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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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