Collaborative Filtering

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???????
????????????? ??? yuxiao-zhu_at_hotmail.com
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????

• ??????????(popularity)
• ????

• ????(?????)

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????

• ???????????
• ????(???????????? )
• ??????
• ??????
• ???????(?????,hub???????,?????????????)
• ?????

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????????????

• ????????????????,???????????????????????????????
  ???????????????????????

• Node-dependent Indices
• Common Neighbors (CN)
• Salton Index
• Jaccard Index

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????????????

• Sorensen Index
• Hub promoted Index (HPI)
• Hub Depressed index (HDI)
• Leicht-Holme-Newman-I (LHN-I)
• Preferencial Attachment (PA)

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????????????

• Adamic-Adar (AA)
• Resource Allocation (RA)

• Path-dependent Indices

• Local Path (LP) ?CN??????????????

A????
????
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????????????

• Katz(???????,?????????????,???????????)

A???? I ???
??????,??????????,???????A?????????

• Leicht-Holme-Newman-? (LHN-?)

D ????A???? m ????
??A?????? ????
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????????????
1)??????????????,?????????????????????? 2)??LHN???
??????? ???????????????????????????
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???popularity????
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???PA??

• PA??

Random(PA) ???????????popularity M
??????
N M C r H ltdgt ltkgt PA Datasets
332 2126 0.749 -0.206 3.46 2.46 12.807 9.923 1222 16717 0.361 -0.079 3.13 2.51 27.360 1.960 297 2148 0.308 0.454 3.47 2.46 14.456 2.512 379 941 0.798 -0.082 1.66 4.93 4.823 7.168 USAir PB Celegans NetScience
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???????popularity???

• ???????????????????????????????

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???????popularity???

• ????????????popularity????PA???????
• ???????,LHN????????popularity?????,??????popularit
  y??????????????

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????????????

• ????
• ????????????popularity,????????populari
  ty??????,????????5????????????10??????P0.2????0
  , 20????,P1????80, 100?
• ??
• 1???NS???,??PA??????????????popularity???????,????
  ?????????P??????????(NS???H????)
• 2??PB?CE?USAir??????,???????????????????????p?????
  ??,???PA?CN?AA?RA?LP?
• 3????????,LHN???popular???unpopular??????????,????
  ????????P????????????

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????????????
1???NS???,????????P?????????(PA????)?(NS
???H????) 2??PB?CE?USAir??????,??????????
?p???????,???PA?CN?AA?RA?LP?
3?LHN??????p????,????????????P????????????
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Top-L-popularity

• Top-L-popularity ?????L??????popularity.
• USAir?PB?C.elegans?NetScience?????,LHN-I??LHN-????
  ?Top-L-popularity????????L??,????????CN?PA?AA?RA?L
  P?Katz?top-100-popularity????LHN???
• ??
• LHN??????????????

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Top-L-popularity
?????????????(PB)
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????????
??????a
a -1 LHN-I?? a-0.5salton a0CN
1)??????a??? ?P??? 2) ?????????,
????a???0. 3) ?????????? ???????
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?????

• ?????????????????????????LHN???????????????????LHN
  ??????????????,??????????????????????????????

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THANK YOU FOR YOUR TIME