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Maximal Biclique Subgraphs and Closed Pattern Pairs of the Adjacency Matrix: A One-to-One Correspondence and Mining Algorithms
December 2007 (vol. 19 no. 12)
pp. 1625-1637
ASCII Text
x 
 
Jinyan Li, Guimei Liu, Haiquan Li, Limsoon Wong, "Maximal Biclique Subgraphs and Closed Pattern Pairs of the Adjacency Matrix: A One-to-One Correspondence and Mining Algorithms," IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 12, pp. 1625-1637, December, 2007.
 
 
BibTex
x
 
@article{ 10.1109/TKDE.2007.190660,
author = {Jinyan Li and Guimei Liu and Haiquan Li and Limsoon Wong},
title = {Maximal Biclique Subgraphs and Closed Pattern Pairs of the Adjacency Matrix: A One-to-One Correspondence and Mining Algorithms},
journal ={IEEE Transactions on Knowledge and Data Engineering},
volume = {19},
number = {12},
issn = {1041-4347},
year = {2007},
pages = {1625-1637},
doi = {http://doi.ieeecomputersociety.org/10.1109/TKDE.2007.190660},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Knowledge and Data Engineering
TI - Maximal Biclique Subgraphs and Closed Pattern Pairs of the Adjacency Matrix: A One-to-One Correspondence and Mining Algorithms
IS - 12
SN - 1041-4347
SP1625
EP1637
EPD - 1625-1637
A1 - Jinyan Li,
A1 - Guimei Liu,
A1 - Haiquan Li,
A1 - Limsoon Wong,
PY - 2007
KW - Mining methods and algorithms
KW - Graph algorithms
VL - 19
JA - IEEE Transactions on Knowledge and Data Engineering
ER -
 
Enumerating maximal biclique subgraphs from a graph is a computationally challenging problem. In this paper, we efficiently enumerate them through the use of closed patterns of the adjacency matrix of the graph. For an undirected graph $G$ without self-loops, we prove that: (i) the number of closed patterns in the adjacency matrix of $G$ is even; and (ii) for every maximal biclique subgraph, there always exists a unique pair of closed patterns that matches the two vertex sets of the subgraph. Therefore, the problem of enumerating maximal bicliques can be solved by using efficient algorithms for mining closed patterns, which are algorithms extensively studied in the data mining field. However, this direct use of existing algorithms causes a duplicated enumeration. To achieve high efficiency, we propose an $O(mn)$ time delay algorithm for a non-duplicated enumeration, in particular for enumerating those maximal bicliques with a large size, where $m$ and $n$ are the number of edges and vertices of the graph respectively. We evaluate the high efficiency of our algorithm by comparing it to state-of-the-art algorithms on many graphs.

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Index Terms:
Mining methods and algorithms, Graph algorithms
Citation:
Jinyan Li, Guimei Liu, Haiquan Li, Limsoon Wong, "Maximal Biclique Subgraphs and Closed Pattern Pairs of the Adjacency Matrix: A One-to-One Correspondence and Mining Algorithms," IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 12, pp. 1625-1637, Dec. 2007, doi:10.1109/TKDE.2007.190660
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