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  https://sungmooncho.com/2012/08/26/pagerank/



¡®½±°Ô ¼³¸íÇÑ¡¯ ±¸±ÛÀÇ ÆäÀÌÁö ·©Å© ¾Ë°í¸®Áò

³×À̹ö °Ë»ö¿£ÁøÀÇ ¹®Á¦Á¡À» óÀ½ ÁöÀûÇÑ ±ÛÀ» ½è´ø 2³â ÀüºÎÅÍ ÀÌ ºí·Î±×¿¡ ¾ðÁ¨°¡ ÇÑ ¹ø ½áº¸°í ½Í¾ú´ø ÁÖÁ¦°¡ Çϳª ÀÖ¾ú´Ù. ±¸±ÛÀÇ PageRank ¾Ë°í¸®ÁòÀ» ¼³¸íÇÏ´Â °ÍÀÌ´Ù. ¿ø¸®´Â °£´ÜÇÏÁö¸¸ ¾Ë°í¸®ÁòÀ» ¼³¸íÇÏ·Á°í ÇÏ¸é ¸»ÀÌ ±æ¾îÁú °Í °°°í ½±°Ô ¼³¸íÇÒ ¼ö ÀÖÀ»±î ½Í¾î ºí·Î±×¿¡ ¾µ±î ¸»±î ¸Á¼³¿´´Âµ¥, ±×³É ÇÑ ¹ø ½ÃÀÛÇغ¸·Á°í ÇÑ´Ù. ¡°Google¡±À̶ó´Â 230Á¶¿øÂ¥¸® ȸ»ç°¡ óÀ½ ½ÃÀÛµÈ °÷ÀÌ ¹Ù·Î ÀÌ ¼¼¸£°ÔÀÌ ºê¸°°ú ·¡¸® ÆäÀÌÁö°¡ ¾´ ³í¹®(The Anatomy of a Large-Scale Hypertextual Web Search Engine)À̾ú´Ù´Â °ÍÀ» »ý°¢Çϸé ÇÑ ¹ø ½Ã°£À» µé¿© ¹è¿öº¼ ¸¸ÇÑ Àǹ̰¡ ÀÖÁö ¾ÊÀ»±î? ÀÌ ³í¹®Àº 1998³â¿¡ ¾²¿©Á³À¸³ª, ³í¹®¿¡¼­ ¼Ò°³µÈ PageRank ¾Ë°í¸®ÁòÀº 14³âÀÌ Áö³­ Áö±Ý¿¡µµ ±¸±Û °Ë»ö ¿£ÁøÀÇ ÇÙ½ÉÀ» ÀÌ·ç°í ÀÖ´Ù.

¿À´Ã³¯ÀÇ ±¸±ÛÀ» ¸¸µç, ÆäÀÌÁö·©Å©(PageRank) ¾Ë°í¸®ÁòÀ» ¼Ò°³ÇÑ ³í¹®¿¡ Æ÷ÇԵǾî ÀÖ´ø ¼¼¸£°ÔÀÌ ºê¸°°ú ·¡¸® ÆäÀÌÁöÀÇ »çÁø. Âü ¾ÜµÈ µÎ ´ëÇпø»ýÀÇ ¸ð½ÀÀÌ´Ù.

³í¹®Àº ÀÌ·¸°Ô ½ÃÀÛÇÑ´Ù.

Our main goal is to improve the quality of web search engines. In 1994, some people believed that a complete search index would make it possible to find anything easily. (¿ì¸®ÀÇ ÁÖ¿ä ¸ñÇ¥´Â °Ë»ö ¿£ÁøÀÇ Ç°ÁúÀ» Çâ»ó½ÃÅ°´Â °ÍÀÔ´Ï´Ù. 1994³â ´ç½Ã, »ç¶÷µéÀº °Ë»ö À妽º¸¦ ¿Ï¼ºÇÏ°í ³ª¸é ¹«¾ùÀÌµç ½±°Ô ãÀ» ¼ö ÀÖÀ» °ÍÀ̶ó°í »ý°¢Çß½À´Ï´Ù.)

However, the Web of 1997 is quite different. Anyone who has used a search engine recently, can readily testify that the completeness of the index is not the only factor in the quality of search results. ¡°Junk results¡± often wash out any results that a user is interested in. (ÇÏÁö¸¸, 1997³âÀÇ À¥Àº »ç¹µ ´Ù¸¨´Ï´Ù. ÃÖ±Ù¿¡ °Ë»ö ¿£ÁøÀ» »ç¿ëÇØ º» »ç¶÷À̶ó¸é ´©±¸³ª À妽º¸¦ ¿Ï¼ºÇÏ´Â °Í¸¸À¸·Î´Â ÁÁÀº Ç°ÁúÀÇ °Ë»ö °á°ú¸¦ ¾òÀ» ¼ö ¾ø´Ù´Â °ÍÀ» ¾Ð´Ï´Ù. ¡®¾²·¹±â Á¤º¸¡¯°¡ Á¾Á¾ »ç¿ëÀÚµéÀÌ ÁøÁ¤ °ü½ÉÀÖ¾îÇÏ´Â Á¤º¸¸¦ °¡·Á¹ö¸³´Ï´Ù.)

One of the main causes of this problem is that the number of documents in the indices has been increasing by many orders of magnitude, but the user¡¯s ability to look at documents has not. People are still only willing to look at the first few tens of results. (±×·¯ÇÑ ÀÌÀ¯ Áß Çϳª´Â, À妽ºµÇ´Â ¹®¼­ÀÇ ¼ýÀÚ´Â ¾öû³­ ¼Óµµ·Î ¼ºÀåÇÏ°í ÀÖÁö¸¸, »ç¶÷µéÀÌ ±× ¹®¼­µéÀ» º¼ ¼ö ÀÖ´Â ´É·ÂÀº °°Àº ¼Óµµ·Î ¼ºÀåÇÏÁö ¾Ê±â ¶§¹®ÀÔ´Ï´Ù. »ç¶÷µéÀº ¿©ÀüÈ÷ °Ë»ö °á°úÁß Ã³À½ ¸î½Ê °³ Á¤µµ¸¸ »ìÆ캼 »ÓÀÔ´Ï´Ù.)

Because of this, as the collection size grows, we need tools that have very high precision. Indeed, we want our notion of ¡°relevant¡± to only include the very best documents since there may be tens of thousands of slightly relevant documents. (±×·¸±â ¶§¹®¿¡, ÀÎÅͳÝÀÌ ¼ºÀåÇÒ¼ö·Ï, ¿ì¸®¿¡°Ô ´õ Á¤¹ÐÇÑ µµ±¸°¡ ÇÊ¿äÇÕ´Ï´Ù. »ç½Ç, ¿ì¸®´Â ¡®°ü·Ã ÀÖ´Â ÆäÀÌÁö¡¯°¡ ¼ö¸¸ °³¶óµµ, ±× Áß ÃÖ°íÀÇ À¥ ÆäÀÌÁö¸¸À» Á¤È®ÇÏ°Ô Ã£¾ÆÁֱ⸦ ¿øÇÕ´Ï´Ù.)

There is quite a bit of recent optimism that the use of more hypertextual information can help improve search and other applications. In particular, link structure and link text provide a lot of information for making relevance judgments and quality filtering. Google makes use of both link structure and anchor text. (ÇÏÀÌÆÛÅؽºÆ® Á¤º¸¸¦ ÀÌ¿ëÇÏ¸é °Ë»ö °á°ú¸¦ ¸¹ÀÌ Çâ»óÇÒ ¼ö ÀÖ´Ù´Â ÃÖ±ÙÀÇ ¿¬±¸ °á°ú°¡ ÀÖ½À´Ï´Ù. ƯÈ÷, À¥ ÆäÀÌÁö »çÀÌÀÇ ¿¬°á °ü°è°¡ »ó´çÈ÷ À¯¿ëÇÑ Á¤º¸¸¦ Á¦°øÇØÁÙ ¼ö ÀÖ½À´Ï´Ù. ±¸±ÛÀº ¹Ù·Î ÀÌ·¯ÇÑ ¸µÅ© ±¸Á¶¿Í ¸µÅ© ´Þ¸° ÅؽºÆ®¸¦ ÀÌ¿ëÇÕ´Ï´Ù.)

±×¸®°í, ÆäÀÌÁö·©Å© ¾Ë°í¸®ÁòÀ» ´ÙÀ½°ú °°ÀÌ ¼Ò°³ÇÑ´Ù.

Academic citation literature has been applied to the web, largely by counting citations or backlinks to a given page. This gives some approximation of a page¡¯s importance or quality. PageRank extends this idea by not counting links from all pages equally, and by normalizing by the number of links on a page. (ÇмúÁö ÀÎ¿ë ¹æ½ÄÀº ±×µ¿¾È À¥¿¡ Àû¿ëµÇ¾î ¿Ô½À´Ï´Ù. ƯÈ÷, ƯÁ¤ ÆäÀÌÁö¸¦ ÀοëÇÏ´Â ´Ù¸¥ ÆäÀÌÁö°¡ ¾ó¸¶³ª ¸¹ÀÌ ÀÖ´À³Ä¸¦ ¼¼´Â ¹æ½ÄÀ¸·Î¿ä. ÀÌ·¸°Ô Çϸé ƯÁ¤ ÆäÀÌÁö°¡ ¾ó¸¶³ª Áß¿äÇÑ Áö ¾Ë ¼ö ÀÖ½º´Ï´Ù. PageRank´Â ÀÌ·¯ÇÑ ¾ÆÀ̵ð¾î¸¦ ¿¬ÀåÇϴµ¥, Áï, ´Ù¸¥ ÆäÀÌÁö¿¡¼­ ¿À´Â ¸µÅ©¸¦ °°Àº ºñÁßÀ¸·Î ¼¼´Â ´ë½Å¿¡, ±× ÆäÀÌÁö¿¡ °É¸° ¸µÅ© ¼ýÀÚ¸¦ ¡®Á¤±ÔÈ­(normalize)¡¯ÇÏ´Â ¹æ½ÄÀ» »ç¿ëÇÕ´Ï´Ù.)

¸»ÀÌ Á» ¾î·Á¿îµ¥, ¾Æ·¡ ¼ö½ÄÀ» ÇÑ ¹ø º¸ÀÚ.

PR(A) = (1-d) + d (PR(T1)/C(T1) + ¡¦ + PR(Tn)/C(Tn))

PRÀº PageRankÀÇ ÁÙÀÓ¸»ÀÌ°í, PR(A)´Â ¡®A¡¯¶ó´Â À¥ÆäÀÌÁöÀÇ ÆäÀÌÁö ·©Å©¸¦ ÀǹÌÇÑ´Ù. T1, T2, ¡¦ TnÀº ±× ÆäÀÌÁö¸¦ °¡¸®Å°´Â ´Ù¸¥ ÆäÀÌÁöµéÀ» ÀǹÌÇÑ´Ù. ±×¸®°í  PR(T1)´Â ´ç¿¬È÷ T1À̶ó´Â ÆäÀÌÁöÀÇ ÆäÀÌÁö ·©Å©°ªÀÌ´Ù. d´Â ¡®Damping Factor¡¯¶ó°í Çϴµ¥, ¼³¸íÀÌ ±æ¾îÁú ¼ö ÀÖÀ¸´Ï Á¶±Ý ÈÄ ¼³¸íÇÏ°Ú´Ù. C(T1)´Â T1À̶ó´Â ÆäÀÌÁö°¡ °¡Áö°í ÀÖ´Â ¸µÅ©ÀÇ ÃÑ °¹¼ö¸¦ ÀǹÌÇÑ´Ù.

d¿¡ ¿¬¿¬ÇÏÁö ¾Ê°í(Áï d=1À̶ó°í °¡Á¤ÇÏ°í) À§ ¼ö½ÄÀ» °¡¸¸È÷ º¸¸é »ç½Ç ¸Å¿ì °£´ÜÇÏ´Ù. ¡®¾î¶² ÆäÀÌÁö AÀÇ ÆäÀÌÁö ·©Å©´Â ±× ÆäÀÌÁö¸¦ ÀοëÇÏ°í ÀÖ´Â ´Ù¸¥ ÆäÀÌÁö T1, T2, T3, .. °¡ °¡Áø ÆäÀÌÁö ·©Å©¸¦ Á¤±ÔÈ­½ÃŲ °ªÀÇ ÇÕ¡®ÀÌ´Ù. ´Ù½Ã ¸»ÇØ ÆäÀÌÁö AÀÇ ÆäÀÌÁö ·©Å©´Â A¶ó´Â ÆäÀÌÁö¸¦ °¡¸®Å°°í ÀÖ´Â ´Ù¸¥ ÆäÀÌÁöÀÇ ÆäÀÌÁö ·©Å©°ªÀÌ ³ôÀ»¼ö·Ï (Áï, ´õ Áß¿äÇÒ¼ö·Ï) ´õ ³ô¾ÆÁø´Ù. ¿©±â¼­ ¡®Á¤±ÔÈ­½ÃŲ °ªÀÇ ÇÕ¡®À̶ó´Â ¸»À» ±»ÀÌ ¾´ ÀÌÀ¯´Â, ÆäÀÌÁö ·©Å©ÀÇ ´Ü¼ø ÇÕ»êÀÌ ¾Æ´Ï±â ¶§¹®ÀÌ´Ù. ¿¹¸¦ µé¾î, T1ÀÇ ÆäÀÌÁö ·©Å©°¡ ³ô´Ù°í ÇÏ´õ¶óµµ, ±× ÆäÀÌÁö¿¡¼­ ¸µÅ©¸¦ ¼öõ °³ ´Þ¾Æ³õ¾Ò´Ù¸é(Áï, C(T1)°ªÀÌ ³ô´Ù¸é) ±× ÆäÀÌÁö°¡ ±â¿©ÇÏ´Â ºñÁßÀº ³·¾ÆÁø´Ù.

ÀÌ ¼ö½ÄÀ» ±×¸²À¸·Î ÇÑ ¹ø Ç¥ÇöÇغ¸°Ú´Ù.

PageRank ¾Ë°í¸®ÁòÀ» ±×¸²À¸·Î Ç¥ÇöÇÑ °Í. Dampen Factor°¡ Àֱ⠶§¹®¿¡ ÀÌ°Í°ú ¶È°°Áö´Â ¾ÊÁö¸¸, °£´ÜÇÏ°Ô Ç¥ÇöÇϸé À§¿Í °°´Ù.

À§ ±×¸²¿¡¼­ À¥ ÆäÀÌÁö A¸¦ °¡¸®Å°´Â ÆäÀÌÁö´Â T1, T2, T3, T4, T5ÀÇ ´Ù¼¸ °³°¡ ÀÖ°í, À̵éÀ» Á¤±ÔÈ­Çؼ­ ÇÕÇÑ °ªÀÌ 0.34À̹ǷÎ, AÀÇ ¡®ÆäÀÌÁö ·©Å©¡¯´Â 0.34°¡ µÈ´Ù. ÀÌ ÆäÀÌÁö·©Å© °ªÀº A°¡ °¡¸®Å°´Â ¶Ç ´Ù¸¥ ÆäÀÌÁöÀÇ PageRank¸¦ °è»êÇÏ´Â µ¥ ¾²ÀÏ °ÍÀÌ´Ù. ±×·³ T1ÀÇ ÆäÀÌÁö ·©Å©´Â ¾î¶»°Ô ±¸Çß³ª? ¸¶Âù°¡Áö·Î T1À» °¡¸®Å°´Â ´Ù¸¥ ÆäÀÌÁöµéÀÇ PageRank°ªÀ¸·ÎºÎÅÍ ±¸ÇÑ´Ù. ÀÌ·¸°Ô Çؼ­ ÆÄ°í ³»·Á°¡¸é ¹«ÇÑÈ÷ °¡°Ô µÉ °Í °°Àºµ¥, ¡®Á¦ÇÑ Á¶°Ç¡¯À» °É¸é ¾ðÁ¨°¡´Â °è»êÀÌ ³¡ÀÌ ³­´Ù. ÀÌ·¯ÇÑ ¹æ¹ýÀ¸·Î °è»êÇÏ´Â °ÍÀ» ÄÄÇ»ÅÍ °úÇп¡¼­´Â ¡®recursive(Àç±ÍÀû)¡®À̶ó°í ÇÑ´Ù. Áï, PageRank´Â Àç±Í È£Ãâ ¾Ë°í¸®ÁòÀÌ´Ù.

ÀÌÁ¦ d, Áï Damping Factor¿¡ ´ëÇØ »ý°¢ÇØ º¸ÀÚ. À§ ¼ö½ÄÀ» ´Ù½Ã ÇÑ ¹ø º¸ÀÚ.

PR(A) = (1-d) + d (PR(T1)/C(T1) + ¡¦ + PR(Tn)/C(Tn))

d °ªÀº 0°ú 1 »çÀÌ¿¡¼­ Á¤ÇØÁö´Âµ¥, d°ªÀÌ Ä¿Á®¼­ 1ÀÌ µÇ¸é ¾ÕÀÇ (1-d)´Â 0ÀÌ µÇ°í, µÚ ¼ö½ÄÀÇ ÇÕÀÌ ±×´ë·Î AÀÇ PageRank°¡ µÈ´Ù. ÀÌ°ÍÀÌ ¹Ù·Î À§ ±×¸²¿¡¼­ °¡Á¤ÇÑ »óȲÀÌ´Ù. ¹Ý´ë·Î d°ªÀÌ ÀÛ¾ÆÁ®¼­ 0ÀÌ µÇ¸é, µÚ ¼ö½ÄÀÇ ÇÕÀº 0ÀÌ µÇ°í, AÀÇ PageRank´Â 1ÀÌ µÈ´Ù. d°¡ 0ÀÌ¸é ¸ðµç ÆäÀÌÁöÀÇ PageRank´Â 1ÀÌ µÇ¹Ç·Î ¾Æ¹« Àǹ̰¡ ¾ø¾îÁø´Ù. ±×·¡¼­ d´Â ½ÇÇèÀ» ÅëÇØ 0°ú 1 »çÀÌÀÇ ¾î¶² °ª¿¡¼­ Á¤ÇØÁö´Âµ¥, ³í¹®¿¡¼­´Â º¸Åë 0.85·Î ¼³Á¤Çسõ¾Ò´Ù°í µÇ¾î ÀÖ´Ù. ³í¹®¿¡ µû¸£¸é damping factor¶õ ¡®¾î¶² ¸¶±¸ÀâÀÌ·Î À¥¼­ÇÎÀ» ÇÏ´Â »ç¶÷ÀÌ ±× ÆäÀÌÁö¿¡ ¸¸Á·À» ¸øÇÏ°í ´Ù¸¥ ÆäÀÌÁö·Î °¡´Â ¸µÅ©¸¦ Ŭ¸¯ÇÒ È®·ü¡®ÀÌ´Ù. Áï, damping factor°¡ 1À̸é, ¹«ÇÑÈ÷ ¸µÅ©¸¦ Ŭ¸¯ÇÑ´Ù´Â ¶æÀÌ°í, 0À̸é óÀ½ ¹æ¹®ÇÑ ÆäÀÌÁö¿¡¼­ ¹«Á¶°Ç ¸ØÃß°í ´õ ÀÌ»ó Ŭ¸¯ÇÏÁö ¾Ê´Â´Ù´Â ¶æÀÌ´Ù. 0.85À̸é, 85%ÀÇ È®·ü·Î ´Ù¸¥ ÆäÀÌÁö¸¦ Ŭ¸¯Çغ¼ °ÍÀ̶ó´Â ¶æÀÌ´Ù. ÀÌ °æ¿ì 15%ÀÇ È®·ü¿¡ °É¸®´Â ¼ø°£ Ŭ¸¯À» ¸ØÃß°í ±× ÆäÀÌÁö¸¦ »ìÆ캻´Ù.

³í¹®¿¡ µû¸£¸é, ¸ðµç À¥ÆäÀÌÁöÀÇ ÆäÀÌÁö·©Å© °ªÀ» ÇÕ»êÇÑ °ªÀº 1ÀÌ µÈ´Ù°í ÇÑ´Ù. ±×·¯³ª ÀÌ ¼ö½ÄÀ» º¸¸é ±×·¸°Ô µÇ¾î ÀÖÁö ¾Ê´Ù. ¿¹¸¦ µé¾î d°¡ 0À̸é PR(A)´Â 1ÀÌ µÇ°í, ¸ðµç À¥ÆäÀÌÁöÀÇ PageRank°¡ 1ÀÌ µÇ±â ¶§¹®¿¡ PageRankÀÇ ÇÕ»êÀº ¸ðµç ÆäÀÌÁöÀÇ ¼ýÀÚ(N)ÀÌ µÈ´Ù.

À§Å°Çǵð¾Æ¿¡ µû¸£¸é, ¼¼¸£°ÔÀÌ¿Í ·¡¸®°¡ ³í¹®À» ¾µ ¶§ ½Ç¼öÇÑ °Í °°´Ù¸ç, ¿Ã¹Ù¸¥ ¼ö½ÄÀº ¾Æ·¡¿Í °°´Ù°í ÇÑ´Ù.

PR(A) = (1-d)/N + d (PR(T1)/C(T1) + ¡¦ + PR(Tn)/C(Tn))

ÀÌ·¸°Ô Çϸé Àüü ÆäÀÌÁöÀÇ PageRank¸¦ ÇÕ»êÇÑ °ªÀÌ 1ÀÌ µÈ´Ù.

ÆäÀÌÁö·©Å©¿Í ±× °ü°è¸¦ µµ½ÄÈ­ÇÑ ±×¸². A, B, C µîÀº ÆäÀÌÁö¸¦ ³ªÅ¸³»°í, ¼ýÀÚ´Â PageRank¸¦ ÀǹÌÇÑ´Ù. CÀÇ °æ¿ì B¿¡¼­ ¸µÅ©¸¦ °É¾ú´Ù´Â °Í¸¸À¸·Îµµ PageRank°ªÀÌ ³ô°Ô Ã¥Á¤µÊÀ» º¼ ¼ö ÀÖ´Ù. (Ãâó: Wikipedia)

ÀÌ°Ô ´ÙÀÌ´Ù. ÀÌ·¸°Ô Çؼ­ ¿Â ¼¼»óÀÇ ¸ðµç ÆäÀÌÁö¸¦ PageRank µî¼ö¿¡ µû¶ó¼­ ¹Ì¸® Á¤·ÄÀ» ÇØ µÎ¸é, ´©±º°¡°¡ °Ë»ö¾î¸¦ ÀÔ·ÂÇÏ´Â ¼ø°£, ±× °Ë»ö¾î°¡ Æ÷ÇÔµÈ ÆäÀÌÁöµéÀ» ¼øÀ§º°·Î ³ª¿­Çϱ⸸ ÇÏ¸é ³¡ÀÌ´Ù. ±¸±ÛÀÇ °Ë»ö ¿£ÁøÆÀ¿¡ ÀÖ´Â ÁöÀÎÀÇ ¸»¿¡ µû¸£¸é, Áö±ÝÀÇ ±¸±Û °Ë»ö ¾Ë°í¸®ÁòÀº ¾öû³ª°Ô ¸¹Àº ´Ù¸¥ ¿ä¼Ò¸¦ °í·ÁÇÏ°í, Æ©´×À» Ç߱⠶§¹®¿¡ À̰ͺ¸´Ù ÈξÀ º¹ÀâÇÏ´Ù°í ÇÑ´Ù. ±×·¯³ª ¾Õ¿¡¼­ ¸»Çßµí, ¡®¿µÇâ·Â ÀÖ´Â ÆäÀÌÁö°¡ ÀοëÇÒ¼ö·Ï ÆäÀÌÁö·©Å©°¡ ¿Ã¶ó°£´Ù¡®´Â ±Ùº»ÀûÀÎ ¾Ë°í¸®ÁòÀº ±×´ë·Î ³²¾Æ ÀÖ´Ù.

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