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# OMNI-Prop: Seamless Node Classification on Arbitrary Label Correlation

Talk at AAAI2015

Talk at AAAI2015

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### OMNI-Prop: Seamless Node Classification on Arbitrary Label Correlation

1. 1. OMNI-­‐Prop:   Seamless  Node  Classiﬁca/on   on  Arbitrary  Label  Correla/on Yuto  Yamaguchi†   Christos  Faloutsos‡   Hiroyuki  Kitagawa†     †U.  of  Tsukuba                                            ‡CMU 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 1 ? ?
2. 2. Node  Classiﬁca/on 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 2 Find: correct labels of unlabeled nodes ? ?
3. 3. Our  focus  –  Label  correla/on  types 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 3 Various  label  correla5on  types Homophily Heterophily Mixed ・  Exis/ng  algorithms:    prior  assump/on  needed    e.g.)  label  propaga*on  [Zhu+,2003]        assumes  homophily     ・  Our  algorithm:    no  prior  assump/on
4. 4. Contribu/ons Propose  OMNI-­‐Prop:  a  node  classiﬁca/on  algorithm   •  Seamless  and  Accurate   –  good  accuracy  on  arbitrary  label  correla/on   •  Fast   –  each  itera/on  is  linear  on  input  graph  size   –  convergence  guarantee   •  (Quasi-­‐parameter  free)  -­‐  omiZed  in  this  talk  for  brevity     –  Just  one  parameter  with  default  value  1   –  No  parameter  to  tune   15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 4
5. 5. ALGORITHM 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 5
6. 6. Basic  Idea 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 6   If most of the neighbors of a node have the same label, then the rest also have the same label. ? Most  neighbors  are  the  same   à  the  rest  is  also  the  same Neighbors  have  diﬀerent  labels   à  say  nothing   ?   ?
7. 7. How  it  works?           15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 7 •  sij:  How  likely  node  i  has  label  j   •  tij:  How  likely  the  neighbors  of  node  i  have  label  j Calculate  two  variables  recursively male male male unknown male male male male? most  friends   are  males! I  am  a  male s-­‐propaga5on t-­‐propaga5on s s s s ß  aggrega/on  of  t ß  aggrega/on  of  s t t t t you  are   probably  males see  paper  for  details ? ?
8. 8. THEORETICAL  RESULTS 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 8
9. 9. Complexity  and  Convergence 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 9 *  K:  #  labels        N:  #  nodes        M:  #  edges   [Theorem 1 - complexity] The time complexity of each iteration of OMNI-Prop is O(K(N+M)) [Theorem 2 - convergence] OMNI-Prop always converges on arbitrary graphs
10. 10. Theore/cal  connec/on  to  SSL 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 10 Label  Propaga/on  [Zhu+,  2003] Original  graph Twin  graph [Theorem 3 - equivalence] The special case of OMNI-Prop is equivalent to LP on twin graph
11. 11. EXPERIMENTAL  RESULTS 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 11
12. 12. Experimental  Segngs 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 12 Datasets Baselines •  Label  Propaga/on  [Zhu+,  2003]   •  Belief  Propaga/on
13. 13. Results 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 13 OMNI-­‐Prop  (red  line)  almost  always  wins  on  all  datasets upper     be[er
14. 14. Summary •  Proposed  OMNI-­‐Prop   –  Seamless  NL  on  arbitrary  label  correla/on   –  Fast   –  (Quasi-­‐parameter  free)   •  Theore/cally   –  Linear  on  input  size  for  each  itera/on   –  Always  converges  on  arbitrary  graphs   –  special  case  =  LP   •  Experimentally   –  Almost  always  wins  on  all  5  datasets 15/01/29 Yuto  Yamaguchi  -­‐  AAAI2015 14