠅ┙ߜነࠆᐫ⥩ߩ௑ะߥߤ߇⇣ߥࠆߎߣ ߇ኈᤃߦᗐ௝ߢ߈ࠆࠃ߁ߦ㧘⾈޿࿁ࠅⴕേߦߪ᭽ޘߥⷐ࿃߇ⶄ㔀ߦ⛊ߺ޽ߞߡ޿ࠆ㧚߹

ߚ㧘᧪ⴝ⠪ߩᐫ⥩߳ߩ┙ߜነࠅⴕേߪ⸘↹⊛ߥ߽ߩߛߌߢߪߥߊ㧘᳇߹ߋࠇߢⴕࠊࠇࠆ ߎߣ߽޽ࠆ㧚ߎߩࠃ߁ߦ㧘᭽ޘߥⷐ⚛߇ⶄ㔀ߦ⛊ߺ޽ߞߡ߅ࠅ㧘ਇ⏕ታߥⴕേ߽ౝ൮ߒ ߡ޿ࠆߚ߼㧘⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺࡞ࠍ૞ᚑߔࠆߎߣߪ㕖Ᏹߦ࿎㔍ߢ޽ࠆ㧚

ᧄ⎇ⓥߢߪ㧘ᐕ㦂߿⡯ᬺߣ޿ߞߚ᧪ⴝ⠪ߩၮᧄዻᕈߦࠃߞߡ㧘⾈޿࿁ࠅⴕേ߇⇣ߥࠆ ߎߣࠍ⴫⃻ߢ߈ࠆࡕ࠺࡞ࠍ᭴▽ߒ㧘ಽᨆࠍⴕ߁ߎߣࠍ⋡⊛ߣߔࠆ㧚᭴▽ߔࠆࡕ࠺࡞ߪ㧘

৻ᣣߩ⾈޿࿁ࠅᐫ⥩ࠍ⴫ߔࡕ࠺࡞ߣ㧘ㅪ⛯ߒߡ⸰ࠇࠆ 2 ᐫ⥩ߩ⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺

࡞ߩ 2 ⒳㘃ߢ޽ࠆ㧚೨⠪ߩࡕ࠺࡞ߢߪ㧘᧪ⴝ⠪ߩၮᧄዻᕈߣ┙ߜነࠅᐫ⥩ߩᬺ⒳ߩ⚵ว ߖߩ㑐ଥࠍ⴫⃻ߔࠆ㧚ᓟ⠪ߩࡕ࠺࡞ߢߪ㧘᧪ⴝ⠪ߩၮᧄዻᕈ㧘ᐫ⥩ߩᬺ⒳㧘ߘߒߡ㧘ᐫ

⥩߇ሽ࿷ߔࠆ࿾඙߿⒖േ⚻〝ߣ޿ߞߚㇺᏒߩⓨ㑆⊛ߥⷐ⚛ߩ㑐ଥࠍ⴫⃻ߔࠆ㧚

ᧄ⎇ⓥߢߪ㧘⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺࡞ࠍ㧘ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢࠍ↪޿ߡ᭴▽ߔ ࠆ㧚ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߢߪ㧘⏕₸੐⽎ࠍࡁ࡯࠼㧘੐⽎㑆ߩ࿃ᨐ㑐ଥࠍ᦭ะ࡝ࡦࠢ

ߢ⴫ߔࠣ࡜ࡈࠍ↪޿ߡࡕ࠺࡞ࠍ⴫⃻ߔࠆ㧚߹ߚ㧘੐⽎㑆ߩ࿃ᨐ㑐ଥߦߪ⏕₸ℂ⺰ࠍ↪޿

ࠆ㧚⏕₸ℂ⺰ࠍ↪޿ߡ޿ࠆߚ߼㧘ਇ⏕ታߥⷐ࿃ࠍ฽߻ࡕ࠺࡞ࠍ⴫⃻ߔࠆߎߣߦะ޿ߡ޿

ࠆ㧚ߎߩߎߣߪ㧘ᱠⴕ⠪ߩ᳇߹ߋࠇߥⴕേߩ⴫⃻ߦᓎ┙ߟߣ⠨߃ࠄࠇࠆ㧚

ᧄ⎇ⓥߢߪ㧘߹ߕ㧘⡞߈ขࠅᑼࠕࡦࠤ࡯࠻⺞ᩏߢ޽ࠆ⥄↱߇ਐ᧪ⴝ⠪⺞ᩏࠍ↪޿ߡቇ

⠌࠺࡯࠲ࠍ૞ᚑߔࠆ㧚ᰴߦ㧘ቇ⠌࠺࡯࠲ࠍ↪޿ߡࡕ࠺࡞ߩផቯࠍⴕ߁㧚ᦨᓟߦ㧘ផቯߒ ߚࡕ࠺࡞ࠍ↪޿ߡಽᨆࠍⴕ޿㧘⾈޿࿁ࠅⴕേߦ㑐ߔࠆ⍮⷗ࠍᓧࠆ㧚

ࠠ࡯ࡢ࡯࠼㧦⾈޿࿁ࠅⴕേ㧘࿁ㆆⴕേ㧘ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢ

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ii

⋡ᰴ

╙ 1 ┨ ᐨ⺰ ... 1

1.1 ⎇ⓥ⢛᥊ߣ⋡⊛ ... 1

1.2 ᧄ⺰ᢥߩ᭴ᚑ ... 2

╙ 2 ┨ ૶↪࠺࡯࠲ ... 3

2.1 ⥄↱߇ਐ᧪ⴝ⠪⺞ᩏ࠺࡯࠲ ... 3

2.1.1 ࿁╵⠪ߩၮᧄዻᕈ ... 4

2.1.2 ⋡⊛ᐫ⥩ ... 7

2.1.3 ┙ߜነࠅᐫ⥩ ... 8

2.2 ⥄↱߇ਐࡀ࠶࠻ࡢ࡯ࠢߩ૞ᚑ ... 10

2.2.1 ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߩ᛽಴ ... 10

2.2.2 ਻ຠ੽Ꮉ✛㆏ߩ 1 ᧦ൻ ... 11

2.2.3 ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢ߳ᐫ⥩ࠍㅊട ... 13

2.2.4 ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢ߳⥄↱߇ਐ㚞ࠍㅊട ... 15

╙ 3 ┨ ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢ ... 18

3.1 ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢ ... 18

3.2 ቇ⠌࠺࡯࠲߆ࠄߩࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩផቯ ... 19

3.2.1 ࡄ࡜ࡔ࡯࠲ቇ⠌ ... 19

3.2.2 ᭴ㅧቇ⠌ ... 21

3.3 ⏕₸ផ⺰ ... 23

3.3.1 ࡐ࠹ࡦࠪࡖ࡞ ... 24

3.2.2 Junction Tree ߳ߩᄌ឵ ... 26

3.3.3 Junction Tree ࠍ↪޿ߚ੐ᓟ⏕₸ߩ⸘▚ ... 30

3.4 Bayes Net Toolbox ... 31

╙ 4 ┨ ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢࠍ↪޿ߚ⾈޿࿁ࠅⴕേߩಽᨆ ... 32

4.1 ⒖േ⚻〝ߩផቯ ... 32

4.1.1 Dijkstra ᴺ ... 32

4.1.2 ⒖േ⚻〝ߩផቯ ... 33

4.2 ㅪ⛯ߒߡ⸰ࠇࠆ 2 ᐫ⥩㑆ߩ⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺࡞ ... 33

4.2.1 ቇ⠌࠺࡯࠲ ... 34

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iii

4.2.2 ࠻ࡐࡠࠫ࡯㗅ᐨ ... 48

4.2.3 ᧪ⴝ⠪ዻᕈߦ㑐ߔࠆᄌᢙߩᦨㆡߥ࠻ࡐࡠࠫ࡯㗅ᐨ ... 49

4.2.4 ⶄᢙߩ౉ജ࠺࡯࠲ߦࠃࠆቇ⠌⚿ᨐߩᲧセ ... 50

4.2.5 CPT ߩಽᨆ ... 56

4.2.6 ⏕₸ផ⺰ ... 59

4.3 ৻ᣣߩ⾈޿࿁ࠅᐫ⥩ࠍ⴫ߔࡕ࠺࡞ ... 62

4.3.1 ቇ⠌࠺࡯࠲ ... 62

4.3.2 ࠻ࡐࡠࠫ࡯㗅ᐨߣᦨㆡߥ᧪ⴝ⠪ዻᕈߩㇱಽࠣ࡜ࡈ ... 65

4.3.3 ቇ⠌⚿ᨐ ... 67

╙ 5 ┨ ⚿⺰ ... 72

5.1 ߹ߣ߼ ... 72

5.2 ੹ᓟߩ⺖㗴 ... 75

⻢ㄉ ... 76

ෳ⠨ᢥ₂ ... 77

㑐ㅪ⊒⴫ ... 78

ઃ㍳ A ㅪ⛯ߔࠆ 2 ᐫ⥩㑆ߩ⾈޿࿁ࠅⴕേࠍ⴫ߔࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩ CPT ... 79

ઃ㍳ B ৻ᣣߩ⾈޿࿁ࠅᐫ⥩ࠍ⴫ߔࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩ CPT ... 84

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1

╙ 1 ┨ ᐨ⺰

1.1 ⎇ⓥ⢛᥊ߣ⋡⊛

᧪ⴝ⠪ߩ⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺࡞ࠍ૞ࠆߎߣ߇ߢ߈ࠇ߫㧘ㇺᏒ㐿⊒߿⚻༡ᚢ⇛ߥߤ ߦᄢ޿ߦᵴ↪ߢ߈ࠆߣ⠨߃ࠄࠇࠆ㧚ߒ߆ߒ㧘ᦐᣣߦࠃࠅ᧪ⴝ⠪ߩᐕ㦂߿⡯ᬺߣ޿ߞߚၮ ᧄዻᕈ߇⇣ߥࠆߎߣ߿㧘᧪ⴝ⠪ߩၮᧄዻᕈߦࠃࠅ┙ߜነࠆᐫ⥩ߩ௑ะߥߤ߇⇣ߥࠆߎߣ ߇ኈᤃߦᗐ௝ߢ߈ࠆࠃ߁ߦ㧘⾈޿࿁ࠅⴕേߦߪ᭽ޘߥⷐ࿃߇ⶄ㔀ߦ⛊ߺ޽ߞߡ޿ࠆ㧚߹

ߚ㧘᧪ⴝ⠪ߩᐫ⥩߳ߩ┙ߜነࠅⴕേߪ⸘↹⊛ߥ߽ߩߛߌߥߊ㧘᳇߹ߋࠇߢⴕࠊࠇࠆߎߣ

߽޽ࠆ㧚ߎߩࠃ߁ߦ㧘᭽ޘߥⷐ⚛߇ⶄ㔀ߦ⛊ߺ޽ߞߡ߅ࠅ㧘ਇ⏕ታߥⴕേ߽ౝ൮ߒߡ޿

ࠆߚ߼㧘⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺࡞ࠍ૞ᚑߔࠆߎߣߪ㕖Ᏹߦ࿎㔍ߢ޽ࠆ㧚

ᧄ⎇ⓥߢߪ㧘ᐕ㦂߿⡯ᬺߣ޿ߞߚ᧪ⴝ⠪ߩၮᧄዻᕈߦࠃߞߡ㧘⾈޿࿁ࠅⴕേ߇⇣ߥࠆ ߎߣࠍ⴫⃻ߢ߈ࠆࡕ࠺࡞ࠍ᭴▽ߒ㧘ಽᨆࠍⴕ߁ߎߣࠍ⋡⊛ߣߔࠆ㧚᭴▽ߔࠆࡕ࠺࡞ߪ㧘

৻ᣣߩ⾈޿࿁ࠅᐫ⥩ࠍ⴫ߔࡕ࠺࡞ߣ㧘ㅪ⛯ߒߡ⸰ࠇࠆ 2 ᐫ⥩ߩ⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺

࡞ߩ 2 ⒳㘃ߢ޽ࠆ㧚೨⠪ߩࡕ࠺࡞ߢߪ㧘᧪ⴝ⠪ߩၮᧄዻᕈߣ┙ߜነࠅᐫ⥩ߩᬺ⒳ߩ⚵ว ߖߩ㑐ଥࠍ⴫⃻ߔࠆ㧚ᓟ⠪ߩࡕ࠺࡞ߢߪ㧘᧪ⴝ⠪ߩၮᧄዻᕈ㧘ᐫ⥩ߩᬺ⒳㧘ߘߒߡ㧘ᐫ

⥩߇ሽ࿷ߔࠆ࿾඙߿⒖േ⚻〝ߣ޿ߞߚㇺᏒߩⓨ㑆⊛ߥⷐ⚛ߩ㑐ଥࠍ⴫⃻ߔࠆ㧚᧪ⴝ⠪ߩ ၮᧄዻᕈ㧘ᐫ⥩ߩᬺ⒳㧘ㇺᏒߩⓨ㑆⊛ߥⷐ⚛ࠍหᤨߦ⴫⃻ߔࠆࡕ࠺࡞ߣߒߡߪ㧘 [5] ߩ ࠃ߁ߥࠛ࡯ࠫࠚࡦ࠻ࡕ࠺࡞߇᜼ߍࠄࠇࠆ㧚

ᧄ⎇ⓥߢߪ㧘⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺࡞ࠍ㧘ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢࠍ↪޿ߡ᭴▽ߔ ࠆ㧚ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߢߪ㧘⏕₸੐⽎ࠍࡁ࡯࠼㧘੐⽎㑆ߩ࿃ᨐ㑐ଥࠍ᦭ะ࡝ࡦࠢ

ߢ⴫ߔࠣ࡜ࡈࠍ↪޿ߡࡕ࠺࡞ࠍ⴫⃻ߔࠆ㧚ࠣ࡜ࡈࠍ↪޿ࠆߎߣߢ㧘ࠛ࡯ࠫࠚࡦ࠻ࡕ࠺࡞

ࠃࠅ߽੐⽎㑆ߩ㑐ଥߩℂ⸃߇ኈᤃߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘੐⽎㑆ߩ࿃ᨐ㑐ଥߦߪ⏕

₸ℂ⺰ࠍ↪޿ࠆ㧚⏕₸ℂ⺰ࠍ↪޿ߡ޿ࠆߚ߼㧘ਇ⏕ታߥⷐ࿃ࠍ฽߻ࡕ࠺࡞ࠍ⴫⃻ߔࠆߎ ߣߦะ޿ߡ޿ࠆ㧚ߎߩߎߣߪ㧘ᱠⴕ⠪ߩ᳇߹ߋࠇߥⴕേߩ⴫⃻ߦᓎ┙ߟߣ⠨߃ࠄࠇࠆ㧚 ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩㆡ↪੐଀ࠍ޿ߊߟ߆⚫੺ߔࠆߣ㧘ᖚ⠪ߩ∛⁁߿ᬌᩏ⚿ᨐ߆ࠄ

∛ฬࠍ⸻ᢿߔࠆࠪࠬ࠹ࡓ㧘ㆊ෰ߩ⾼⾈ጁᱧ߿㑛ⷩጁᱧ߆ࠄ໡ຠផ⮈ࠍⴕ߁ࠪࠬ࠹ࡓߥߤ ߇᜼ߍࠄࠇࠆ㧚

⾈޿࿁ࠅⴕേࠍ⴫ߔࡕ࠺࡞ߩ᭴▽㧘ಽᨆߦࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢࠍㆡ↪ߒߚᣢሽ⎇

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2 ⓥߣߒߡ㧘 ^㨇 ⁸ ^㨉 ߇᜼ߍࠄࠇࠆ㧚 ^㨇 ⁸ ^㨉 ߢߪ㧘 2 ᐫ⥩㑆ߩ⾈޿࿁ࠅⴕേߦᵈ⋡ߒ㧘ࡌࠗࠫࠕ ࡦࡀ࠶࠻ࡢ࡯ࠢߩࡁ࡯࠼ࠍ㧘ᐕ㦂㧘ᕈ೎㧘಴⊒ߔࠆᐫ⥩㧘಴⊒ߔࠆᐫ⥩ߩ⸰໧⋡⊛㧘಴

⊒ߔࠆᐫ⥩ߢߩ⾼⾈ߩ᦭ή㧘೔⌕ߔࠆᐫ⥩㧘೔⌕ߔࠆᐫ⥩ߩ⸰໧⋡⊛㧘೔⌕ߔࠆᐫ⥩ߢ ߩ⾼⾈ߩ᦭ήߩ 8 ୘ߣߒߡ޿ࠆ㧚ᧄ⎇ⓥߢ᭴▽ߔࠆ 2 ᐫ⥩㑆ߩ⾈޿࿁ࠅⴕേߩࡕ࠺࡞ߢ ߪ㧘ᐕ㦂ߩઁߦ᧪ⴝᦐᣣ߿⡯ᬺߣ޿ߞߚᄙ᭽ߥ᧪ⴝ⠪ߩၮᧄዻᕈ㧘ᐫ⥩ߩᬺ⒳㧘᧪ⴝ೨ ߩ┙ߜነࠅ⸘↹ߩ᦭ήࠍ⴫ߔࡁ࡯࠼㧘ߘߒߡ㧘ᐫ⥩߇ሽ࿷ߔࠆ႐ᚲ㧘 2 ᐫ⥩㑆ߩ⒖േ⚻

〝ߣ޿ߞߚㇺᏒߩⓨ㑆⊛ߥⷐ⚛ߦ㑐ߔࠆࡁ࡯࠼ࠍ↪޿ࠆ㧚ߚߛߒ㧘ᧄ⎇ⓥߢ↪޿ࠆࠕࡦ ࠤ࡯࠻࠺࡯࠲ߢߪ㧘ᕈ೎㧘ᐫ⥩ߩ⸰໧⋡⊛㧘ᐫ⥩ߢߩ⾼⾈ߩ᦭ήߣ޿ߞߚ࿁╵㗄⋡߇ή

޿ߩߢࡁ࡯࠼ߣߒߡ↪޿ࠆߎߣ߇ߢ߈ߥ޿㧚ࠃߞߡ㧘ᧄ⎇ⓥߢ↪޿ࠆࡁ࡯࠼ߪ 15 ୘ߣ ߥࠆ㧚

߹ߚ㧘ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩࠣ࡜ࡈ᭴ㅧߩ᭴▽ߦߪ㧘࠺࡯࠲߆ࠄࠣ࡜ࡈ᭴ㅧࠍቇ

⠌ߔࠆᣇᴺߣ㧘⢛᥊⍮⼂ߦၮߠ߈ᚻേߢࠣ࡜ࡈࠍ᭴▽ߔࠆᣇᴺ߇޽ࠆ㧚 [8] ߢߪ㧘ᓟ⠪

ߩᣇᴺࠍ↪޿ߡࠣ࡜ࡈࠍ᭴▽ߒߡ޿ࠆ㧚ߒ߆ߒ㧘⢛᥊⍮⼂߆ࠄ᭴▽ߒߚࠣ࡜ࡈ߇ᦨㆡߥ

ࠣ࡜ࡈ᭴ㅧߣߪ㒢ࠄߕ㧘߹ߚ㧘ቇ⠌࠺࡯࠲߆ࠄᕁ޿߇ߌߥ޿ᄌᢙ㑆ߩ࿃ᨐ㑐ଥࠍᓧࠆߎ ߣ߇޽ࠆ㧚ߘߩߚ߼㧘ᧄ⎇ⓥߢߪ᭴ㅧቇ⠌ࠕ࡞ࠧ࡝࠭ࡓߦቇ⠌࠺࡯࠲ࠍਈ߃ࠆߎߣߢࠣ

࡜ࡈࠍ᭴▽ߔࠆ㧚

1.2 ᧄ⺰ᢥߩ᭴ᚑ

߹ߕ㧘╙ 2 ┨ߢ㧘ᧄ⎇ⓥߢ↪޿ࠆ⡞߈ขࠅᑼࠕࡦࠤ࡯࠻⺞ᩏߢ޽ࠆ⥄↱߇ਐ᧪ⴝ⠪⺞

ᩏߦߟ޿ߡ⺑᣿ߔࠆ㧚߹ߚ㧘⒖േ⚻〝ߩផቯߩߚ߼ߦ↪޿ࠆ⥄↱߇ਐ㚞๟ㄝߩᱠⴕ⠪ㅢ

ⴕน⢻㆏〝ߣᐫ⥩ࠍ⴫ߒߚࡀ࠶࠻ࡢ࡯ࠢߩ᭴▽ᣇᴺߦߟ޿ߡ⺑᣿ߔࠆ㧚⛯ߊ╙ 3 ┨ߢߪ㧘 ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߦߟ޿ߡ⺑᣿ߔࠆ㧚ቇ⠌࠺࡯࠲ࠍ↪޿ߚࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯

ࠢߩ᭴▽ߩߚ߼ߩࠕ࡞ࠧ࡝࠭ࡓ߿㧘⏕₸ផ⺰ߩࠕ࡞ࠧ࡝࠭ࡓࠍ⚫੺ߔࠆ㧚ߘߒߡ㧘╙ 4

┨ߢߪ㧘⥄↱߇ਐ᧪ⴝ⠪⺞ᩏ߆ࠄ૞ᚑߒߚቇ⠌࠺࡯࠲߆ࠄ㧘 2 ᐫ⥩㑆ߩ⾈޿࿁ࠅⴕേࠍ

⴫ߔࡕ࠺࡞ߣ৻ᣣߩ⾈޿࿁ࠅᐫ⥩ࠍ⴫ߔࡕ࠺࡞ࠍផቯߔࠆ㧚߹ߚ㧘ផቯߒߚࡌࠗࠫࠕࡦ

ࡀ࠶࠻ࡢ࡯ࠢࠍ↪޿ߡಽᨆࠍⴕ޿㧘⾈޿࿁ࠅⴕേߦ㑐ߔࠆ⍮⷗ࠍᓧࠆ㧚

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3

╙ 2 ┨

૶↪࠺࡯࠲

ᧄ┨ߢߪ㧘ᧄ⎇ⓥߢ૶↪ߔࠆ⥄↱߇ਐ᧪ⴝ⠪⺞ᩏ࠺࡯࠲ߣ㧘࠺ࠫ࠲࡞࿾࿑࠺࡯࠲߆ࠄ૞ᚑ ߒߚ⥄↱߇ਐࡀ࠶࠻ࡢ࡯ࠢߦߟ޿ߡ⺑᣿ߔࠆ㧚

2.1 ⥄↱߇ਐ᧪ⴝ⠪⺞ᩏ࠺࡯࠲

⥄↱߇ਐ᧪ⴝ⠪⺞ᩏ࠺࡯࠲ߪ㧘ᩣᑼળ␠᧲ᕆ✚ว⎇ⓥᚲߦࠃߞߡ㧘⥄↱߇ਐ㚞ᱜ㕙ญ࡮ධ ญ㧔᧲੩ㇺ⋡㤥඙㧕ߦߡ 2005 ᐕ 9 ᦬ 29 ᣣ㧔ᧁ㧕ߦ 78 ੱ㧘หᐕ 10 ᦬ 2 ᣣ㧔ᣣ㧕ߦ 81 ੱ㧘 ว⸘ 159 ੱߩᅚᕈ߆ࠄ᦭ലߥ࿁╵߇ᓧࠄࠇߚ⡞߈ขࠅᑼࠕࡦࠤ࡯࠻⺞ᩏߢ޽ࠆ㧚⥄↱߇ਐ᧪

ⴝ⠪⺞ᩏ࠺࡯࠲ߩ⺞ᩏ㗄⋡ߪએਅߩߣ߅ࠅߢ޽ࠆ㧚

࡮ ࿁╵⠪ߩၮᧄዻᕈ㧔ᐕ㦂㧘ᇕᆪߩ᦭ή㧘⡯ᬺ㧘หዬኅᣖ᭴ᚑ㧘หዬኅᣖੱᢙ㧘⥄ቛ߆ࠄߩ ᚲⷐᤨ㑆㧘⺞ᩏᣣ㧘⺞ᩏ࿾ὐ㧘᧪ⴝ㗫ᐲ㧕

࡮ ⋡⊛ᐫ⥩

࡮ ┙ߜነࠅᐫ⥩

࡮ ࿁╵⠪߇⥄↱߇ਐߣ޿߁ⴝߦࠗࡔ࡯ࠫ࡮ᗵᗐ

࡮ లታߒߡ᰼ߒ޿ᣉ⸳࡮ࠨ࡯ࡆࠬ

࡮ ⥄↱߇ਐߩⴝߦኻߔࠆᗧ⷗࡮ⷐᦸ

࡮ ᥉Ბߩ⾼⺒㔀⹹

⋡⊛ᐫ⥩ߦߪ㧘࿁╵⠪߇⥄↱߇ਐߦ᧪ⴝߔࠆ೨ߦ┙ߜነࠅࠍ⸘↹ߒߡ޿ߚᐫ⥩㧘߹ߚߪ㧘

ᬺ⒳㧔⮎ዪ㧘߅߽ߜ߾ደߥߤ㧕߇⸥タߐࠇߡ޿ࠆ㧚┙ߜነࠅᐫ⥩ߦߪ㧘࿁╵⠪߇ታ㓙ߦ┙ߜ ነߞߚᐫ⥩ฬ㧘߹ߚߪ㧘ᱠⴕ⚻〝ߩ৻ㇱ㧔⥄↱߇ਐ 2 㧙 16 ৻Ꮺ㧘ࡅ࡞ࠨࠗ࠼㧿㨠߆ࠄࠞ࠻࡟

ࠕ㧿㨠৻Ꮺࠍ㚞ᱜ㕙ญ߹ߢߥߤ㧕߇⸥タߐࠇߡ޿ࠆ㧚

ᧄ⎇ⓥߢߪ㧘࿁╵⠪ߩၮᧄዻᕈ㧘⋡⊛ᐫ⥩㧘┙ߜነࠅᐫ⥩ߩ 3 ߟߩ࿁╵㗄⋡ࠍ↪޿ࠆ㧚

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4 2.1.1 ࿁╵⠪ߩၮᧄዻᕈ

ࠕࡦࠤ࡯࠻࿁╵⠪ߩၮᧄዻᕈࠍ㧘ᐔᣣ㧔 2005 ᐕ 9 ᦬ 29 ᣣ㧕 78 ੱ㧘ભᣣ㧔 2005 ᐕ 10 ᦬ 2 ᣣ㧕 81 ੱߦಽߌߡ㧘એਅߦ␜ߔ㧚ฦᏪࠣ࡜ࡈౝߦ⸥ߐࠇߡ޿ࠆᢙ୯ߪታᢙߢ޽ࠅ㧘න૏ߪ [ ੱ ] ߢ޽ࠆ㧚

࿁╵⠪ߩᐕ㦂ߩഀวࠍ࿑ 2.1 ߦ␜ߔ㧚 20 ઍ㧘 30 ઍߩ࿁╵⠪ߩഀว߇㜞޿ߎߣ߇ࠊ߆ࠆ㧚ᦐ ᣣ೎ߦ⷗ࠆߣ㧘ᐔᣣࠃࠅભᣣߩᣇ߇ 30 ઍએਅߩ࿁╵⠪߇භ߼ࠆഀว߇㜞ߊ㧘⧯޿ੱ߇ᄙߊ᧪

ⴝߒߡ޿ࠆߎߣ߇ಽ߆ࠆ㧚

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㪇㩼㪈㪇㩼㪉㪇㩼㪊㪇㩼㪋㪇㩼㪌㪇㩼㪍㪇㩼㪎㪇㩼㪏㪇㩼㪐㪇㩼㪈㪇㪇㩼 ભᣣ

ᐔᣣ

ోᣣ

㪈㪇ᱦ䋭㪈㪐ᱦ 㪉㪇ᱦ䋭㪉㪐ᱦ 㪊㪇ᱦ䋭㪊㪐ᱦ 㪋㪇ᱦ䋭㪋㪐ᱦ 㪌㪇ᱦ䋭㪌㪐ᱦ 㪍㪇ᱦ䋭㪍㪐ᱦ 㪎㪇ᱦ䋭㪎㪐ᱦ

࿑ 2.1 ᐕ㦂ߩഀว

࿁╵⠪ߩᇕᆪߩ᦭ήߩഀวࠍ࿑ 2.2 ߦ␜ߔ㧚ᧂᇕ⠪ߣᣢᇕ⠪ߩഀวߪ߶߷หߓߛ߇㧘ᐔᣣ ߪᣢᇕ⠪ߩੱᢙ߇㧘ભᣣߪᧂᇕ⠪ߩੱᢙߩᣇ߇ᄙ޿ߎߣ߇⺒ߺขࠇࠆ㧚

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ᧂᇕ⠪ ᣢᇕ⠪

࿑ 2.2 ᇕᆪߩ᦭ήߩഀว

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5 ࿁╵⠪ߩ⡯ᬺߩഀวࠍ࿑ 2.3 ߦ␜ߔ㧚ߘߩઁߦߪ⥄༡ᬺ㧘ή⡯߇฽߹ࠇߡ޿ࠆ㧚ో૕ࠍ⷗

ࠆߣ㧘ળ␠ຬ㧘ኾᬺਥᇚ߇භ߼ࠆഀว߇㜞޿ߎߣ߇ಽ߆ࠆ㧚ᐔᣣߪኾᬺਥᇚ߇භ߼ࠆഀว߇ 㜞޿㧚৻ᣇ㧘ᐔᣣߦᲧߴߡભᣣߪ㧘ቇ↢㧘ળ␠ຬߩഀว߇⚂ 2 ୚ߢ޽ࠅ㧘ኾᬺਥᇚߩഀว߇ ૐ޿㧚

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ቇ↢ ળ␠ຬ 䊌䊷䊃䊶䉝䊦䊋䉟䊃 ኾᬺਥᇚ 䈠䈱ઁ

࿑ 2.3 ⡯ᬺߩഀว

࿁╵⠪ߩหዬኅᣖ᭴ᚑߩഀวࠍ࿑ 2.4 ߦ␜ߔ㧚ߘߩઁߦߪ㧘ఱᒉߣ૑ࠎߢ޿ࠆੱ㧘ᄦᇚߩ ߁ߜ ᣇߣᕷሶߣ૑ࠎߢ޿ࠆੱߥߤ߇฽߹ࠇߡ޿ࠆ㧚ᐔᣣߪ㧘৻ੱ᥵ࠄߒߣ 3 ਎ઍหዬ߇භ

߼ࠆഀว߇ૐߊ㧘ᄦᇚߣሶଏ߇භ߼ࠆഀว߇㜞޿㧚৻ᣇ㧘ભᣣߪ㧘ᄦᇚߣሶଏ߇භ߼ࠆഀว ߇ૐ޿ઍࠊࠅߦ㧘৻ੱ᥵ࠄߒߣ㧘 3 ਎ઍหዬ߇භ߼ࠆഀว߇㜞޿㧚

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ᐔᣣ

ోᣣ

৻ੱ᥵䉌䈚 ᄦᇚ䈱䉂 ᄦᇚ䈫ሶଏ 㪊਎ઍหዬ 䈠䈱ઁ

࿑ 2.4 หዬኅᣖ᭴ᚑߩഀว

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6 ࿁╵⠪ߩ⥄ቛ߆ࠄߩᚲⷐᤨ㑆ߩഀวࠍ࿑ 2.5 ߦ␜ߔ㧚⥄ቛ߆ࠄ 30 ಽᧂḩߢ⥄↱߇ਐߦ᧪ⴝ ߒߡ޿ࠆ࿁╵⠪ߩഀว߇㕖Ᏹߦ㜞޿㧚ᐔᣣߩ⥄ቛ߆ࠄߩᚲⷐᤨ㑆ߩᐔဋߪ 20.6 ಽߢ޽ࠆߩߦ ኻߒ㧘ભᣣߩ⥄ቛ߆ࠄߩᚲⷐᤨ㑆ߩᐔဋߪ 24.1 ಽߢ޽ࠆ㧚ભᣣߩᣇ߇㧘㆙ߊ߆ࠄ᧪ⴝߒߚ࿁

╵⠪߇㧘ᄙ޿ߎߣ߇ࠊ߆ࠆ㧚

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ోᣣ

ㅳ䈮㪊࿁એ਄ ㅳ䈮㪈䌾㪉࿁ ᦬䈮㪉䌾㪊࿁ ᦬䈮㪈࿁⒟ᐲ ᐕ䈮㪊䌾㪋࿁

ᐕ䈮㪉䌾㪊࿁ ᐕ䈮㪈࿁ᧂḩ

࿑ 2.5 ⥄ቛ߆ࠄߩᚲⷐᤨ㑆ߩഀว

࿁╵⠪ߩ᧪ⴝ㗫ᐲߩഀวࠍ࿑ 2.6 ߦ␜ߔ㧚᧪ⴝ㗫ᐲ߇㜞޿࿁╵⠪߶ߤ㧘㜞޿ഀวࠍභ߼ߡ

޿ࠆߎߣ߇ಽ߆ࠆ㧚߹ߚ㧘ભᣣࠃࠅᐔᣣߩᣇ߇㧘᧪ⴝ㗫ᐲ߇㜞޿࿁╵⠪߇ᄙ޿ߣ޿߃ࠆ㧚᧪

ⴝ㗫ᐲ߇ㅳߦ 3 ࿁એ਄ߣ╵߃ߡ޿ࠆੱߪㅢൕ㧘ㅢቇߢ⥄↱߇ਐߦㅢߞߡ޿ࠆ߆㧘⥄↱߇ਐߩ ㄭߊߦ૑ࠎߢ޿ߡ㘩ᢱ࡮ᣣᏱຠࠍ⾈޿‛ߦ᧪ߡ޿ࠆߣផ᷹ߢ߈ࠆ㧚

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㪈㪌ಽᧂḩ 㪈㪌ಽએ਄㪊㪇ಽᧂḩ 㪊㪇ಽએ਄㪋㪌ಽᧂḩ 㪋㪌ಽએ਄

࿑ 2.6 ᧪ⴝ㗫ᐲߩഀว

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7 2.1.2 ⋡⊛ᐫ⥩

ᧄ㗄ߢߪ㧘⋡⊛ᐫ⥩ߩ࿁╵ౝኈߦߟ޿ߡ⸃⺑ࠍⴕ߁㧚

᧪ⴝ೨ߦ┙ߜነࠅ⸘↹ࠍߒߡ޿ߚ࿁╵⠪߇ 3 ੱએ਄޿ࠆᐫ⥩ࠍ㒠㗅ߦ⴫ 2.1 ߦ␜ߔ㧚ࠬ࡯

ࡄ࡯ࡑ࡯ࠤ࠶࠻㧔એਅ㧘ࠬ࡯ࡄ࡯ߣߔࠆ㧕㧘㔀⽻ᐫ㧘᦯㘼ᐫࠍ⋡⊛ߣߒߡ⥄↱߇ਐߦ᧪ⴝߒߡ

޿ࠆੱ߇ᄙ޿ߎߣ߇ಽ߆ࠆ㧚

⴫ 2.1 ᧪ⴝ೨ߦ┙ߜነࠅࠍ⸘↹ߒߡ޿ߚ࿁╵⠪߇ᄙ޿ᐫ⥩

ᐫ⥩ฬ ᬺ⒳ ࿁╵⠪ᢙ=ੱ?

ᄢਣࡇ࡯ࠦ࠶ࠢ ࠬ࡯ࡄ࡯ 22

᧲ᕆࠬ࠻ࠕ ࠬ࡯ࡄ࡯ 18

ήශ⦟ຠ 㔀⽻ 15

GAP 㩷 ᦯㘼 12

⑳ߩㇱደ 㔀⽻ 8

࡙࠾ࠢࡠ ᦯㘼 5

Afternoon Tea ༛⨥ᐫ 4

ABC ࡑ࡯࠻ 㕦 3

TSUTAYA ࡟ࡦ࠲࡞ࡆ࠺ࠝ 3

⥄↱߇ਐࠬࠗ࡯࠷ࡈࠜ࡟ࠬ࠻ ᵗ⩻ሶ 3

ࡔ࡞ࠨ 1 ⶄวᣉ⸳ 3

ࡔ࡞ࠨ 2 ⶄวᣉ⸳ 3

࿁╵⠪ߩ⋡⊛ᐫ⥩ᢙࠍ࿑ 2.7 ߦ␜ߔ㧚⋡⊛ᐫ⥩ᢙ߇ᦨ߽ᄙ޿࿁╵⠪ߩ⋡⊛ᐫ⥩ᢙߪ 5 ᐫ⥩

ߢ޽ࠆ㧚࿑ 2.7 ࠃࠅ㧘⋡⊛ᐫ⥩߇ 1 ᐫ⥩ߢ޽ࠆ࿁╵⠪߇ᦨ߽ᄙߊ㧘ᰴ޿ߢ㧘⋡⊛ᐫ⥩߇ή޿

࿁╵⠪߇ᄙ޿ߎߣ߇ಽ߆ࠆ㧚 1 ੱ޽ߚࠅߩᐔဋ⋡⊛ᐫ⥩ᢙߪ⚂ 1.7 ᐫ⥩ߢ޽ࠆ㧚

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⋡⊛ᐫ⥩ᢙ㩷㪲㩷ᐫ㩷㪴

ੱᢙ㩷㪲㩷ੱ㩷㪴

࿑ 2.7 ⋡⊛ᐫ⥩ᢙ

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8 2.1.3 ┙ߜነࠅᐫ⥩

ᧄ㗄ߢߪ㧘┙ߜነࠅᐫ⥩ߩ࿁╵㗄⋡ߦߟ޿ߡ⸃⺑ࠍⴕ߁㧚

┙ߜነࠅᐫ⥩ߣߒߡ࿁╵ߐࠇߚᐫ⥩ߪ 147 ᐫ⥩ߢ޽ࠆ㧚ᧄ⎇ⓥߢߪ㧘ࠗࡦ࠲࡯ࡀ࠶࠻ߦࠃ ࠆᬌ⚝㧘⃻࿾⺞ᩏߦࠃࠅ㧘 147 ᐫ⥩ਛ 131 ᐫ⥩ߩ૑ᚲࠍ․ቯߒߚ㧚૑ᚲ߇․ቯߔࠆߎߣ߇಴

᧪ߥ߆ߞߚ 16 ᐫ⥩ߩౝ⸶ߪ㧘 ޟ⥄↱߇ਐ㧞ৼ⋡㧝㧞⇟࿾㧔ᐫฬߥߒ㧕 ޠ 㧘 ޟ᦯ደ㧔⥄↱߇ਐ㧝㧙㧝㧕 ޠߥߤ㧘ᐫ⥩ฬ߇ਇ᣿ߢ޽ࠆᐫ⥩߇ 11 ᐫ⥩㧘ᐫ⥩ฬ߇⸥タߐࠇߡ޿ࠆ߇ᐫ⥩ࠍ⊒⷗ߔࠆ ߎߣ߇಴᧪ߥ߆ߞߚᐫ⥩߇ 5 ᐫ⥩ߢ޽ࠆ㧚૑ᚲ߇․ቯߢ߈ߥ޿ 16 ᐫ⥩ߪ㧘┙ߜነࠅᐫ⥩ߩ࿁

╵߆ࠄ㒰ᄖߔࠆ㧚ߔߥࠊߜ㧘┙ߜነࠅ߇ⴕࠊࠇߥ߆ߞߚߣ⠨߃ࠆ㧚

┙ߜነࠅᐫ⥩ߦߪ㧘ⶄᢙߩᐫ⥩߇౉ᐫߒߡ޿ࠆⶄวᣉ⸳߇࿁╵ߐࠇߡ޿ࠆߎߣ߽޽ࠇ߫㧘 ⶄวᣉ⸳ߩਛߦ౉ᐫߒߡ޿ࠆ㧘޽ࠆ 1 ᐫ⥩߇࿁╵ߐࠇߡ޿ࠆߎߣ߽޽ࠆ㧚଀߃߫㧘ࡔ࡞ࠨ 1 ߣ޿߁ⶄวᣉ⸳߳ߩ┙ߜነࠅ߇࿁╵ߐࠇߡ޿ࠆߎߣ߽޽ࠇ߫㧘ࡔ࡞ࠨ 1 ౝߦ౉ᐫߒߡ޿ࠆ࡙

࠾ࠢࡠߣ޿߁ᐫ⥩߳ߩ┙ߜነࠅ߇࿁╵ߐࠇߡ޿ࠆߎߣ߽޽ࠆ㧚ᧄ⎇ⓥߢߪ㧘ߎߩ 2 ߟߩ┙ߜ ነࠅߪ⁛┙ߦᛒ߁㧚ߟ߹ࠅ㧘ࡔ࡞ࠨ 1 ߳ߩ┙ߜነࠅߣ࡙࠾ࠢࡠ߳ߩ┙ߜነࠅߪ೎ޘߦขࠅᛒ ߁㧚

5 ੱએ਄ߩ࿁╵⠪߇┙ߜነࠅࠍⴕߞߚᐫ⥩ࠍ⴫ 2.2 ߦ␜ߔ㧚⋡⊛ᐫ⥩ߣห᭽ߦࠬ࡯ࡄ࡯㧘᦯

㘼ᐫ㧘㔀⽻ᐫߩ࿁╵⠪ᢙ߇ᄙ޿ߎߣ߇ಽ߆ࠆ㧚߹ߚ㧘ࡔ࡞ࠨ 1 㧘ࡔ࡞ࠨ 2 㧘⥄↱߇ਐ࠺ࡄ࡯࠻

ߣ޿ߞߚⶄวᣉ⸳ߦ┙ߜነߞߚ࿁╵⠪߽ᄙ޿㧚⋡⊛ᐫ⥩ߢߪⶄวᣉ⸳ߩ࿁╵߇ዋߥ߆ߞߚߎ

ߣࠍ⠨߃ࠆߣ㧘ⶄวᣉ⸳߳ߩ┙ߜነࠅߪ஧⊒⊛ߦⴕࠊࠇߡ޿ࠆߩߢߪߥ޿߆ߣផ᷹ߢ߈ࠆ㧚

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9 ⴫ 2.2 ┙ߜነࠅੱᢙ߇ᄙ޿ᐫ⥩

ᐫ⥩ฬ ᬺ⒳ ┙ߜነࠅੱᢙ [ ੱ ]

ᄢਣࡇ࡯ࠦ࠶ࠢ ࠬ࡯ࡄ࡯ 27

᧲ᕆࠬ࠻ࠕ ࠬ࡯ࡄ࡯ 24

GAP ᦯㘼 24

ήශ⦟ຠ 㔀⽻ 22

⑳ߩㇱደ 㔀⽻ 15

ࡔ࡞ࠨ 2 ⶄวᣉ⸳ 15

ࡔ࡞ࠨ 1 ⶄวᣉ⸳ 14

⥄↱߇ਐ࠺ࡄ࡯࠻ ⶄวᣉ⸳ 9

Afternoon Tea ༛⨥ᐫ 8

ࠠࡖ࠻࡞࠮࠱ࡦ࠻ࠠࠝ 㔀⽻ 7

ࠢ࡝ࠬ࠲࡞ 100 ౞࡚ࠪ࠶ࡊ 6

CAFE DENMARK ༛⨥ᐫ 6

LAURA ASHLEY HOME ᦯㘼 6

NEXT ᦯㘼 6

OUTLET 㔀⽻ 5

FUJIYA BOOK ᦠᐫ 5

LAURA ASHLEY HOME ᦯㘼 5

⥄↱߇ਐࠬࠗ࡯࠷ࡈࠜ࡟ࠬ࠻ ᵗ⩻ሶ 5

TSUTAYA ࡟ࡦ࠲࡞ࡆ࠺ࠝ 5

࿁╵⠪ߩ┙ߜነࠅᐫ⥩ᢙࠍ࿑ 2.8 ߦ␜ߔ㧚ᦨ߽ᄙߊߩᐫ⥩ߦ┙ߜነߞߡ޿ࠆ࿁╵⠪ߩ┙ߜ ነࠅᐫ⥩ᢙߪ 10 ᐫ⥩ߢ޽ࠆ㧚ࠣ࡜ࡈࠃࠅ㧘┙ߜነࠅᐫ⥩ᢙ߇ 1 ᐫ⥩߆ࠄ 4 ᐫ⥩ߢ޽ࠆ࿁╵⠪

߇ᄙ޿ߎߣ߇ಽ߆ࠆ㧚㧝ੱ޽ߚࠅߩᐔဋ┙ߜነࠅᐫ⥩ᢙߪ⚂ 2.6 ᐫ⥩ߢ޽ࠆ㧚ߚߛߒ㧘┙ߜ

ነࠅᐫ⥩ᢙ߇ 0 ߩ⠪ࠍ㒰ᄖߒߚ႐วߩᐔဋ┙ߜነࠅᐫ⥩ᢙߪ⚂ 2.8 ᐫ⥩ߢ޽ࠆ㧚

(14)

10

㪈㪊

㪊㪌

㪋㪈

㪉㪎㪉㪍

㪎㪌

㪈㪈㪉㪈

㪇㪌㪈㪇㪈㪌㪉㪇㪉㪌㪊㪇㪊㪌㪋㪇㪋㪌

㪇㪈㪉㪊㪋㪌㪍㪎㪏㪐㪈㪇

┙䈤ነ䉍ᐫ⥩ᢙ㩷㪲㩷ᐫ㩷㪴

ੱᢙ㩷㪲㩷ੱ㩷㪴

࿑ 2.8 ┙ߜነࠅᐫ⥩ᢙ

2.2 ⥄↱߇ਐࡀ࠶࠻ࡢ࡯ࠢߩ૞ᚑ

ᧄ▵ߢߪ㧘⥄↱߇ਐ㚞๟ㄝߩᱠ㆏㧘ᐫ⥩ߩ૏⟎ࠍ⴫ߔࡀ࠶࠻ࡢ࡯ࠢࠍ᭴▽ߔࠆ㧚߹ߕ㧘⥄

↱߇ਐ㚞๟ㄝߩᱠⴕ⠪ㅢⴕน⢻㆏〝ߩࡀ࠶࠻ࡢ࡯ࠢ㧔એਅ㧘ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߣߔࠆ㧕ࠍ࠺

ࠫ࠲࡞࿾࿑࠺࡯࠲߆ࠄ᛽಴ߔࠆ㧚ᰴߦ㧘ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߢ 2 ᧦ൻߐࠇߡ޿ࠆ࡝ࡦࠢߩ৻ㇱ ࠍ 1 ᧦ߩ࡝ࡦࠢߦୃᱜߔࠆ㧚ᦨᓟߦ㧘ᐫ⥩㧘⥄↱߇ਐ㚞ࠍ⴫ߔࡁ࡯࠼ߣ㧘ᐫ⥩ౝ㧘⥄↱߇ਐ 㚞᭴ౝߩ࡝ࡦࠢࠍࡀ࠶࠻ࡢ࡯ࠢߦㅊടߔࠆ㧚

2.2.1 ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߩ᛽಴

ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢࠍᤘᢥ␠߇⊒ⴕߒߡ޿ࠆ Mapple ᱠⴕ⠪ࡀ࠶࠻ࡢ࡯ࠢ࠺࡯࠲߆ࠄ᛽಴ߔ ࠆ㧚 Mapple ᱠⴕ⠪ࡀ࠶࠻ࡢ࡯ࠢ࠺࡯࠲ߪ㧘ᱠⴕ⠪ㅢⴕน⢻㆏〝ߢ᭴ᚑߐࠇߡ޿ࠆ࿾࿑࠺࡯࠲

ߢ޽ࠆ㧚ᱠⴕ⠪ᮮᢿ⑌ᱛ㆏〝߿ߘࠇߦḰߕࠆᐢ޿㆏〝ߢߪ㧘ᱠⴕน⢻ߥᱠ㆏ㇱಽࠍੑ᧦ൻߒ ߡࡀ࠶࠻ࡢ࡯ࠢൻߒߡ߅ࠅ㧘߹ߚ㧘ᮮᢿᱠ㆏㧘ᱠ㆏ᯅ㧘࿾ਅㅢ〝㧘㚞᭴ౝㅢ〝ߥߤ߽෼㍳ߐ ࠇߡ߅ࠅ㧘ᱠⴕ⠪⚻〝ត⚝ߦㆡߒߚ࠺࡯࠲ߢ޽ࠆ㧚ߥ߅㧘❗ዤߪ 1/10000 ߢ㧘ᐳᮡ♽ߪ⚻✲

ᐲᐳᮡ♽ߢ޽ࠆ㧚ᧄ⎇ⓥߢߪ㧘ᐳᮡ♽ࠍᐔ㕙⋥ⷺᐳᮡ♽ߦᄌ឵ߒߡ೑↪ߔࠆ㧚

࡝ࡦࠢߪᱠⴕ⠪ㅢⴕน⢻㆏〝ࠍ⴫ߒߡ߅ࠅ㧘㆏〝⒳೎㧘ᒻ⁁ὐ✚ᢙ㧘᏷ຬ୯ [ m ] 㧘࡝ࡦ

ࠢ㐳 [ m ] 㧘൨㈩୯ [ % ] ߩᖱႎࠍᜬߞߡ޿ࠆ㧚࡝ࡦࠢߪⶄᢙߩᒻ⁁ὐ㧔ࡁ࡯࠼㧕߆ࠄᚑࠅ

┙ߞߡ߅ࠅ㧘ᒻ⁁ὐߩ x ᐳᮡߣ y ᐳᮡߩ୯ࠍ଻᦭ߒߡ޿ࠆ㧚

Mapple ᱠⴕ⠪ࡀ࠶࠻ࡢ࡯ࠢ࠺࡯࠲߆ࠄ㧘⥄↱߇ਐ㚞ࠍਛᔃߣߔࠆ৻ㄝ߇ 2600m ߩᱜᣇᒻ

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11 ߩ▸࿐ౝߦ޽ࠆᱠⴕ⠪ㅢⴕน⢻㆏〝ࠍ᛽಴ߔࠆ㧚᛽಴ߔࠆࡀ࠶࠻ࡢ࡯ࠢߩⷙᮨߪ㧘ࡁ࡯࠼ᢙ 4669 㧘࡝ࡦࠢᢙ 6000 ߢ޽ࠆ㧚᛽಴ߒߚᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢࠍ࿑ 2.9 ߦ␜ߔ㧚࿑ 2.9 ਛߩ㕍޿

ᤊߪ⥄↱߇ਐ㚞㧘⿒޿✢ߢ࿐߹ࠇߚ▸࿐ߦ޽ࠆ㆏〝ߪ਻ຠ੽Ꮉ✛㆏ࠍ⴫ߒߡ޿ࠆ㧚

࿑ 2.9 ᛽಴ߒߚᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢ

2.2.2 ਻ຠ੽Ꮉ✛㆏ߩ 1 ᧦ൻ

࿑ 2.9 ߢߪ㧘਻ຠ੽Ꮉ✛㆏߇ 2 ᧦ߩ࡝ࡦࠢߢ⴫ߐࠇߡ޿ࠆߎߣ߇ಽ߆ࠆ㧚਻ຠ੽Ꮉ✛㆏ߩ

᭽ሶࠍ࿑ 2.10 ߦ␜ߔ㧚࿑ 2.10 ࠃࠅ㧘਻ຠ੽Ꮉ✛㆏ߩਛᄩಽ㔌Ꮺߦߪࡌࡦ࠴㧘⧎ს㧘ⴝ〝᮸㧘

ⴝἮߥߤ߇⸳⟎ߐࠇߡ޿ࠆ߇㧘ᱠⴕ⠪ߪਛᄩಽ㔌Ꮺࠍㅢࠅᛮߌߡ㆏ࠍᮮᢿߔࠆߎߣ߿㧘ਛᄩ

ಽ㔌Ꮺࠍᱠ㆏ߣߒߡ↪޿ࠆߎߣ߇ߢ߈ࠆߎߣ߇ࠊ߆ࠆ㧚

(16)

12 ࿑ 2.10 ਻ຠ੽Ꮉ✛㆏ߩ᭽ሶ

ࠃߞߡ㧘਻ຠ੽Ꮉ✛㆏ࠍ 2 ᧦ߩᱠ㆏ߢߪߥߊᄥ޿ 1 ᧄߩᱠ㆏ߦୃᱜߔࠆߎߣߢ㧘ᱠⴕ⠪ㅢⴕ น⢻㆏〝ߩ᭽ሶࠍࠃࠅ⃻ታߦහߒߚ߽ߩߦߔࠆߎߣ߇ߢ߈ࠆ㧚਻ຠ੽Ꮉ✛㆏ࠍ⴫ߔ 2 ᧦ߩ࡝

ࡦࠢࠍߘߩ㑆ࠍㅢࠆ 1 ᧦ߩ࡝ࡦࠢߢ⟎߈឵߃㧘ࡀ࠶࠻ࡢ࡯ࠢࠍౣ᭴▽ߒߚᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢ

ࠍ࿑ 2.11 ߦ␜ߔ㧚࿑ 2.11 ߢߪ㧘 1 ᧦ߩ࡝ࡦࠢߢ⟎߈឵߃ߚ਻ຠ੽Ꮉ✛㆏ࠍ⿒޿✢ߢ࿐ࠎߢ޿

ࠆ㧚 ਻ຠ੽Ꮉ✛㆏ࠍ 1 ᧦ൻߒߚࡀ࠶࠻ࡢ࡯ࠢߩⷙᮨߪࡁ࡯࠼ᢙ 4606 㧘 ࡝ࡦࠢᢙ 5924 ߢ޽ࠆ㧚

࿑ 2.11 ਻ຠ੽Ꮉ✛㆏ࠍ 1 ᧦ൻߒߚᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢ

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13 2.2.3 ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢ߳ᐫ⥩ࠍㅊട

2.2.2 㗄ߢ਻ຠ੽Ꮉ✛㆏ࠍ 1 ᧦ൻߒߚᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߦ㧘ᐫ⥩ࠍ⴫ߔࡁ࡯࠼ࠍㅊടߔࠆ㧚 ㅊടߔࠆᐫ⥩ߪ⥄↱߇ਐ᧪ⴝ⠪⺞ᩏߩ┙ߜነࠅᐫ⥩ߢ࿁╵߇޽ߞߚᐫ⥩ߩ߁ߜ㧘૑ᚲ߇․ቯ ߢ߈ߚ 131 ᐫ⥩ߢ޽ࠆ㧚

ᐫ⥩ߩઍ⴫⊛ߥ಴౉ࠅญ߇޽ࠆᐳᮡߦࡁ࡯࠼ࠍ૞ᚑߒ㧘૞ᚑߒߚࡁ࡯࠼ࠍᱠ㆏ࡀ࠶࠻ࡢ࡯

ࠢߣ࡝ࡦࠢߢ⚿߱㧚ㅊടߔࠆࡁ࡯࠼ߣᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢࠍ⚿߱࡝ࡦࠢߪ㧘ㅊടߔࠆࡁ࡯࠼߆ ࠄᦨ߽ㄭ޿ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߩ࡝ࡦࠢ߳ਅࠈߒߚု✢ߣߥࠆ㧚

޽ࠆὐ P 㧔 _P

_x

^, _P

_y

㧕߆ࠄ㧘ὐ A 㧔 _A

_x

^, _A

_y

㧕ߣὐ B 㧔 _B

_x

^, _B

_y

㧕ࠍ┵ὐߣߔࠆ✢ಽ AB ߦะ߆ߞߡု

✢ࠍᒁߊߎߣ߇ߢ߈ࠆ߆ߤ߁߆ߪ㧘એਅߩᑼࠍ⸃ߊߎߣߢ್ቯߔࠆ㧚

)}

)(

( )

)(

)}{(

)(

( )

)(

{( A

_y

P

_y

A

_y

B

_y

A

_x

P

_x

A

_x

B

_x

B

_y

P

_y

A

_y

B

_y

B

_x

P

_x

A

_x

B

_x

F (2.1)

F ߩ୯߇ 0 㧘߹ߚߪ⽶ߥࠄ߫㧘ὐ P ߆ࠄ✢ಽ AB ߳ߪု✢ࠍᒁߊߎߣ߇ߢ߈ࠆ߇㧘ᱜߥࠄ

߫ု✢ࠍᒁߊߎߣߪߢ߈ߥ޿㧚ု✢߇ᒁߊߎߣ߇ߢ߈ࠆ႐ว㧘ုὐ M ߩ x ᐳᮡ _M

_x

ߣ㧘 y ᐳᮡ

M

y

ߪએਅߩᑼߢ⴫ߔߎߣ߇ߢ߈ࠆ㧚

) 2 2 (

) (

) 2 2 (

) (

) )(

)(

(

B y A y

B x A x

B y A y

A x B x

A x P x

B x A x

B y A y

A y P y

P x M x

(2.2)

) 2 2 (

) (

) 2 2 (

) (

) )(

)(

(

B y A y

B x A x

A y B y

A y P y

B y A y

B x A x

A x P x

P y M y

(2.3)

ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߩోߡߩ࡝ࡦࠢߦኻߒ㧘ㅊടߔࠆࡁ࡯࠼߆ࠄု✢߇ᒁߌࠆ߆ุ߆ߩ್ቯ ࠍⴕ߁㧚ု✢ࠍᒁߊߎߣ߇ߢ߈ࠆ႐วߪု✢ߩ㐳ߐࠍਃᐔᣇߩቯℂࠍ↪޿ߡ⸘▚ߔࠆ㧚ᒁߊ ߎߣ߇ߢ߈ࠆోߡߩု✢ߩߥ߆ߢ㐳ߐ߇ᦨ⍴ߢ޽ࠆု✢ࠍ↪޿ߡ㧘ᐫ⥩ߩ಴౉ࠅญࠍ⴫ߔࡁ

࡯࠼ࠍᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߦㅊടߔࠆ㧚

ᐫ⥩ߩ಴౉ࠅญߩࡁ࡯࠼ P ߆ࠄ㧘ࡁ࡯࠼ A ߣࡁ࡯࠼ B ࠍ┵ὐߣߔࠆ࡝ࡦࠢ AB ਄ߦሽ࿷ߔ ࠆုὐ M ߦะ߆ߞߡ㧘ု✢ PM ߇ᒁ߆ࠇߚߣߔࠆ㧚ࡁ࡯࠼ P ࠍᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߦઃߌട߃ ࠆ㓙ߦߪ㧘ࡁ࡯࠼ P 㧘ࡁ࡯࠼ M ߣ㧘࡝ࡦࠢ PM ࠍᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߦട߃ࠆߛߌߢߥߊ㧘࡝

ࡦࠢ AB ࠍ࡝ࡦࠢ AM ߣ࡝ࡦࠢ MB ߦಽഀߔࠆ㧚߹ߚ㧘࡝ࡦࠢ PM ߩ࡝ࡦࠢ㐳ߪ 0 ߣߔࠆ㧚

࿑ 2.12 ߦߘߩ᭽ሶࠍ␜ߔ㧚

(18)

14 ࿑ 2.12 ᐫ⥩ࡁ࡯࠼ࠍᱠⴕ⠪ࡀ࠶࠻ࡢ࡯ࠢߦㅊടߔࠆ᭽ሶ

123 ߩᐫ⥩ߦߟ޿ߡߪ㧘ᐫ⥩ߩ಴౉ࠅญࠍ⴫ߔࡁ࡯࠼ࠍࡀ࠶࠻ࡢ࡯ࠢߦ 1 ߟㅊടߒ㧘ߘߩ ᐫ⥩ࠍ⴫ߔࡁ࡯࠼ߣߒߡᛒ߁㧚

ࡔ࡞ࠨ 1 㧘ࡔ࡞ࠨ 2 ߩ 2 ߟߩⶄวᣉ⸳ߪ಴౉ࠅญࠍ 2 ߟᜬߟᐫ⥩ߢ޽ࠆ߇㧘ߤߜࠄࠍઍ⴫

⊛ߥ಴౉ࠅญߣߒߡᛒ߁߆᳿߼ࠆߎߣߪ㔍ߒߊ㧘߹ߚ㧘 2 ߟߩ಴౉ࠅญߪᄢ߈ߊ㔌ࠇߡ߅ࠅ 㕙ߔࠆ㆏〝߽⇣ߥࠆ㧚ߘߎߢ㧘ࡔ࡞ࠨ 1 㧘ࡔ࡞ࠨ 2 ߩߺ಴౉ࠅญࠍ⴫ߔࡁ࡯࠼ࠍ 2 ߟߕߟ૞

ᚑߔࠆ㧚߹ߕ㧘ฦ಴౉ࠅญࠍࡀ࠶࠻ࡢ࡯ࠢߦㅊടߔࠆ㧚ᰴߦ㧘 2 ߟߩ಴౉ࠅญߩਛᔃߦᐫ⥩

ਛᔃࡁ࡯࠼ࠍ૞ᚑߒ㧘ᐫ⥩ਛᔃࡁ࡯࠼ߣ 2 ߟߩ಴౉ࠅญࠍ࡝ࡦࠢ㧔એਅ㧘ᐫ⥩ౝ࡝ࡦࠢߣߔ ࠆ㧕ߢ⚿߱㧚ᦨᓟߦ㧘ࡔ࡞ࠨ 1 ߣࡔ࡞ࠨ 1 ౝߦ౉ᐫߒߡ޿ࠆ 4 ᐫ⥩㧘ࡔ࡞ࠨ 2 ߣࡔ࡞ࠨ 2 ౝ ߦ౉ᐫߒߡ޿ࠆ 2 ᐫ⥩ࠍ⴫ߔࡁ࡯࠼ࠍߘࠇߙࠇߩᐫ⥩ਛᔃࡁ࡯࠼ߩㄭߊߦ૞ᚑߒ㧘ᐫ⥩ਛᔃ ࡁ࡯࠼ߣ࡝ࡦࠢ㐳 0 ߩ࡝ࡦࠢߢ⚿߱㧚࿑ 2.13 ߦߘߩ᭽ሶࠍ␜ߔ㧚࿑ 2.13 ߢߪ㧘ฦ౞ߪࡁ࡯

࠼ࠍ⴫ߒߡ߅ࠅ㧘㤛⦡ߩࡁ࡯࠼߇ᐫ⥩ߩ಴౉ࠅญࠍ⴫ߔࡁ࡯࠼㧘⿒޿ࡁ࡯࠼߇ᐫ⥩ਛᔃࡁ࡯

࠼㧘✛߇ᐫ⥩ࠍ⴫ߔࡁ࡯࠼㧘⿒޿࡝ࡦࠢ߇ᐫ⥩ౝ࡝ࡦࠢࠍ⴫ߒߡ޿ࠆ㧚

ᐫ⥩ౝ࡝ࡦࠢߩ࡝ࡦࠢ㐳ߪචಽᄢ߈޿୯ߣߔࠆ㧚ߎࠇߦࠃࠅ㧘ᐫ⥩ࠍ೑↪ߒߥ޿⠪߇ᐫ⥩

M P

PM

M A

AM

B M

MB

┵ὐߘߩ

࡝ࡦࠢ

B

A M

B A

AB

┵ὐߘߩ

࡝ࡦࠢ

P

B A

P

(19)

15 ౝ࡝ࡦࠢࠍ೑↪ߔࠆߎߣ߇ή޿㧘⸒޿឵߃ࠆߣ㧘ㅢࠅᛮߌ⋡⊛ߢᐫ⥩ౝ࡝ࡦࠢ߇↪޿ࠄࠇࠆ ߎߣ߇ή޿㧚৻ᣇ㧘ᐫ⥩ࠍ೑↪ߔࠆ⠪ߪ 2 ߟߩ಴౉ࠅญߩߤߜࠄ߆ࠄߢ߽ᐫ⥩ߦ౉ᐫߔࠆߎ ߣ߇ߢ߈㧘߹ߚ㧘ᐫ⥩߆ࠄ┙ߜ෰ࠆ㓙ߦߪᰴߩ⋡⊛࿾߳⒖േߔࠆߩߦㄭ޿ᣇߩ಴౉ࠅญࠍ↪

޿ࠆߎߣ߇ߢ߈ࠆ㧚

࿑ 2.13 ಴౉ࠅญ߇ 2 ߟ޽ࠆᐫ⥩ࠍࡀ࠶࠻ࡢ࡯ࠢ߳ㅊടߔࠆᣇᴺ

2.2.4 ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢ߳⥄↱߇ਐ㚞ࠍㅊട

⥄↱߇ਐ㚞ᱜ㕙ญߩᐳᮡࠍᜬߟࡁ࡯࠼㧔એਅ㧘ᱜ㕙ญࡁ࡯࠼ߣߔࠆ㧕ߣ㧘⥄↱߇ਐ㚞ධญ ߩᐳᮡࠍᜬߟࡁ࡯࠼㧔એਅ㧘ධญࡁ࡯࠼ߣߔࠆ㧕ࠍ㧘 2.2.3 㗄ߢᐫ⥩ߩ಴౉ࠅญࠍㅊടߒߚߩ ߣห᭽ߩᣇᴺߢᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߦㅊടߔࠆ㧚߹ߚ㧘㚞ਛᔃߩᐳᮡࠍᜬߟࡁ࡯࠼㧔એਅ㧘㚞 ਛᔃࡁ࡯࠼ߣߔࠆ㧕ߣ㧘㚞ਛᔃࡁ࡯࠼ߣᱜ㕙ญࡁ࡯࠼ࠍ┵ὐߣߔࠆ࡝ࡦࠢ㧘㚞ਛᔃࡁ࡯࠼ߣ ධญࡁ࡯࠼ࠍ┵ὐߣߔࠆ࡝ࡦࠢ㧔એਅ㧘ߎߩ 2 ᧄߩ࡝ࡦࠢࠍ㚞᭴ౝ࡝ࡦࠢߣߔࠆ㧕ࠍ૞ᚑߒ㧘 ᱠ㆏ࡀ࠶࠻ࡢ࡯ࠢߦㅊടߔࠆ㧚ߚߛߒ㧘⥄↱߇ਐ㚞᭴ౝㅢ〝ߪᡷᧅࠍㅢࠄߕߦㅢࠅᛮߌࠆߎ ߣ߇ߢ߈ߥ޿ߚ߼㧘ᱠⴕ⠪࿁ㆆⴕേߩ⚻〝ផቯߦ߅޿ߡ㧘ᐫ⥩߆ࠄᐫ⥩߳ߩ⒖േࠍⴕ߁㓙ߦ 㚞᭴ౝㅢ〝߇↪޿ࠄࠇࠆߎߣߪ߰ߐࠊߒߊߥ޿㧚ࠃߞߡ㧘㚞᭴ౝ࡝ࡦࠢߩ࡝ࡦࠢ㐳ߪචಽ㐳

޿୯ࠍᒰߡߪ߼ࠆ㧚

ᱠⴕ⠪ㅢⴕน⢻㆏〝ࡀ࠶࠻ࡢ࡯ࠢߦ਻ຠ੽Ꮉ✛㆏ࠍ 1 ᧦ൻߔࠆߣ޿߁ୃᱜࠍട߃㧘ߐࠄߦ㧘 131 ߩᐫ⥩ߣ⥄↱߇ਐ㚞ࠍㅊടߒ㧘ౣ᭴▽ߒߚࡀ࠶࠻ࡢ࡯ࠢࠍ⥄↱߇ਐࡀ࠶࠻ࡢ࡯ࠢߣߔࠆ㧚

⥄↱߇ਐࡀ࠶࠻ࡢ࡯ࠢߩⷙᮨߪࡁ࡯࠼ᢙ 4864 㧘࡝ࡦࠢᢙ 6185 ߢ޽ࠆ㧚࿑ 2.14 ߦ⥄↱߇ਐࡀ

ࡔ࡞ࠨ 1

ࡔ࡞ࠨ 1 ౝߩᐫ⥩ 1 ࡔ࡞ࠨ 1 ౝߩᐫ⥩ 2

䎆

ࡔ࡞ࠨ 2

ࡔ࡞ࠨ 2 ౝߩᐫ⥩ 1

䎆

(20)

16 ࠶࠻ࡢ࡯ࠢࠍ␜ߔ㧚࿑ 2.14 ߢߪ㧘㕍޿✢ߪᱠⴕ⠪ㅢⴕน⢻㆏〝㧘✛ߩ✢ߪ㚞᭴ౝ࡝ࡦࠢ㧘㤛

⦡ߩ✢ߪᐫ⥩ౝ࡝ࡦࠢ㧘⿒޿✢ߪ࡝ࡦࠢߩ┵ὐߩ 1 ߟ߇ᐫ⥩ߩ಴౉ࠅญࠍ⴫ߔࡁ࡯࠼ߢ޽ࠆ

࡝ࡦࠢࠍ⴫ߒߡ߅ࠅ㧘߹ߚ㧘⿒޿౞ߪᐫ⥩㧘᳓⦡ߩ౞ߪᐫ⥩ౝࡁ࡯࠼㧘㤛⦡ߩ౞ߪ಴౉ࠅญ ߇ⶄᢙ޽ࠆᐫ⥩ߩ಴౉ࠅญ㧘✛ߩ౞ߪ㚞ਛᔃࡁ࡯࠼㧘ᱜ㕙ญࡁ࡯࠼㧘ධญࡁ࡯࠼ࠍ⴫ߒߡ޿

ࠆ㧚

࿑ 2.14 ⥄↱߇ਐࡀ࠶࠻ࡢ࡯ࠢ

(21)

17 2.1.3 㗄ߩ⴫ 2.2 ߢ␜ߒߚ┙ߜነࠅੱᢙ߇ᄙ޿ᐫ⥩ߩ߁ߜ㧘਄૏ 10 ᐫ⥩ࠍᤊශߢ⴫ߒߚ߽

ߩࠍ࿑ 2.15 ߦ␜ߔ㧚

࿑ 2.15 ┙ߜነࠅੱᢙ਄૏ 10 ᐫ⥩ߩ૏⟎

᧲ᕆࠬ࠻ࠕ ࡇ࡯ࠦ࠶ࠢ

⑳ߩㇱደ

ࠠࡖ࠻࡞࠮࠱ࡦ

࠻ࠠࠝ

⥄↱߇ਐ

࠺ࡄ࡯࠻

ࡔ࡞ࠨ 1 ࡔ࡞ࠨ 2

GAP Afternoon

Tea

ήශ⦟ຠ

⥄↱ 䈏ਐ 㚞

(22)

18

╙ 3 ┨

ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢ

ᧄ┨ߢߪ㧘ᧄ⎇ⓥߢ↪޿ࠆࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߣ㧘߹ߚ㧘ቇ⠌࠺࡯࠲߆ࠄࡌࠗࠫࠕࡦ ࡀ࠶࠻ࡢ࡯ࠢߩផቯߔࠆࠕ࡞ࠧ࡝࠭ࡓߦߟ޿ߡ⺑᣿ߔࠆ㧚߹ߚ㧘ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩ ಽᨆߦࠃߊ↪޿ࠄࠇࠆ㧘⏕₸ផ⺰ߩᣇᴺߦߟ޿ߡ߽⺑᣿ߔࠆ㧚

3.1 ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢ

ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߢߪ㧘⏕₸ᄌᢙࠍࡁ࡯࠼ߣߒ㧘⏕₸ᄌᢙ㑆ߩ࿃ᨐ㑐ଥࠍ᦭ะ࡝ࡦ

ࠢߢ⴫ߒߚ㕖ᓴⅣ᦭ะࠣ࡜ࡈ㧔 DAG 㧦 Directed Acyclic Graph 㧕ߢࡕ࠺࡞ࠍ⴫ߔ㧚⏕₸ᄌᢙ 㑆ߩ࿃ᨐ㑐ଥߪ⏕₸ℂ⺰ࠍ↪޿ࠆ㧚߹ߚ㧘ቇ⠌࠺࡯࠲ࠍ↪޿ߚ⛔⸘⊛ߥቇ⠌ࠍⴕ߁ߎߣ߽น

⢻ߢ޽ࠆ㧚

ᧄ⎇ⓥߢขࠅᛒ߁ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩ⏕₸ᄌᢙߪ㧘ోߡ㔌ᢔᄌᢙߢ޽ࠆ㧚⏕₸ᄌᢙ ߇㔌ᢔᄌᢙߢ޽ࠆ႐ว㧘⏕₸ᄌᢙߪⷫࡁ࡯࠼ߩ⁁ᘒߏߣߩ᧦ઙઃ⏕₸ಽᏓࠍਗߴߚ⴫㧘᧦ઙ

ઃ⏕₸ಽᏓ⴫㧔એਅ㧘 CPT 㧦 Conditional Probability Table ߣߔࠆ㧕ࠍᜬߟ㧚

଀ߣߒߡ㧘࿑ 3.1 ߦࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩ଀ࠍ␜ߔ㧚 Cloudy 㧔㔕ߩ᦭ή㧕㧘 Rain 㧔㒠

㔎ߩ᦭ή㧕㧘 Sprinkler 㧔ᢔ᳓ᯏߩ૞േߩ᦭ή㧕㧘 Wet grass 㧔⦼↢ߩߒ߼ࠅߩ᦭ή㧕ߪߘࠇߙ

ࠇ⏕₸ᄌᢙߢ޽ࠅ㧘⁁ᘒᢙߪ 2 ߟߢ޽ࠆ㧚 Sprinkler 㧘 Rain ߩ 2 ߟߩࡁ࡯࠼ߪ౒ߦ Cloudy

ࠍⷫࡁ࡯࠼ߒߡᜬߟߩߢ㧘 Cloudy ߇ߣࠆ⁁ᘒߦࠃߞߡ⏕₸ಽᏓ߇⇣ߥࠆ㧚߹ߚ㧘 Wet Grass

ߪ Sprinkler 㧘 Rain ߩ 2 ߟߩࡁ࡯࠼ࠍⷫࡁ࡯࠼ߒߡᜬߟߩߢ㧘 2 ߟߩࡁ࡯࠼߇ߣࠆ⁁ᘒߦࠃ

ߞߡ⏕₸ಽᏓ߇⇣ߥࠆ㧚

(23)

19 Cloudy

0.5 P(Cloudy=T

䋩

0.5 P(Cloudy=F

䋩

0.5 P(Cloudy=T

䋩

0.5 P(Cloudy=F

䋩

0.1 0.5

P

䋨

Sprinkler=T

䋩

0.9 0.5

P

䋨

Sprinkler=F

䋩

Cloudy=T Cloudy=F

0.1 0.5

P

䋨

Sprinkler=T

䋩

0.9 0.5

P

䋨

Sprinkler=F

䋩

Cloudy=T Cloudy=F

0.8 0.2

P

䋨

Rain=T

䋩

0.2 0.8

P

䋨

Rain=F

䋩

Cloudy=T Cloudy=F

0.8 0.2

P

䋨

Rain=T

䋩

0.2 0.8

P

䋨

Rain=F

䋩

Cloudy=T Cloudy=F

Sprinkler=T Sprinkler=F

0.99 0.9

0.9 0.0

P

䋨

Wet Grass=T

䋩

0.01 0.1

0.1 1.0

P

䋨

Wet Grass=F

䋩

Rain=T Rain=F

Sprinkler=T Sprinkler=F

0.99 0.9

0.9 0.0

P

䋨

Wet Grass=T

䋩

0.01 0.1

0.1 1.0

P

䋨

Wet Grass=F

䋩

Rain=T Rain=F

Sprinkler Rain

Wet Grass

࿑ 3.1 ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩ଀

3.2 ቇ⠌࠺࡯࠲߆ࠄߩࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩផቯ

ቇ⠌࠺࡯࠲߆ࠄࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩࠣ࡜ࡈ᭴ㅧߣ CPT ࠍផቯߔࠆߎߣ߇ߢ߈ࠆ㧚࠺

࡯࠲߆ࠄࠣ࡜ࡈ᭴ㅧࠍቇ⠌ߔࠆߎߣࠍ᭴ㅧቇ⠌ߣ޿޿㧘߹ߚ㧘࠺࡯࠲߆ࠄ CPT ࠍቇ⠌ߔࠆߎ ߣࠍࡄ࡜ࡔ࡯࠲ቇ⠌ߣ޿߁㧚ᧄ⎇ⓥߢ↪޿ࠆ᭴ㅧቇ⠌ࠕ࡞ࠧ࡝࠭ࡓߢߪ㧘⸘▚ㅜਛߦࡄ࡜ࡔ

࡯࠲ቇ⠌ࠍ➅ࠅ㄰ߒⴕ߁ᔅⷐ߇޽ࠆ㧚ߘߩߚ߼㧘߹ߕ㧘ࡄ࡜ࡔ࡯࠲ቇ⠌ߩᚻᴺࠍ⚫੺ߒ㧘ᰴ

ߦ㧘᭴ㅧቇ⠌ࠕ࡞ࠧ࡝࠭ࡓࠍ⚫੺ߔࠆ㧚

3.2.1 ࡄ࡜ࡔ࡯࠲ቇ⠌

ࡄ࡜ࡔ࡯࠲ቇ⠌ߩᚻᴺߣߒߡ㧘ᦨዕផቯᴺߣࡌࠗ࠭ផቯᴺ߇޽ߍࠄࠇࠆ㧘ߤߜࠄߩᚻᴺ߽

౉ജߣߒߡᔅⷐߥ߽ߩߪ㧘ᰳ៊୯߇ή޿ቇ⠌࠺࡯࠲ߣࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩࠣ࡜ࡈ᭴ㅧ ߢ޽ࠆ㧚ࡌࠗ࠭ផቯᴺߩᣇ߇ᦨዕផቯᴺࠃࠅ߽৻⥸⊛ߢ޽ࠆߣ⸒ࠊࠇߡ޿ࠆ߇㧘ᧄ⎇ⓥߢߪ ᦨዕផቯᴺࠍ↪޿ߡࡄ࡜ࡔ࡯࠲ቇ⠌ࠍⴕ߁㧚ᧄ▵ߢߪ㧘ᦨዕផቯᴺ㧘ࡌࠗ࠭ផቯᴺߩਔᣇࠍ

⚫੺ߒ㧘ᦨዕផቯᴺࠍណ↪ߔࠆℂ↱ߦߟ޿ߡ߽ㅀߴࠆ㧚

(24)

20 㧔γ㧕ᦨዕផቯᴺ

⏕₸ᄌᢙߩᢙࠍ n ^{㧘⏕₸ᄌᢙ} i ߩⷫࡁ࡯࠼ߩ⚵߇ขࠅᓧࠆ⁁ᘒߩ⚵ߺวࠊߖߩᢙࠍ q

_i

^㧘⏕₸

ᄌᢙ i ^{߇ขࠅᓧࠆ⁁ᘒߩᢙࠍ} r

_i

^ߣߔࠆ㧚

N

ijk

ࠍ㧘ᄌᢙ i ߩⷫࡁ࡯࠼ߩ㓸ว߇ _j ⇟⋡ߩࡄ࠲࡯ࡦࠍߣࠅ㧘ᄌᢙ i ^߇ ^k ^{⇟⋡ߩ୯ࠍߣߞߚቇ}

⠌࠺࡯࠲ߩᢙߣቯ⟵ߔࠆ㧚଀߃߫㧘࿑ 3.2 ߩࠃ߁ߥࠣ࡜ࡈ᭴ㅧߣ⴫ 3.1 ߩࠃ߁ߥ 6 ઙߩቇ⠌

࠺࡯࠲߇ਈ߃ࠄࠇߡ޿ࠆߣ߈㧘 N

_Cjk

ߪ⴫ 3.2 ߩࠃ߁ߦߥࠆ㧚

⴫ 3.1 ቇ⠌࠺࡯࠲ߩ଀

ᄌᢙ A ^ᄌᢙ B ^ᄌᢙ C

࠺࡯࠲ 1 a

₁

b

₁

c

₁

࠺࡯࠲ 2 _a

₁

b

₁

c

₂

࠺࡯࠲ 3 a

₁

b

₂

c

₁

࠺࡯࠲ 4 a

₂

b

₁

c

₁

࠺࡯࠲ 5 a

₂

b

₂

c

₂

࠺࡯࠲ 6 a

₂

b

₂

c

₂

⴫ 3.2 ቇ⠌࠺࡯࠲߆ࠄᓧࠄࠇߚ N

_Cjk

a

1

A A a

₁

b

1

B B b

₂

B b

₁

B b

₂

c

1

C ^N

_C^{_A _a₁^,_B _b₁^}_c₁

=1

1 2

1, }

{A a B b c

N

C

=1

1 1

2 , }

{A a B b c

N

C

=1

1 2

2, }

{A a B b c

N

C

=0

c

2

C ^N

_C^{_A _a₁^,_B _b₁^}_c₂

⁼¹ ^N

_C^{_A _a₁^,_B _b₂^}_c₂

⁼⁰ ^N

_C^{_A _a₂^,_B _b₁^}_c₂

⁼⁰ ^N

_C^{_A _a₂ ^,_B _b₂^}_c₂

⁼²

߹ߚ㧘 T

_ijk

^ࠍ㧘ᄌᢙ _i ߩⷫࡁ࡯࠼ߩ㓸ว߇⁁ᘒ j ߢ޽ࠆߣ߈㧘ᄌᢙ i ߇⁁ᘒ k ^{ߢ޽ࠆ᧦ઙઃ⏕}

₸ߣቯ⟵ߔࠆ㧚

ቇ⠌࠺࡯࠲ࠃࠅ N

_ijk

߇ਈ߃ࠄࠇߚߣ߈㧘ᦨዕផቯᴺࠍ↪޿ߡᓧࠄࠇࠆ᧦ઙઃ⏕₸ T

_ijk

^ߪᑼ

㧔 3.1 㧕߆ࠄ᳞߼ࠆߎߣ߇ߢ߈ࠆ㧚

ij ijk ijk

N

T N 㧔 3.1 㧕

ߚߛߒ㧘 _¦

¹

0 ri

k ijk

ij

N

N ߣߔࠆ㧚߹ߚ㧘ᧄ⎇ⓥߢߪ N

_ij

0 ^ߩߣ߈ T

_ijk

1 / r

_i

^{ߣߔࠆ㧚ߎߩߎߣߪ㧘} ቇ⠌࠺࡯࠲߇ή޿႐ว㧘⏕₸ಽᏓߪ৻᭽ಽᏓߢ޽ࠆߣ઒ቯߔࠆߎߣߣห⟵ߢ޽ࠆ㧚

㧔δ㧕ࡌࠗ࠭ផቯᴺ

ᦨዕផቯᴺߢᓧࠄࠇࠆ CPT ߪ㧘ࠃࠅᄙߊߩቇ⠌࠺࡯࠲ࠍ↪޿ࠆ߆㧘᦭⋉ߥ੐೨ಽᏓࠍ↪޿

C

A B

࿑ 3.2 ᦨዕផቯᴺߩࠣ࡜ࡈ

(25)

21 ࠆߎߣߢ㧘ࠃࠅ⃻ታߦㄭ޿୯߇ᓧࠄࠇࠆ㧚੐೨ಽᏓߣߪ㧘ቇ⠌࠺࡯࠲߇ਈ߃ࠄࠇࠆ೨ߦᜬߞ ߡ޿ࠆ CPT ߦ㑐ߔࠆ⍮⼂ࠍ⴫ߒߚ߽ߩߢ޽ࠆ㧚ࡌࠗ࠭ផቯᴺࠍ↪޿ࠆߎߣߢ੐೨ಽᏓࠍቇ⠌

ᓟߩ CPT ߦขࠅ౉ࠇࠆߎߣ߇ߢ߈ࠆ㧚߹ߚ㧘੐೨ಽᏓࠍขࠅ౉ࠇࠆߎߣߢ㧘࠺࡯࠲߆ࠄߩㆊ ቇ⠌ࠍ㒐ߋߎߣ߽ߢ߈ࠆ㧚

੐೨ಽᏓߪᡆૃ⸘ᢙ㧔 pseudo counts 㧕 N

_ijk

c ߩⷰὐ߆ࠄ◲නߥ⸃㉼߇ਈ߃ࠄࠇࠆ㧚ቇ⠌࠺࡯

࠲߇ਈ߃ࠄࠇࠆ೨ߦ㧘ᡆૃ⸘ᢙ N

_ijk

c ߩ࿁ᢙߛߌ N

_ijk

߇᷹ⷰߐࠇߚߣߔࠆ㧚੐೨ಽᏓࠃࠅ N

_ijk

c 㧘 ቇ⠌࠺࡯࠲ࠃࠅ N

_ijk

߇ਈ߃ࠄࠇߚߣ߈㧘ࡌࠗ࠭ផቯᴺࠍ↪޿ߡᓧࠄࠇࠆ᧦ઙઃ⏕₸ T ^ˆ

_ijk

^ߪᑼ

㧔 3.2 㧕߆ࠄ᳞߼ࠆߎߣ߇ߢ߈ࠆ㧚

ij ij

ijk ijk ijk

N N

c c

T ^ˆ 㧔 3.2 㧕

ߚߛߒ㧘 c _¦

¹

c

0 ri

k ijk

ij

N

N ^㧘 N

_ijk

c t ⁰ ߣߔࠆ㧚੐೨ಽᏓߪછᗧߦቯ߼ߡࠃ޿㧚੐೨ಽᏓߩ⍮⼂߇ή

޿႐ว㧘৻᭽ߥಽᏓ߇੐೨ಽᏓߣߒߡ↪޿ࠄࠇࠆߎߣ߇޽ࠆ㧚 D

_i

^{ࠍᱜߩታᢙߣߔࠆߣ㧘}

i r

k q

ij _i _i

N ^c

_{₁_,_, _} _{₀_,_, ₁_}

D ߣߔࠆߎߣߢ৻᭽ߥ੐೨ಽᏓࠍਈ߃ࠆߎߣߦߥࠆ㧚৻᭽ߥ੐೨ಽᏓࠍਈ ߃ࠆߣ T ^ˆ

_ijk

^ߪ T

_ijk

^ࠃࠅ߽ ¹ ^/ _r

_i

^{ߦㄭ޿୯ߦߥࠆ㧚} D

_i

^ߪฦ ^CPT ߦኻߔࠆ੐೨ಽᏓߩᒝߐߣ⸃㉼ߔࠆ ߎߣ߇ߢ߈㧘 D

_i

^{߇ᄢ߈޿߶ߤ} T ^ˆ

_ijk

^ߪࠃࠅ ¹ ^/ _r

_i

ߦㄭߠ޿ߡ޿ߊ㧚ߟ߹ࠅ㧘ቇ⠌࠺࡯࠲ߩᢙߦኻߒ ߡ N

_ijk

c ߩ୯ࠍᄢ߈ߊߔࠆߣ㧘ᓧࠄࠇࠆ CPT ߪቇ⠌࠺࡯࠲ߩᓇ㗀ࠍฃߌߦߊߊߥࠆ㧚߹ߚ㧘ᦨ ዕផቯᴺߪ੐೨ಽᏓࠍ N

_ijk

c 0 ߩߣ߈ߩࡌࠗ࠭ផቯᴺߢ޽ࠆߣ޿߁ߎߣ߇ߢ߈ࠆ㧚

ᧄ▵ߩ౨㗡ߢㅀߴߚࠃ߁ߦ㧘ᦨዕផቯᴺࠃࠅ߽ࡌࠗ࠭ផቯᴺߩᣇ߇৻⥸⊛ߢ޽ࠆ㧚ߒ߆ߒ㧘 ᧄ⎇ⓥߢߪ CPT ߦ㑐ߔࠆ᦭⋉ߥ੐೨⍮⼂߇ή޿㧚߹ߚ㧘৻᭽ߥಽᏓࠍ੐೨ಽᏓߣߒߡਈ߃ࠆ ߣߒߡ߽㧘ߤߩࠃ߁ߥ D

_i

߇ㆡಾߥߩ߆್ᢿߔࠆၮḰ߇ήߊ㧘ߒ߆߽㧘ࡄ࡜ࡔ࡯࠲ቇ⠌߆ࠄᓧ ࠄࠇߚ CPT ߦߟ޿ߡ⼏⺰ߔࠆ㓙ߦ T ^ˆ

_ijk

ࠍ↪޿ࠆߣ㧘੐೨ಽᏓ߇ߤߩ⒟ᐲ T ^ˆ

_ijk

^{ߦᓇ㗀ࠍਈ߃ߚ߆}

ࠍᏱߦ⠨ᘦߔࠆᔅⷐ߇޽ࠅ㧘⼏⺰߇ⶄ㔀ߦߥࠆ㧚એ਄ߩℂ↱ߦࠃࠅ㧘ᧄ⎇ⓥߢߪᦨዕផቯᴺ ࠍ↪޿ߡࡄ࡜ࡔ࡯࠲ቇ⠌ࠍⴕ߁ߎߣߦߔࠆ㧚

3.2.2 ᭴ㅧቇ⠌

ᧄ⎇ⓥߢߪ㧘᭴ㅧቇ⠌ࠕ࡞ࠧ࡝࠭ࡓߩ 1 ߟߢ޽ࠆ K2 ࠕ࡞ࠧ࡝࠭ࡓࠍ↪޿ࠆ㧚 K2 ࠕ࡞ࠧ࡝

࠭ࡓߪ⽽᰼⸃ᴺߢ޽ࠅ㧘᳞߹ࠆ⸃ߪㄭૃ⸃ߢ޽ࠆ㧚߹ߚ㧘 K2 ࠕ࡞ࠧ࡝࠭ࡓߪ㧘౉ജߣߒߡᰳ

៊୯߇฽߹ࠇߡ޿ߥ޿ቇ⠌࠺࡯࠲ߩઁߦࡁ࡯࠼ߩ࠻ࡐࡠࠫ࡯㗅ᐨ߇ᔅⷐߣߥࠆ㧚

࠻ࡐࡠࠫ࡯㗅ᐨߣߪ㧘ሶ߇ⷫߩ೨ߦ᧪ࠆߎߣ߇ή޿㗅ᐨߢ޽ࠆ㧚࿑ 3.1 ߩ࠻ࡐࡠࠫ࡯㗅ᐨ

ߪޟ Cloudy 㧘 Sprinkler 㧘 Rain 㧘 Wet Grass ޠ 㧘߹ߚߪ㧘 ޟ Cloudy 㧘 Rain 㧘 Sprinkler 㧘 Wet Grass ޠ

ߩ 2 ㅢࠅ߇⠨߃ࠄࠇࠆ㧚౉ജߣߒߡ࠻ࡐࡠࠫ࡯㗅ᐨࠍਈ߃ࠆ㓙ߦߪ㧘࠻ࡐࡠࠫ࡯㗅ᐨࠍછᗧ

(26)

22 ߦቯ߼ߡࠃ޿㧚৻⥸⊛ߦ㧘ᤨ♽೉ߩ㗅ᐨ㧘੐೨ߦᓧࠄࠇߡ޿ࠆ⍮⷗㧘ቇ⠌ᓟߩࡌࠗࠫࠕࡦࡀ

࠶࠻ࡢ࡯ࠢߩ೑↪⋡⊛ߥߤࠍ✚ว⊛ߦ⠨ᘦߒߡ࠻ࡐࡠࠫ࡯㗅ᐨࠍ᳿ቯߔࠆ㧚

ࡁ࡯࠼ᢙߣ᭴ㅧቇ⠌ߩ⸃ߩ୥⵬ᢙߩ㑐ଥࠍ⴫ 3.3 ߦ␜ߔ㧚᭴ㅧቇ⠌ߩ⸃ߩ୥⵬ߪ㧘ࡁ࡯࠼

ᢙߣ౒ߦ῜⊒⊛ߦჇടߔࠆߎߣ߇ಽ߆ࠆ㧚ߘߎߢ㧘࠻ࡐࡠࠫ࡯㗅ᐨࠍ೙⚂᧦ઙߣߒߡਈ߃ࠆ ߎߣߢ㧘⸘▚㊂ࠍᛥ߃ߡ޿ࠆ㧚

⴫ 3.3 ࡁ࡯࠼ᢙߣ᭴ㅧቇ⠌ߩ⸃ߩ୥⵬

ࡁ࡯࠼ᢙ ⸃ߩ୥⵬

1 1 2 3 3 25 4 543 5 29,281 6 3,781,503 7 1 . 1 u 10

⁹

8 7 . 8 u 10

¹¹

9 1 . 2 u 10

¹⁵

10 4 . 2 u 10

¹⁸

n ^{୘ߩ⏕₸ᄌᢙ} X ߇޽ࠅ㧘࠻ࡐࡠࠫ࡯㗅ᐨ߇ { X

₁

, X

₂

, , X

_n

} ߣਈ߃ࠄࠇߡ޿ࠆߣߔࠆ㧚߹ߚ㧘

⏕₸ᄌᢙ X

_i

ߩⷫࡁ࡯࠼ߩ⚵ࠍ pa ( X

_i

) ߣ⴫ߔߣߔࠆ㧚ߎߩߣ߈㧘 K2 ࠕ࡞ࠧ࡝࠭ࡓߪએਅߩᚻ 㗅ߢⴕࠊࠇࠆ㧚

Step 1 i 1 ^{ߣߔࠆ㧚߹ߚ㧘} _pa ⁽ _X

_i

⁾ I ^ߣߔࠆ㧚

Step 2 P ( X

_i

| pa ( X

_i

) X

_j

) ߩ⹏ଔ୯ࠍᦨᄢߣߔࠆࠃ߁ߥ X

_j

ࠍ᳞߼ࠆ㧚ߚߛߒ㧘 1 d j d i 1 ߆ ߟ pa ( X

_i

) X

_j

ߣߔࠆ㧚

Step 3 P ( X

_i

| pa ( X

_i

)) ߣ P ( X

_i

| pa ( X

_i

) X

_j

) ߩ⹏ଔ୯ࠍᲧセߔࠆ㧚 P ( X

_i

| pa ( X

_i

)) ߩᣇ߇⹏ଔ ߇⦟޿㧘߹ߚߪ㧘ਔ⠪ߩ⹏ଔ߇╬ߒ޿႐วߥࠄ߫ Step3-1 ߳㧘 P ( X

_i

| pa ( X

_i

) X

_j

) ߩ ᣇ߇⹏ଔ߇⦟޿ߥࠄ߫㧘 Step3-2 ߳㧚

Step 3-1 i n ߥࠄ߫ࠕ࡞ࠧ࡝࠭ࡓࠍ⚳ੌߒ㧘 i n ߥࠄ߫ i ߦ 1 ࠍട▚ߒ Step2 ߳㧚

Step 3-2 pa ( X

_i

) ࠍ pa ( X

_i

) X

_j

ߦᦝᣂߒ㧘 Step2 ߳㧚ߚߛߒ㧘 pa ( X

_i

) { X

₁

, X

₂

, , X

_i₁

} ߣߥ ߞߚ႐วߪ㧘 i ߦ 1 ࠍട▚ߒߡ߆ࠄ Step2 ߳㧚

ߎߎߢ㧘⹏ଔ୯ߦߟ޿ߡ⺑᣿ߔࠆ㧚 K2 ࠕ࡞ࠧ࡝࠭ࡓߢ↪޿ࠄࠇࠆ⹏ଔ୯ߪ᭽ޘ޽ࠆ߇㧘ᧄ

⎇ⓥߢߪᦨᄢኻᢙዕᐲࠍ↪޿ߡ⸃ߩ⹏ଔࠍⴕ߁㧚ࠣ࡜ࡈ᭴ㅧ B

_s

㧘᧦ઙઃ⏕₸ T

_ijk

^ߩ㓸ว 4 ^㧘

ቇ⠌࠺࡯࠲ D ߇ਈ߃ࠄࠇߚߣ߈㧘ቇ⠌࠺࡯࠲ D ߩࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢ߳ߩᒰߡߪ߹ࠅߩ

(27)

23 ࠃߐࠍ⴫ߔዕᐲ p ( D | 4 , B

_s

) ߪ 㨇 6 㨉 ࠃࠅ㧘ᑼ㧔 3.3 㧕ߢ⴫ߐࠇࠆ㧚

¦

v 4

n

i

q

j

r

k

N ijk r

k

N ijk n

i

q

j r

k ijk

r

k ijk

s

i i

ijk i

i i

N N B

D p

1 1

1

0 1

0

1 1 1

0 1

0

!

! )

,

|

( T T ^㧔 ^3.3 ^㧕

ࡄ࡜ࡔ࡯࠲ቇ⠌߆ࠄᓧࠄࠇߚ᧦ઙઃ⏕₸ߩ㓸ว

Bs

4 ߪዕᐲࠍᦨᄢߦߔࠆ㧚߹ߚ㧘ᦨᄢዕᐲ )

,

|

( D B

_s

p 4 ߪ

ⁿ

i

q j

r k

ijkN

i i ijk

1 1

1

0

T ߦᲧ଀ߔࠆߩߢ㧘ᦨᄢዕᐲߩኻᢙ log p ( D | 4 , B

_s

) ߪ ¦ ¦ ¦

n

i

q j

r

k ijk ijk

i i

N

1 1 0

1

log T

ߦᲧ଀ߔࠆ㧚ࠃߞߡ㧘ቇ⠌࠺࡯࠲ D ߇ਈ߃ࠄࠇߚߣ߈ߩࠣ࡜ࡈ᭴ㅧ B

_s

ߩᦨᄢኻᢙዕᐲߪ㧘ࡄ

࡜ࡔ࡯࠲ቇ⠌ࠍⴕ߁ߎߣߢᓧࠄࠇࠆ

Bs

4 ࠍ↪޿ߡ㧘ᑼ㧔 3.4 㧕ߢ⴫ߐࠇࠆ l

_B_s

( 4

_B_s

| D ) ߩᄢ߈ߐ ߢ⹏ଔߐࠇࠆ㧚

¦¦¦

4

n

i

q

j

r

k ijk ijk

B B

i i

s

D N

l

1 1 0

1

log

)

|

( T ^㧔 ^3.4 ^㧕

)

|

( D

l

_B_s

4

_B_s

߇ᄢ߈޿߶ߤ⹏ଔ߇㜞޿㧚ᑼ㧔 3.4 㧕ࠍ⷗ࠆߣ㧘ࠣ࡜ࡈ᭴ㅧ B

_s

ߩᦨᄢኻᢙዕᐲߪ㧘

⏕₸ᄌᢙ X

_i

ߣߘߩⷫࡁ࡯࠼ߩ㓸วߢ޽ࠆ pa ( X

_i

) ߆ࠄᚑࠅ┙ߟዪᚲᧁߩᦨᄢኻᢙዕᐲߩ✚๺

ߢ޽ࠆߎߣ߇ಽ߆ࠆ㧚ߒߚ߇ߞߡ㧘 pa ( X

_i

) ߪ ¦ ¦

i i

q j

r

k

N

ijk ijk

1 0

1

log T ߢ⹏ଔߔࠆߎߣ߇ߢ߈ࠆ㧚

ᦨᄢኻᢙዕᐲએᄖߩઍ⴫⊛ߥ⹏ଔ୯ߣߒߡ㧘 BIC 㧔 Bayesian information criterion 㧕ࠍ⚫

੺ߔࠆ㧚 BIC ߢߪㆊቇ⠌ࠍ㒐ߋߚ߼ߦ㧘ࠣ࡜ࡈ᭴ㅧ߇ⶄ㔀ߢ޽ࠆ߶ߤ㧘⹏ଔ୯ߦࡍ࠽࡞࠹ࠖ

ࠍਈ߃ࠆ㧚ࠣ࡜ࡈ᭴ㅧ B

_s

^ߩⶄ㔀ߐ ^k

_B_s

ߪ㧘ฦ⏕₸ᄌᢙߩⷫࡁ࡯࠼߇ߣࠆ⁁ᘒߩࡄ࠲࡯ࡦߩᢙߩ

✚๺ߢ⴫ߐࠇ㧘 ¦

ⁿ

i i

B

q

k

_s

1

ߢ޽ࠆ㧚ቇ⠌࠺࡯࠲ߩઙᢙࠍ _N ߣߔࠆߣ㧘ࠣ࡜ࡈ᭴ㅧ B

_s

߇ਈ߃ࠄࠇ ߚߣ߈ߩ BIC ࠍ↪޿ߚ⹏ଔ୯

Bs

BIC ߪᑼ㧔 3.5 㧕ߢ⴫ߐࠇࠆ㧚

) (log

)

| (

2 l D k N

BIC

_B_s

4

_B_s

^㧔 ^3.5 ^㧕

ᦨᄢኻᢙዕᐲߣߪㅒߦ㧘 BIC ߪ୯߇ዊߐ޿߶ߤ⹏ଔ߇㜞޿ߎߣߦᵈᗧ߇ᔅⷐߢ޽ࠆ㧚

3.3 ⏕₸ផ⺰

1 ߟ㧘߹ߚߪ㧘ⶄᢙߩ⏕₸ᄌᢙߩ୯߇᷹ⷰߐࠇߚߣ߈㧘᷹ⷰߐࠇߚ୯ࠍ evidence ߣ޿߁㧚 evidence ߇ࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߦਈ߃ࠄࠇߚߣ߈㧘ᧂ᷹ⷰߩ⏕₸ᄌᢙߩ੐ᓟ⏕₸ࠍ᳞߼

ࠆߎߣࠍ⏕₸ផ⺰ߣ޿߁㧚࿑ 3.1 ߩࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢࠍ଀ߦ↪޿ߡ⺑᣿ߔࠆߣ㧘⦼↢

߇Ứࠇߡ޿ࠆߣ߈ߦᢔ᳓ᯏ߇૞േߒߚ⏕₸ߪ , ޟ Wet grass = T ޠߣ޿߁ evidence ࠍࡌࠗࠫࠕ

ࡦࡀ࠶࠻ࡢ࡯ࠢߦઃਈߒ㧘⏕₸ផ⺰ࠍ↪޿ߡ⏕₸ᄌᢙ Sprinkler ߩ੐ᓟ⏕₸ࠍ⸘▚ߔࠆߎߣ

(28)

24 ߢ᳞߼ࠆߎߣ߇ߢ߈ࠆ㧚

ᧄ⎇ⓥߢߪ㧘 Junction Tree ࠕ࡞ࠧ࡝࠭ࡓࠍ↪޿ߡ⏕₸ផ⺰ࠍⴕ߁㧚 Junction Tree ࠕ࡞ࠧ

࡝࠭ࡓߩ೑ὐߪ㧘ਈ߃ࠄࠇߚࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢߩࠣ࡜ࡈ᭴ㅧߦ㑐ࠊࠄߕ෩ኒ⸃߇ᓧࠄ ࠇࠆߎߣߢ޽ࠆ㧚෩ኒ⸃߇ᓧࠄࠇࠆ⏕₸ផ⺰ߩߘߩઁߩࠕ࡞ࠧ࡝࠭ࡓߣߒߡߪ㧘⏕₸વ᠞㧔ା

ᔨવ᠞㧧 Belief Propagation 㧕ᴺ߇⍮ࠄࠇߡ޿ࠆ㧚ߒ߆ߒ㧘⏕₸વ᠞ᴺߪන⚿วࡀ࠶࠻ࡢ࡯ࠢ

㧔ᧁ᭴ㅧߩࡀ࠶࠻ࡢ࡯ࠢ㧕ߢߪ⸃߇෼᧤ߔࠆ߇㧘ⶄ⚿วࡀ࠶࠻ࡢ࡯ࠢ㧔࡝ࡦࠢߩะ߈ࠍήⷞ ߒߚߣ߈ߦ㐽〝ࠍᜬߟࡀ࠶࠻ࡢ࡯ࠢ㧕ߢߪ⸃ߩ෼᧤߇଻⸽ߐࠇߥ޿㧚 Junction Tree ࠕ࡞ࠧ࡝

࠭ࡓߢߪ㧘ࠣ࡜ࡈࠍ Junction Tree ߣ๭߫ࠇࠆන⚿วࡀ࠶࠻ࡢ࡯ࠢߦᄌ឵ߒߡ߆ࠄ੐ᓟ⏕₸

ࠍ⸘▚ߔࠆߩߢ㧘ⶄ⚿วࡀ࠶࠻ࡢ࡯ࠢߢ߽⸃߇෼᧤ߔࠆ㧚

Junction Tree ࠕ࡞ࠧ࡝࠭ࡓߢߪ㧘੐ᓟ⏕₸ߩ⸘▚ߦᓟㅀߔࠆࡐ࠹ࡦࠪࡖ࡞ࠍ↪޿ࠆ㧚ߘߎ ߢ㧘߹ߕ㧘 3.3.1 㗄ߢࡐ࠹ࡦࠪࡖ࡞ߩᕈ⾰㧘ࡐ࠹ࡦࠪࡖ࡞ࠍ↪޿ߚ⸘▚ߦߟ޿ߡ⺑᣿ߔࠆ㧚ᰴ

ߦ㧘 3.3.2 㗄ߢࡌࠗࠫࠕࡦࡀ࠶࠻ࡢ࡯ࠢࠍ Junction Tree ߦᄌ឵ߔࠆᚻ㗅ࠍ⺑᣿ߔࠆ㧚 ᦨᓟߦ㧘 3.3.3 㗄ߢ Junction Tree ਄ߢࡐ࠹ࡦࠪࡖ࡞ࠍ↪޿ߡ੐ᓟ⏕₸ࠍ᳞߼ࠆᣇᴺࠍ⺑᣿ߔࠆ㧚

3.3.1 ࡐ࠹ࡦࠪࡖ࡞

ࡐ࠹ࡦࠪࡖ࡞ߣߪ㧔᧦ઙઃ㧕⏕₸ಽᏓ⴫ߩߎߣߢ޽ࠆ㧚ࡐ࠹ࡦࠪࡖ࡞ I ^ߩ㗔ၞࠍ ^dom( I ⁾

ߣቯ⟵ߔࠆ㧚଀߃߫㧘ࡐ࠹ࡦࠪࡖ࡞ P ( A , B | C ) ߪ dom ( P ( A , B | C )) { A , B , C } ߢ޽ࠆ㧚

2 ߟߩࡐ࠹ࡦࠪࡖ࡞ࠍដߌࠆߎߣ߇ߢ߈ࠆ㧚 ࡐ࠹ࡦࠪࡖ࡞ߩⓍ▚ߪᰴߩࠃ߁ߥᕈ⾰ࠍᜬߟ㧚

Ԙ dom( I

₁

I

₂

^{) = dom(} I

₁

⁾ ^dom( I

₂

⁾

ԙ ੤឵ᴺೣ㧦 I

₁

I

₂

I

₂

I

₁

Ԛ ⚿วᴺೣ㧦 ( I

₁

I

₂

) I

₃

I

₁

( I

₂

I

₃

)

ԛ න૏ߩሽ࿷㧦න૏ࡐ࠹ࡦࠪࡖ࡞ 1 ߪ 1 ߩߺࠍ฽߻ࡐ࠹ࡦࠪࡖ࡞ߢ޽ࠅ㧘ߤߩࠃ߁ߥ 㗔ၞߢ߽㧘ోߡߩࡐ࠹ࡦࠪࡖ࡞ I ^ߦኻߒߡ㧘 1 I I ߣቯ⟵ߐࠇࠆ㧚

ࡐ࠹ࡦࠪࡖ࡞߆ࠄ޽ࠆᄌᢙࠍᶖ෰ߔࠆߎߣࠍ๟ㄝൻߣ޿߁㧚ࡐ࠹ࡦࠪࡖ࡞ I ^߆ࠄᄌᢙ _A ^ࠍ

ᶖ෰ߔࠆ๟ㄝൻߩ⸘▚ߪ㧘 _¦

_A

I ^㧔 ^¦

_A

I ^ߩ㗔ၞߪ ^{dom (} ^¦

_A

I ^{) = dom} ⁽ I ⁾ ^/ _A ^{㧕ߣ৻⥸ൻߔࠆߎߣ}

߇ߢ߈ࠆ㧚ߘߒߡ㧘๟ㄝൻߩ⸘▚ߢߪ੤឵ᴺೣ߇ᚑࠅ┙ߟ㧚

Ԝ ๟ㄝൻߦ߅ߌࠆ੤឵ᴺೣ㧦 _{¦ ¦}

_{A B}

I _{¦ ¦}

_B _A

I

Q ^{ࠍᄌᢙߩ㓸วߣߔࠆ㧚} _P ⁽ _A ^| Q ⁾ ߣ޿߁ࡐ࠹ࡦࠪࡖ࡞ߦ߅޿ߡ㧘ᰴ߇ᚑࠅ┙ߟ㧚

ԝ න૏ࡐ࠹ࡦࠪࡖ࡞ߩᕈ⾰㧦 _¦

_A

P ( A | Q ) 1

(29)

25 ࡐ࠹ࡦࠪࡖ࡞ߩⓍߩ๟ㄝൻߦߟ޿ߡ㧘ᰴ߇ᚑࠅ┙ߟ㧚

Ԟ ಽ㈩ᴺೣ㧦߽ߒ㧘 A ^dom( I

₁

⁾ ^ߥࠄ߫㧘 ^¦

_A

I

₁

I

₂

I

₁

^¦

_A

I

₂

ࡐ࠹ࡦࠪࡖ࡞ߩ⸘▚଀ࠍ⴫ 3.4 ߆ࠄ⴫ 3.9 ߦ␜ߔ㧚⴫ 3.4 ߢቯ⟵ߒߚࡐ࠹ࡦࠪࡖ࡞ I

₁

^ߣࡐ࠹

ࡦࠪࡖ࡞ I

₂

^{ࠍ↪޿ߡ㧘⴫} ^3.5 ߢߪࡐ࠹ࡦࠪࡖ࡞ߩⓍ▚ߩ⸘▚଀ࠍ␜ߔ㧚⴫ 3.5 ߩฦ࠮࡞ߩ 2 ߟߩᢙ୯ߪᏀ஥߇ c

₁

㧘ฝ஥߇ c

₂

^{ߩ⁁ᘒߦ⋧ᒰߔࠆ㧚} ⴫ 3.6 㧘⴫ 3.7 ߢߪࡐ࠹ࡦࠪࡖ࡞ࠍ↪޿ߚ

๟ㄝൻߩ⸘▚଀ࠍ␜ߔ㧚⴫ 3.8 ߢߪࡐ࠹ࡦࠪࡖ࡞ߩಽ㈩ᴺೣߩ⸘▚଀ࠍ␜ߔ㧚ಽ㈩ᴺೣࠃࠅ㧘

¦

_C

I

₁

( A , B ) I

₂

( C , B ) ⁼ I

₁

⁽ _A ^, _B ⁾ ^¦

_C

I

₂

⁽ _C ^, _B ⁾ ^{ߢ޽ࠆ㧚⴫} ^3.7 ^ߣ⴫ ^3.8 ߩฦ࠮࡞ߩ୯߇╬ߒߊ㧘ಽ㈩ᴺ

ೣ߇ᚑࠅ┙ߞߡ޿ࠆߎߣ߇⏕⹺ߢ߈ࠆ㧚

⴫ 3.4 ࡐ࠹ࡦࠪࡖ࡞ I

₁

( A , B ) ^{ߣࡐ࠹ࡦࠪࡖ࡞} I

₂

⁽ _C ^, _B ⁾

) ,

1

( A B

I I

₂

( C , B ) A

B \ 㩷 a

₁

㩷 a

₂

㩷㩷 B \ C 㩷 c

₁

㩷 c

₂

㩷

b

1

^㩷 x

₁

^㩷 x

₂

^㩷 ^㩷 b

₁

^㩷 y

₁

^㩷 y

₂

^㩷 b

2

㩷 x

₃

㩷 x

₄

㩷㩷 b

₂

㩷 y

₃

㩷 y

₄

㩷

⴫ 3.5 I

₁

( A , B ) I

₂

( C , B ) A

B \ 㩷 a

₁

㩷 a

₂

㩷

b

1

^㩷 x

₁

y

₁

, x

₁

y

₂

x

₂

y

₁

, x

₂

y

₂

b

2

㩷 x

₃

y

₃

, x

₃

y

₄

x

₄

y

₃

, x

₄

y

₄

⴫ 3.6 _¦

_C

I

₂

( C , B )

B 㩷㩷

b

1

^㩷 y

₁

⁺ y

₂

^㩷 b

2

㩷 y

₃

+ y

₄

㩷

⴫ 3.7 _¦

_C

I

₁

( A , B ) I

₂

( C , B ) A

B \ 㩷 a

₁

㩷 a

₂

㩷

b

1

^㩷 x

₁

y

₁

x

₁

y

₂

x

₂

y

₁

x

₂

y

₂

b

2

㩷 x

₃

y

₃

x

₃

y

₄

x

₄

y

₃

x

₄

y

₄

⴫ 3.8 I

₁

( A , B ) _¦

_C

I

₂

( C , B ) A

B \ 㩷 a

₁

㩷 a

₂

㩷

b

1

^㩷 x

₁

( y

₁

y

₂

) x

₂

( y

₁

y

₂

)

b

2

㩷 x

₃

( y

₃

y

₄

) x

₄

( y

₃

y

₄