äå=æç=[\{J. Fac. Sci. Tech., Seikei Univ.
Vol.47 No.2 (2010) pp.15-22

ฦ⒳⋥੤ᄌ឵ࠍ↪޿ߚᢥ┨㑆ߩ㘃ૃᕈ್ቯ᧻Ỉ ᒰ 㧖㧘ᮘญ ᡽๺ 㧖㧘᧛਄ ੳᏆ 㧖

The Judgment of Document Similarities Using Various Orthogonal Transformations
Ataru MATSUZAWA㧖, Masakazu HIGUCHI㧖, Hitomi MURAKAMI㧖,ABSTRACT㧦The objective of this work is to propose a new method to judge similarities between two
documents by simple calculation using orthogonal transformations and show the performance for actual
plagiarisms of sentences. Specifically, Japanese characters in document are represented by Shift-JIS codein computer and then transformed by an orthogonal transformation algorithms, such as Fourier, Cosine,
Haar wavelet and Hadamard system. As a criterion of similarity judgments of documents, the correlationof these transformed coefficients are applied. In order to examine the performance of the method, suchcorrelation calculations are performed for actual plagiarisms. As a result of the experiments it isconfirmed that Fourier transformation is effective for documents that include various types of charactermodifications especially for plagiarisms that have shifted the order of the words.
Keywords㧦document similarity, orthogonal transformation, character code, plagiarism
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: ᖱႎ⑼ቇ⑼ᢎ᝼ (hi-murakami@st.seikei.ne.jp)FÌÉW8ÈÉW(ÒflÝÀZWÞCßàWlpqrO78áâ/)*Z[\ã#$%8°NS"% Shift-JIS 0$)&㧙㧙㧠㧚⋑૞ᢥࠍࡕ࠺࡞ߦߒߚታ㛎㧟㧚ฦ⒳⋥੤ᄌ឵ᧄ⎇ⓥߢᢥሼࠦ࡯࠼ߩ࠺࡯࠲೉ߦኻߒߡⴕߞߚᄌ឵ߪ㧘 ⋑૞ᢥߩ․ᓽ

ฦ⒳࠺ࠖࠫ࠲࡞ାภಣℂߦ↪޿ࠄࠇࠆઍ⴫⊛ߥ㧘એਅߦᧄታ㛎ߢߪ㘃ૃᕈߩ㜞޿ᢥ┨ߩࡕ࠺࡞ߣߒߡ⋑૞ᢥࠍ␜ߔ㔌ᢔࡈ࡯࡝ࠛᄌ឵㧔DFT㧕㧘㔌ᢔࠦࠨࠗࡦᄌ឵㧔DCT㧕㧘↪޿ߚ‫ޕ‬ᰴߦ⋑૞ᢥߩ․ᓽࠍ␜ߔ[5]‫ޕ‬㗅ᐨ㜞ㅦࡂ࡯࡞࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵㧔HWT㧕㧘ࠕ࠳ࡑ࡯࡞ᄌ឵㧔HT㧕ߩ 4 ⒳㘃ߢ޽ࠅ[2][3][4]㧘ߘࠇࠄߩᄌ឵ᑼࠍએਅߦ␜ߔ‫ޕ‬ࠝ࡝ࠫ࠽࡞ߩᢥߦ㧘Ԙ0~5 ᢥሼ⒟ᐲߩන⺆߇Ꮕߒᦧ߃
ࠄࠇࠆ㧔એਅ̈Ꮕߒᦧ߃̉㧘ߣ⒓ߔࠆ㧕㧘ԙᢥਛߩ⺆߇౉ࠇᦧ߃ࠄࠇࠆ㧔̈౉ࠇᦧ߃̉㧕㧘߹ߚԚ0~5 ᢥሼ⒟ᐲߩන⺆

F j = ∑ fken −12πi
jk−n

k =0

‫ޓޓޓޓޓޓޓޓޓ‬(1)߇Ꮕߒㄟ߹ࠇࠆ㧔̈Ꮕߒㄟߺ̉㧕㧘ߣ޿߁․ᓽ߇ઍ⴫⊛ߢ޽ࠆ‫߽ߦઁߩߘޕ‬ṽሼ߿ᐔ઒ฬࠞ࠲ࠞ࠽ߩᄌ឵㧘⸒޿࿁ߒ

Fc j = ∑ f k cos{n −1k =01π
( k + ) j }‫ ( ޓޓޓޓ‬2)n2

ᑼ(1)㧘ᑼ(2)ߪߘࠇߙࠇ㔌ᢔࡈ࡯࡝ࠛᄌ឵㧘㔌ᢔࠦࠨࠗࡦᄌ឵ᑼߢ޽ࠆ‫ߢߎߎޕ‬㧘 f k ߪ౉ജାภߩ࠺࡯࠲೉㧘

Fc j ߪߘࠇߙࠇ౉ജାภߦኻߔࠆ㔌ᢔࡈ࡯࡝ࠛᄌ
Fj,‫ޓ‬

឵ଥᢙ㧘㔌ᢔࠦࠨࠗࡦᄌ឵ଥᢙࠍ⴫ߔ‫ ޕ‬n ߪ౉ജ࠺࡯࠲ߩ㆑޿ߥߤ߇᜼ߍࠄࠇࠆ߇㧘ᧄታ㛎ߢߪ⋑૞ᢥߦ⷗ࠄࠇࠆઍ⴫⊛ߥ․ᓽߢ޽ࠆԘ~Ԛߦߟ޿ߡ⺞ߴࠆ[6]‫ޕ‬ ⋑૞ᢥࠍࡕ࠺࡞ߦߒߚታ㛎ᣇᴺ ᧄ⎇ⓥߢߪ  ߟߩᄌ឵ࠍ↪޿  ߟߩ⇣ߥࠆ․ᓽࠍᜬߟᢥ┨ߦኻߒߡታ㛎ࠍⴕߞߚ‫࡞࡯ࡑ࠳ࠕޕ‬ᄌ឵߅ࠃ߮ࡂ࡯
࡞࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ߩ౉ജ࠺࡯࠲ᢙ߇ 2 ߩ⚥ਸ਼ߣ޿߁ᢙ㧘 i ߪ⯯ᢙන૏ߢ޽ࠆ‫ޕ‬ᑼ(1)ߦࠃࠅᄌ឵ߐࠇߚାภߪ

᧦ઙ㧘߹ߚታ㓙ߩ⋑૞ᢥߦㄭ޿ᢥሼᢙߣ޿߁ℂ↱߆ࠄ㧘ⶄ⚛ᢙߣߥࠆߩߢ㧘㘃ૃᕈᲧセߢߪߘߩᝄ᏷ࠬࡍࠢ࠻࡞↪޿ࠆ౉ജᢥሼᢙߪ 128 ᢥሼߣߒߚ‫ޕ‬એਅߦߎߎߢታ㓙ߦ̈Ꮕߒᦧ߃̉ߦ↪޿ߚ 128 ᢥሼߩᢥ┨଀ߩ 1 ߟࠍ␜ߔ‫ޕ‬ࠍ⸘▚ߒߚ‫ޕ‬

 f 2 j + f 2 j +1
N− 1)
‫ޓ‬
(0 ≤ j ≤
22( 3) ‫ޓޓ‬
f 'j = −ff
N2 j +1 2j≤ j ≤ N − 1)
(‫ޓ‬
22
ᑼ(3)ߪࡂ࡯࡞࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ࠍ⴫ߔ‫ޕ‬N ߪ 2 ߩ⚥ౕ૕଀㧦‫ޟ‬ᢥ┨㑆ߩ㘃ૃᕈࠍ್ቯߔࠆߦ޽ߚߞߡ㧘ㄉᦠߦଐሽߖߕ್ᢿߔࠆߎߣࠍ⹜ߺࠆ‫ޕ‬ኻ⽎ߣߔࠆᢥሼߪࠦࡦࡇࡘ࡯࠲਄ߩᢥሼߢ㧘ฦᢥሼߦߪᢥሼࠦ࡯࠼߇ഀࠅᒰߡࠄࠇߡ޿ࠆ‫ޕ‬ᢥሼࠦ࡯࠼ߪᢛᢙߢഀࠅᒰߡࠄࠇߡ޿ߡ㧘ඨⷺߪ㧝ߟోⷺߪ 2 ߟߩᢙሼ߇ഀࠅᒰߡࠄࠇߡ޿ࠆ‫଀ޕ‬ᢥ㧝૞ᚑ⚳ੌ㧘‫ޠ‬ਸ਼ߩ࠺࡯࠲ᢙߢ޽ࠆ‫ޕ‬Fh =1Nታ㛎 1 ߢߪ㘃ૃᢥࠍ⋧ኻ⊛ߥዤᐲߢ⹏ଔߔࠆߚ߼㧘⋑

Hf‫ޓޓޓޓޓޓޓޓޓޓޓޓޓޓ‬(4)

ᑼ(4)ߦࠕ࠳ࡑ࡯࡞ᄌ឵ࠍ␜ߔ‫ ޕ‬F h ߪࠕ࠳ࡑ࡯࡞ᄌ឵

૞ᢥߢߥ޿⥄ὼߥ 2 ߟߩᢥ┨㧔એਅ㧘㕖㘃ૃᢥߣ⒓ߔࠆ㧕ࠍ↪޿ߚ‫޿⸒ޕ‬࿁ߒ߿⺆የߩ⇣ߥࠆࠫࡖࡦ࡞ߩᢥ┨㧔㖸ᭉ࡮࠹࡟ࡆ࡮ࠬࡐ࡯࠷ߥߤ㧕ࠍ 15 ⒳㘃Ḱ஻ߒ㧘ߘߎ߆ࠄᢥሼࠦ࡯࠼ൻߐࠇߚੑߟࠍㆬ߮㧘ో 105 ㅢࠅߩ⋧੕⋧㑐ଥᢙߢ޽ࠅ㧘 f ߪ౉ജାภߢ޽ࠆ‫ޕ‬ᑼ(4)ߢߪ F h ߅ࠃࠍ⸘▚ߔࠆ‫ߪߢߎߎޕ‬㧘ోⷺᢥሼߩߺߩ႐ว㧘ඨⷺᢥሼN × N ߩࠕ࠳ࡑ࡯࡞ⴕ೉ߢ޽ࠅ㧘 N ߪ 2 ߩ⚥ਸ਼ߢ޽ߡߘࠇߙࠇ⋧੕⋧㑐ࠍ⸘▚ߒߚ‫ޕ‬߮ F ࠍ N ᰴరࡌࠢ࠻࡞ߣߒߡ⸘▚ߒߚ‫ ޕ‬H ߪߩߺߩ႐ว㧘ోⷺᢥሼߣඨⷺᢥሼ߇ᷙ࿷ߩ 3 ㅢࠅߦߟ޿
ታ㛎 2~4 ߢߪ 2 ߟߩ㘃ૃᢥ[5]ߦኻߒ⹏ଔࠍⴕߞߚ‫ߎޕ‬ࠆ‫ ޕ‬N = 4 ߩ႐วߩࠕ࠳ࡑ࡯࡞ⴕ೉ࠍᑼ(5)ߦ␜ߔ‫ޕ‬ߩ㘃ૃᢥߩ଀ࠍ㧘એਅߦ␜ߔ‫ޕ‬

1 1 1 1 1 − 1 1 − 1 ‫ޓޓޓޓޓޓޓޓޓޓޓ‬(5)
H =
1 1 − 1 − 1
1 − 1 − 1 1 㘃ૃᢥߩ଀㧦
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êæ=õö(µY·¸uv:%78^!")&=2Á)W2003, pp.81-86.

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ዊ᥵㓁ñ, ૒ᧁ⦟テ(✬) : “/V8A6%Å

ðñ¨©”, ⻠⺣ý, lþ(1999).

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⾆ኅੳᔒ : “èé¶¤¥êæ”, ᤘᤩၴ, lþ,pp.95-99(1997)
Ẃ᫜U¤ùû :http://mandanatsusin.cocolog-nifty.com/blog/2007/06/
post_a49c.html

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