Yuzhong Qu Nanjing University Consensus partition Yuzhong Qu Nanjing University

Problem W is a set of properties At some moments, a user might It has a public alignment, e.g. an equivalence relation R on W. An equivalence relation can also be represented by a partition At some moments, a user might See a list of a subset of W Align elements of W (move/remove an item to/from a partition) The problem How to preserve personal alignment for each user? How to improve (optimize) the public alignment according to users’ alignments?

Global alignment (Representation) Global alignment: an equivalence relation on W A function from W to {0}N (c: W{0}N)

User’s alignment (Representation) A (partial) function from Wi to {0, i}N (ci: Wi {0, i}N) Personalized alignment ci  c|W-Wi : W{0, i}N

Optimizing the global alignment Input: a family of users’ partitions {ci} Output: an optimal partition c* on Wi min id(c*, ci) Bn=j=1..n S(n,j)

Partition distance Vertex cover problem

Consensus Partition Clique partitioning problem  having a maximum total weight

Reference Gusfield D. Partition-distance: A problem and class of perfect graphs arising in clustering[J]. Information Processing Letters, 2002, 82(3): 159-164. Guénoche A. Consensus of partitions: a constructive approach[J]. Advances in Data Analysis and Classification, 2011, 5(3): 215-229

Websoft Research Group Acknowledgement Websoft Research Group http://ws.nju.edu.cn