Sublinear-Time Clustering Oracle for Signed Graphs

被引:0
|
作者
Neumann, Stefan [1 ]
Peng, Pan [2 ]
机构
[1] KTH Royal Inst Technol, Stockholm, Sweden
[2] Univ Sci & Technol China, Sch Comp Sci & Technol, Hefei, Peoples R China
基金
欧洲研究理事会;
关键词
D O I
暂无
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
Social networks are often modeled using signed graphs, where vertices correspond to users and edges have a sign that indicates whether an interaction between users was positive or negative. The arising signed graphs typically contain a clear community structure in the sense that the graph can be partitioned into a small number of polarized communities, each defining a sparse cut and indivisible into smaller polarized sub-communities. We provide a local clustering oracle for signed graphs with such a clear community structure, that can answer membership queries, i.e., "Given a vertex v, which community does v belong to?", in sublinear time by reading only a small portion of the graph. Formally, when the graph has bounded maximum degree and the number of communities is at most O(log n), then with (O) over tilde(root n poly(1/epsilon)) preprocessing time, our oracle can answer each membership query in (O) over tilde(root n poly(1/epsilon)) time, and it correctly classifies a (1 - epsilon)-fraction of vertices w.r.t. a set of hidden planted ground-truth communities. Our oracle is desirable in applications where the clustering information is needed for only a small number of vertices. Previously, such local clustering oracles were only known for unsigned graphs; our generalization to signed graphs requires a number of new ideas and gives a novel spectral analysis of the behavior of random walks with signs. We evaluate our algorithm for constructing such an oracle and answering membership queries on both synthetic and real-world datasets, validating its performance in practice.
引用
收藏
页数:33
相关论文
共 50 条
  • [1] Sublinear-time algorithms for tournament graphs
    Dantchev, Stefan
    Friedetzky, Tom
    Nagel, Lars
    [J]. JOURNAL OF COMBINATORIAL OPTIMIZATION, 2011, 22 (03) : 469 - 481
  • [2] Sublinear-Time Algorithms for Tournament Graphs
    Dantchev, Stefan
    Friedetzky, Tom
    Nagel, Lars
    [J]. COMPUTING AND COMBINATORICS, PROCEEDINGS, 2009, 5609 : 459 - 471
  • [3] Sublinear-time algorithms for tournament graphs
    Stefan Dantchev
    Tom Friedetzky
    Lars Nagel
    [J]. Journal of Combinatorial Optimization, 2011, 22 : 469 - 481
  • [4] Differentially-Private Sublinear-Time Clustering
    Blocki, Jeremiah
    Grigorescu, Elena
    Mukherjee, Tamalika
    [J]. 2021 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2021, : 332 - 337
  • [5] Sublinear-time approximation for clustering via random sampling
    Czumaj, A
    Sohler, C
    [J]. AUTOMATA , LANGUAGES AND PROGRAMMING, PROCEEDINGS, 2004, 3142 : 396 - 407
  • [6] Sublinear-time Algorithms
    Czumaj, Artur
    Sohler, Christian
    [J]. PROPERTY TESTING: CURRENT RESEARCH AND SURVEYS, 2010, 6390 : 41 - +
  • [7] SUBLINEAR-TIME ALGORITHMS
    Woeginger, Gerhard J.
    Czumaj, Artur
    Sohler, Christian
    [J]. BULLETIN OF THE EUROPEAN ASSOCIATION FOR THEORETICAL COMPUTER SCIENCE, 2006, (89): : 23 - 47
  • [8] Sublinear-time approximation algorithms for clustering via random sampling
    Czumaj, Artur
    Sohler, Christian
    [J]. RANDOM STRUCTURES & ALGORITHMS, 2007, 30 (1-2) : 226 - 256
  • [9] Sublinear-time algorithms for monomer-dimer systems on bounded degree graphs
    Lelarge, Marc
    Zhou, Hang
    [J]. THEORETICAL COMPUTER SCIENCE, 2014, 548 : 68 - 78
  • [10] On derandomizing probabilistic sublinear-time algorithms
    Zimand, Marius
    [J]. TWENTY-SECOND ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY, PROCEEDINGS, 2007, : 1 - +