Charalampos (Babis) E. Tsourakakis KDD 2013 KDD'131.

Slides:

Advertisements

Similar presentations

Impact of Interference on Multi-hop Wireless Network Performance

Advertisements

Network Design with Degree Constraints Guy Kortsarz Joint work with Rohit Khandekar and Zeev Nutov.

Weighted Matching-Algorithms, Hamiltonian Cycles and TSP

Impact of Interference on Multi-hop Wireless Network Performance Kamal Jain, Jitu Padhye, Venkat Padmanabhan and Lili Qiu Microsoft Research Redmond.

Partitional Algorithms to Detect Complex Clusters

Minimum Clique Partition Problem with Constrained Weight for Interval Graphs Jianping Li Department of Mathematics Yunnan University Jointed by M.X. Chen.

Approximation Algorithms

An Evaluation of Community Detection Algorithms on Large-Scale Traffic 1 An Evaluation of Community Detection Algorithms on Large-Scale Traffic.

Gene duplication models and reconstruction of gene regulatory network evolution from network structure Juris Viksna, David Gilbert Riga, IMCS,

LEARNING INFLUENCE PROBABILITIES IN SOCIAL NETWORKS Amit Goyal Francesco Bonchi Laks V. S. Lakshmanan University of British Columbia Yahoo! Research University.

Mauro Sozio and Aristides Gionis Presented By:

Analysis and Modeling of Social Networks Foudalis Ilias.

Approximating Maximum Subgraphs Without Short Cycles Guy Kortsarz Join work with Michael Langberg and Zeev Nutov.

Online Social Networks and Media. Graph partitioning The general problem – Input: a graph G=(V,E) edge (u,v) denotes similarity between u and v weighted.

CS774. Markov Random Field : Theory and Application Lecture 17 Kyomin Jung KAIST Nov

Los Angeles September 27, 2006 MOBICOM Localization in Sparse Networks using Sweeps D. K. Goldenberg P. Bihler M. Cao J. Fang B. D. O. Anderson.

Introduction to Approximation Algorithms Lecture 12: Mar 1.

Visual Analysis of Large Graphs Using (X, Y)-clustering and Hybrid Visualizations V. Batagelj, W. Didimo, G. Liotta, P. Palladino, M. Patrignani (Univ.

Gene Co-expression Network Analysis BMI 730 Kun Huang Department of Biomedical Informatics Ohio State University.

Computational Complexity, Physical Mapping III + Perl CIS 667 March 4, 2004.

The community-search problem and how to plan a successful cocktail party Mauro SozioAris Gionis Max Planck Institute, Germany Yahoo! Research, Barcelona.

NP-complete and NP-hard problems. Decision problems vs. optimization problems The problems we are trying to solve are basically of two kinds. In decision.

Systems Biology, April 25 th 2007Thomas Skøt Jensen Technical University of Denmark Networks and Network Topology Thomas Skøt Jensen Center for Biological.

CSE 522 – Algorithmic and Economic Aspects of the Internet Instructors: Nicole Immorlica Mohammad Mahdian.

Part I: Introductory Materials Introduction to Graph Theory Dr. Nagiza F. Samatova Department of Computer Science North Carolina State University and Computer.

Graph-based consensus clustering for class discovery from gene expression data Zhiwen Yum, Hau-San Wong and Hongqiang Wang Bioinformatics, 2007.

Charalampos (Babis) E. Tsourakakis Brown University Brown University May 22 nd 2014 Brown University1.

Neighbourhood Sampling for Local Properties on a Graph Stream A. Pavan, Iowa State University Kanat Tangwongsan, IBM Research Srikanta Tirthapura, Iowa.

Fair Allocation with Succinct Representation Azarakhsh Malekian (NWU) Joint Work with Saeed Alaei, Ravi Kumar, Erik Vee UMDYahoo! Research.

Feature Matching Longin Jan Latecki. Matching example Observe that some features may be missing due to instability of feature detector, view change, or.

Finding dense components in weighted graphs Paul Horn

1 Introduction to Approximation Algorithms. 2 NP-completeness Do your best then.

Greedy Approximation Algorithms for finding Dense Components in a Graph Paper by Moses Charikar Presentation by Paul Horn.

A Clustering Algorithm based on Graph Connectivity Balakrishna Thiagarajan Computer Science and Engineering State University of New York at Buffalo.

Computational Molecular Biology Non-unique Probe Selection via Group Testing.

An Efficient Algorithm for Enumerating Pseudo Cliques Dec/18/2007 ISAAC, Sendai Takeaki Uno National Institute of Informatics & The Graduate University.

Memory Allocation of Multi programming using Permutation Graph By Bhavani Duggineni.

Computational Molecular Biology Non-unique Probe Selection via Group Testing.

Overlapping Community Detection in Networks

Robust Local Community Detection: On Free Rider Effect and Its Elimination 1 Case Western Reserve University Yubao Wu 1, Ruoming Jin 2, Jing Li 1, Xiang.

1 Microarray Clustering. 2 Outline Microarrays Hierarchical Clustering K-Means Clustering Corrupted Cliques Problem CAST Clustering Algorithm.

Correlation Clustering Shuchi Chawla Carnegie Mellon University Joint work with Nikhil Bansal and Avrim Blum.

Network Partition –Finding modules of the network. Graph Clustering –Partition graphs according to the connectivity. –Nodes within a cluster is highly.

Network applications Sushmita Roy BMI/CS 576 Dec 9 th, 2014.

A SENSITIVITY ANALYSIS OF A BIOLOGICAL MODULE DISCOVERY PIPELINE James Long International Arctic Research Center University of Alaska Fairbanks March 25,

Mining Coherent Dense Subgraphs across Multiple Biological Networks Vahid Mirjalili CSE 891.

Outline Introduction State-of-the-art solutions Equi-Truss Experiments

Graph clustering to detect network modules

Impact of Interference on Multi-hop Wireless Network Performance

Cohesive Subgraph Computation over Large Graphs

Finding Dense and Connected Subgraphs in Dual Networks

DOULION: Counting Triangles in Massive Graphs with a Coin

Introduction to Approximation Algorithms

Groups of vertices and Core-periphery structure

Polynomial integrality gaps for

Graph partitioning I: Dense Sub-Graphs

Tatsuie Tsukiji (speaker) Tokyo Denki University

Markov Random Fields with Efficient Approximations

Greedy Algorithm for Community Detection

June 2017 High Density Clusters.

Computability and Complexity

Finding Subgraphs with Maximum Total Density and Limited Overlap

Noémi Gaskó, Rodica Ioana Lung, Mihai Alexandru Suciu

Problem Solving 4.

3.3 Network-Centric Community Detection

SEG5010 Presentation Zhou Lanjun.

Asymmetric Transitivity Preserving Graph Embedding

The Complexity of Approximation

Approximate Graph Mining with Label Costs

Presentation transcript:

Charalampos (Babis) E. Tsourakakis KDD 2013 KDD'131

2 Francesco Bonchi Yahoo! Research Aristides Gionis Aalto University Francesco Gullo Yahoo! Research Maria Tsiarli University of Pittsburgh

 Densest subgraph problem is very popular in practice. However, not what we want for many applications.  δ=edge density,D=diameter,τ=triangle density KDD'133

 Thematic communities and spam link farms [Gibson, Kumar, Tomkins ‘05]  Graph visualization[Alvarez-Hamelin etal.’05]  Real time story identification [Angel et al. ’12]  Motif detection [Batzoglou Lab ‘06]  Epilepsy prediction [Iasemidis et al. ‘01]  Finding correlated genes [Horvath et al.]  Many more.. KDD'134

 Clique: each vertex in S connects to every other vertex in S.  α-Quasi-clique: the set S has at least α|S|(|S|-1)/2 edges.  k-core: every vertex connects to at least k other vertices in S. KDD'135 K4

KDD'136 Average degree Density Triangle Density

 General framework which subsumes popular density functions.  Optimal quasi-cliques.  An algorithm with additive error guarantees and a local-search heuristic.  Variants  Top-k optimal quasi-cliques  Successful team formation KDD'137

 Experimental evaluation  Synthetic graphs  Real graphs  Applications  Successful team formation of computer scientists  Highly-correlated genes from microarray datasets KDD'138 First, some related work.

KDD'139 K4

KDD'1310 A single edge achieves always maximum possible δ(S) Densest subgraph problem k-Densest subgraph problem DalkS (Damks)

 Maximize average degree  Solvable in polynomial time  Max flows (Goldberg)  LP relaxation (Charikar)  Fast ½-approximation algorithm (Charikar) KDD'1311

 k-densest subgraph problem is NP-hard  Feige, Kortsatz, Peleg Bhaskara, Charikar, Chlamtac, Vijayraghavan Asahiro et al. Andersen Khuller, Saha [approximation algorithms], Khot [no PTAS]. KDD'1312

KDD'1313

KDD'1314

KDD'1315

KDD'1316

KDD'1317

 Notice that in general the optimal value can be negative.  We can obtain guarantees for a shifted objective but introduces large additive error making the algorithm almost useless, i.e., except for very special graphs.  Other type of guarantees more suitable. KDD'1318

KDD'1319

KDD'1320

KDD'1321

KDD'1322 DSM1M2DSM1M2DSM1M2DSM1M2 Wiki ‘ K Youtube1.9K

KDD'1323

KDD'1324

 Suppose that a set Q of scientists wants to organize a workshop. How do they invite other scientists to participate in the workshop so that the set of all participants, including Q, have similar interests ? KDD'1325

KDD' vertices, δ(S)= 0.81

KDD' vertices, δ(S)=0.49

 Given a microarray dataset and a set of genes Q, find a set of genes S that includes Q and they are all highly correlated.  Co-expression network  Measure gene expression across multiple samples  Create correlation matrix  Edges between genes if their correlation is > ρ.  A dense subgraph in a co-expression network corresponds to a set of highly correlated genes. KDD'1328

KDD'1329

KDD'1330

KDD'1331