APPROXIMATE ALGORITHMS FOR GRAPH CLUSTERING PROBLEM

2019 ◽  
pp. 64-77
Author(s):  
V. P. Il’ev ◽  
◽  
S. D. Il’eva ◽  
A. V. Morshinin ◽  
◽  
...  
Keyword(s):  
Graph Clustering ◽  
Approximate Algorithms ◽  
Clustering Problem

A local search for a graph clustering problem

2016 ◽  
Author(s):  
Anna Navrotskaya ◽  
Victor Il’ev
Keyword(s):  
Local Search ◽  
Graph Clustering ◽  
Clustering Problem

The graph clustering problem has a perfect zero-knowledge interactive proof

1999 ◽  
Vol 69 (4) ◽  
pp. 201-206 ◽  
Author(s):  
Alfredo De Santis ◽  
Giovanni Di Crescenzo ◽  
Oded Goldreich ◽  
Giuseppe Persiano
Keyword(s):  
Graph Clustering ◽  
Interactive Proof ◽  
Zero Knowledge ◽  
Clustering Problem

scholarly journals Market Graph Clustering via QUBO and Digital Annealing

2021 ◽  
Vol 14 (1) ◽  
pp. 34
Author(s):  
Seo Woo Hong ◽  
Pierre Miasnikof ◽  
Roy Kwon ◽  
Yuri Lawryshyn
Keyword(s):  
Graph Clustering ◽  
Small Subset ◽  
Index Tracking ◽  
Np Hard ◽  
Tracking Problem ◽  
Financial Industry ◽  
Graph Models ◽  
Clustering Problem ◽  
Market Graph ◽  
Common Task

We present a novel technique for cardinality-constrained index-tracking, a common task in the financial industry. Our approach is based on market graph models. We model our reference indices as market graphs and express the index-tracking problem as a quadratic K-medoids clustering problem. We take advantage of a purpose-built hardware architecture to circumvent the NP-hard nature of the problem and solve our formulation efficiently. The main contributions of this article are bridging three separate areas of the literature, market graph models, K-medoid clustering and quadratic binary optimization modeling, to formulate the index-tracking problem as a binary quadratic K-medoid graph-clustering problem. Our initial results show we accurately replicate the returns of various market indices, using only a small subset of their constituent assets. Moreover, our binary quadratic formulation allows us to take advantage of recent hardware advances to overcome the NP-hard nature of the problem and obtain solutions faster than with traditional architectures and solvers.

ADAPTIVE K-MEANS ALGORITHM FOR OVERLAPPED GRAPH CLUSTERING

2012 ◽  
Vol 22 (05) ◽  
pp. 1250018 ◽  
Author(s):  
GEMA BELLO-ORGAZ ◽  
HÉCTOR D. MENÉNDEZ ◽  
DAVID CAMACHO
Keyword(s):  
Genetic Algorithm ◽  
Social Networks ◽  
Graph Theory ◽  
Clustering Algorithms ◽  
Graph Clustering ◽  
Clustering Problem ◽  
Fitness Functions ◽  
Automatic Adaptation ◽  
Clustering Approach ◽  
Definition Of

The graph clustering problem has become highly relevant due to the growing interest of several research communities in social networks and their possible applications. Overlapped graph clustering algorithms try to find subsets of nodes that can belong to different clusters. In social network-based applications it is quite usual for a node of the network to belong to different groups, or communities, in the graph. Therefore, algorithms trying to discover, or analyze, the behavior of these networks needed to handle this feature, detecting and identifying the overlapped nodes. This paper shows a soft clustering approach based on a genetic algorithm where a new encoding is designed to achieve two main goals: first, the automatic adaptation of the number of communities that can be detected and second, the definition of several fitness functions that guide the searching process using some measures extracted from graph theory. Finally, our approach has been experimentally tested using the Eurovision contest dataset, a well-known social-based data network, to show how overlapped communities can be found using our method.

scholarly journals Local clustering via approximate heat kernel PageRank with subgraph sampling

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhenqi Lu ◽  
Johan Wahlström ◽  
Arye Nehorai
Keyword(s):  
Heat Kernel ◽  
Clustering Algorithm ◽  
State Of The Art ◽  
Graph Clustering ◽  
Approximate Algorithms ◽  
Local Cluster ◽  
Massive Graphs ◽  
Approximation Errors ◽  
Local Clustering ◽  
Large Systems

AbstractGraph clustering, a fundamental technique in network science for understanding structures in complex systems, presents inherent problems. Though studied extensively in the literature, graph clustering in large systems remains particularly challenging because massive graphs incur a prohibitively large computational load. The heat kernel PageRank provides a quantitative ranking of nodes, and a local cluster can be efficiently found by performing a sweep over the heat kernel PageRank vector. But computing an exact heat kernel PageRank vector may be expensive, and approximate algorithms are often used instead. Most approximate algorithms compute the heat kernel PageRank vector on the whole graph, and thus are dependent on global structures. In this paper, we present an algorithm for approximating the heat kernel PageRank on a local subgraph. Moreover, we show that the number of computations required by the proposed algorithm is sublinear in terms of the expected size of the local cluster of interest, and that it provides a good approximation of the heat kernel PageRank, with approximation errors bounded by a probabilistic guarantee. Numerical experiments verify that the local clustering algorithm using our approximate heat kernel PageRank achieves state-of-the-art performance.

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