A Local Algorithm for Finding Well-Connected Clusters. Lattanzi. Mirrokni, Zhu. ICML 2013 Talk.


From http://techtalks.tv/talks/a-local-algorithm-for-finding-well-connected-clusters/58322/

  1. A good cluster should have few edges going relative to the size of the size of the cluster
  2. Called the conductance (clustering by cutting according to that criteria)
  3. Google research, so google scale, doesn’t want even linear data cost
  4. Algorithm is initialized on some vertex, moves around locally, and then finally produces some set S, hopefully with a low conductance
  5. Has theoretical bounds, cant do better than that due to Cheeger’s inequality
  6. Algs have runtime linear in size of cluster made from starting point
  7. Algorithm is quite simple
  8. Proposes a different metric than standard conductance; connectivity
  9. Want small conductance and high connectivity (imposed by a relative combination); want better connection inside than outside
  10. This metric improves theoretical bounds, this beats other random walk based spectral algorithms
  11. Use of this extra data allows for tighter bounds
  12. <Proofs>
  13. Claim a followup work that is local but is big-O optimal based on flow analysis
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