Mining frequent subgraphs over uncertain graph databases under probabilistic semantics

Mining frequent subgraphs over uncertain graph databases under probabilistic semantics Frequent subgraph mining has been extensively studied on certain graph data. However, uncertainty is intrinsic in graph data in practice, but there is very few work on mining uncertain graph data. This paper focuses on mining frequent subgraphs over uncertain graph data under the probabilistic semantics. Specifically, a measure called $${\varphi}$$ -frequent probability is introduced to evaluate the degree of recurrence of subgraphs. Given a set of uncertain graphs and two real numbers $${0 < \varphi, \tau < 1}$$ , the goal is to quickly find all subgraphs with $${\varphi}$$ -frequent probability at least τ . Due to the NP-hardness of the problem and to the #P-hardness of computing the $${\varphi}$$ -frequent probability of a subgraph, an approximate mining algorithm is proposed to produce an $${(\varepsilon, \delta)}$$ -approximate set Π of “frequent subgraphs”, where $${0 < \varepsilon < \tau}$$ is error tolerance, and 0 < δ < 1 is a confidence bound. The algorithm guarantees that (1) any frequent subgraph S is contained in Π with probability at least ((1 − δ ) /2) s , where s is the number of edges in S ; (2) any infrequent subgraph with $${\varphi}$$ -frequent probability less than $${\tau - \varepsilon}$$ is contained in Π with probability at most δ /2. The theoretical analysis shows that to obtain any frequent subgraph with probability at least 1 − Δ , the input parameter δ of the algorithm must be set to at most $${1 - 2 (1 - \Delta)^{1 / \ell_{\max}}}$$ , where 0 < Δ < 1, and ℓ max is the maximum number of edges in frequent subgraphs. Extensive experiments on real uncertain graph data verify that the proposed algorithm is practically efficient and has very high approximation quality. Moreover, the difference between the probabilistic semantics and the expected semantics on mining frequent subgraphs over uncertain graph data has been discussed in this paper for the first time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The VLDB Journal Springer Journals

Mining frequent subgraphs over uncertain graph databases under probabilistic semantics

Loading next page...
 
/lp/springer_journal/mining-frequent-subgraphs-over-uncertain-graph-databases-under-YzszLiWT54
Publisher
Springer-Verlag
Copyright
Copyright © 2012 by Springer-Verlag Berlin Heidelberg
Subject
Computer Science; Database Management
ISSN
1066-8888
eISSN
0949-877X
D.O.I.
10.1007/s00778-012-0268-8
Publisher site
See Article on Publisher Site

Abstract

Frequent subgraph mining has been extensively studied on certain graph data. However, uncertainty is intrinsic in graph data in practice, but there is very few work on mining uncertain graph data. This paper focuses on mining frequent subgraphs over uncertain graph data under the probabilistic semantics. Specifically, a measure called $${\varphi}$$ -frequent probability is introduced to evaluate the degree of recurrence of subgraphs. Given a set of uncertain graphs and two real numbers $${0 < \varphi, \tau < 1}$$ , the goal is to quickly find all subgraphs with $${\varphi}$$ -frequent probability at least τ . Due to the NP-hardness of the problem and to the #P-hardness of computing the $${\varphi}$$ -frequent probability of a subgraph, an approximate mining algorithm is proposed to produce an $${(\varepsilon, \delta)}$$ -approximate set Π of “frequent subgraphs”, where $${0 < \varepsilon < \tau}$$ is error tolerance, and 0 < δ < 1 is a confidence bound. The algorithm guarantees that (1) any frequent subgraph S is contained in Π with probability at least ((1 − δ ) /2) s , where s is the number of edges in S ; (2) any infrequent subgraph with $${\varphi}$$ -frequent probability less than $${\tau - \varepsilon}$$ is contained in Π with probability at most δ /2. The theoretical analysis shows that to obtain any frequent subgraph with probability at least 1 − Δ , the input parameter δ of the algorithm must be set to at most $${1 - 2 (1 - \Delta)^{1 / \ell_{\max}}}$$ , where 0 < Δ < 1, and ℓ max is the maximum number of edges in frequent subgraphs. Extensive experiments on real uncertain graph data verify that the proposed algorithm is practically efficient and has very high approximation quality. Moreover, the difference between the probabilistic semantics and the expected semantics on mining frequent subgraphs over uncertain graph data has been discussed in this paper for the first time.

Journal

The VLDB JournalSpringer Journals

Published: Dec 1, 2012

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off