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 ? _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.