Yiping Ke

Fg-index: towards verification-free query processing on graph databases

Graphs are prevalently used to model the relationships between objects in various domains. With the increasing usage of graph databases, it has become more and more demanding to efficiently process graph queries. Querying graph databases is costly since it involves subgraph isomorphism testing, which is an NP-complete problem. In recent years, some effective graph indexes have been proposed to first obtain a candidate answer set by filtering part of the false results and then perform verification on each candidate by checking subgraph isomorphism. Query performance is improved since the number of subgraph isomorphism tests is reduced. However, candidate verification is still inevitable, which can be expensive when the size of the candidate answer set is large. In this paper, we propose a novel indexing technique that constructs a nested inverted-index, called FG-index, based on the set of Frequent subGraphs (FGs). Given a graph query that is an FG in the database, FG-index returns the exact set of query answers without performing candidate verification. When the query is an infrequent graph, FG-index produces a candidate answer set which is close to the exact answer set. Since an infrequent graph means the graph occurs in only a small number of graphs in the database, the number of subgraph isomorphism tests is small. To ensure that the index fits into the main memory, we propose a new notion of δ-Tolerance Closed Frequent Graphs (δ-TCFGs), which allows us to flexibly tune the size of the index in a parameterized way. Our extensive experiments verify that query processing using FG-index is orders of magnitude more efficient than using the state-of-the-art graph index.

A survey on algorithms for mining frequent itemsets over data streams

The increasing prominence of data streams arising in a wide range of advanced applications such as fraud detection and trend learning has led to the study of online mining of frequent itemsets (FIs). Unlike mining static databases, mining data streams poses many new challenges. In addition to the one-scan nature, the unbounded memory requirement and the high data arrival rate of data streams, the combinatorial explosion of itemsets exacerbates the mining task. The high complexity of the FI mining problem hinders the application of the stream mining techniques. We recognize that a critical review of existing techniques is needed in order to design and develop efficient mining algorithms and data structures that are able to match the processing rate of the mining with the high arrival rate of data streams. Within a unifying set of notations and terminologies, we describe in this paper the efforts and main techniques for mining data streams and present a comprehensive survey of a number of the state-of-the-art algorithms on mining frequent itemsets over data streams. We classify the stream-mining techniques into two categories based on the window model that they adopt in order to provide insights into how and why the techniques are useful. Then, we further analyze the algorithms according to whether they are exact or approximate and, for approximate approaches, whether they are false-positive or false-negative. We also discuss various interesting issues, including the merits and limitations in existing research and substantive areas for future research.

A model-based approach to attributed graph clustering

Graph clustering, also known as community detection, is a long-standing problem in data mining. However, with the proliferation of rich attribute information available for objects in real-world graphs, how to leverage structural and attribute information for clustering attributed graphs becomes a new challenge. Most existing works take a distance-based approach. They proposed various distance measures to combine structural and attribute information. In this paper, we consider an alternative view and propose a model-based approach to attributed graph clustering. We develop a Bayesian probabilistic model for attributed graphs. The model provides a principled and natural framework for capturing both structural and attribute aspects of a graph, while avoiding the artificial design of a distance measure. Clustering with the proposed model can be transformed into a probabilistic inference problem, for which we devise an efficient variational algorithm. Experimental results on large real-world datasets demonstrate that our method significantly outperforms the state-of-art distance-based attributed graph clustering method.

Efficient processing of distance queries in large graphs: a vertex cover approach

We propose a novel disk-based index for processing single-source shortest path or distance queries. The index is useful in a wide range of important applications (e.g., network analysis, routing planning, etc.). Our index is a tree-structured index constructed based on the concept of vertex cover. We propose an I/O-efficient algorithm to construct the index when the input graph is too large to fit in main memory. We give detailed analysis of I/O and CPU complexity for both index construction and query processing, and verify the efficiency of our index for query processing in massive real-world graphs.

Fast algorithms for maximal clique enumeration with limited memory

Maximal clique enumeration (MCE) is a long-standing problem in graph theory and has numerous important applications. Though extensively studied, most existing algorithms become impractical when the input graph is too large and is disk-resident. We first propose an efficient partition-based algorithm for MCE that addresses the problem of processing large graphs with limited memory. We then further reduce the high cost of CPU computation of MCE by a careful nested partition based on a cost model. Finally, we parallelize our algorithm to further reduce the overall running time. We verified the efficiency of our algorithms by experiments in large real-world graphs.

Correlation search in graph databases

Correlation mining has gained great success in many application domains for its ability to capture the underlying dependency between objects. However, the research of correlation mining from graph databases is still lacking despite the fact that graph data, especially in various scientific domains, proliferate in recent years. In this paper, we propose a new problem of correlation mining from graph databases, called Correlated Graph Search (CGS). CGS adopts Pearsons correlation coefficient as a correlation measure to take into consideration the occurrence distributions of graphs. However, the problem poses significant challenges, since every subgraph of a graph in the database is a candidate but the number of subgraphs is exponential. We derive two necessary conditions which set bounds on the occurrence probability of a candidate in the database. With this result, we design an efficient algorithm that operates on a much smaller projected database and thus we are able to obtain a significantly smaller set of candidates. To further improve the efficiency, we develop three heuristic rules and apply them on the candidate set to further reduce the search space. Our extensive experiments demonstrate the effectiveness of our method on candidate reduction. The results also justify the efficiency of our algorithm in mining correlations from large real and synthetic datasets.

Mining quantitative correlated patterns using an information-theoretic approach

Existing research on mining quantitative databases mainly focuses on mining associations. However, mining associations is too expensive to be practical in many cases. In this paper, we study mining correlations from quantitative databases and show that it is a more effective approach than mining associations. We propose a new notion of Quantitative Correlated Patterns (QCPs), which is founded on two formal concepts, mutual information and all-confidence. We first devise a normalization on mutual information and apply it to QCP mining to capture the dependency between the attributes. We further adopt all-confidence as a quality measure to control, at a finer granularity, the dependency between the attributes with specific quantitative intervals. We also propose a supervised method to combine the consecutive intervals of the quantitative attributes based on mutual information, such that the interval combining is guided by the dependency between the attributes. We develop an algorithm, QCoMine, to efficiently mine QCPs by utilizing normalized mutual information and all-confidence to perform a two-level pruning. Our experiments verify the efficiency of QCoMine and the quality of the QCPs.

\delta-Tolerance Closed Frequent Itemsets

In this paper, we study an inherent problem of mining frequent itemsets (FIs): the number of FIs mined is often too large. The large number of FIs not only affects the mining performance, but also severely thwarts the application of FI mining. In the literature, Closed FIs (CFIs) and Maximal FIs (MFIs) are proposed as concise representations of FIs. However, the number of CFIs is still too large in many cases, while MFIs lose information about the frequency of the FIs. To address this problem, we relax the restrictive definition of CFIs and propose the (delta-Tolerance CFIs delta- TCFIs). Mining delta-TCFIs recursively removes all subsets of a delta-TCFI that fall within a frequency distance bounded by delta. We propose two algorithms, CFI2TCFI and MineTCFI, to mine delta-TCFIs. CFI2TCFI achieves very high accuracy on the estimated frequency of the recovered FIs but is less efficient when the number of CFIs is large, since it is based on CFI mining. MineTCFI is significantly faster and consumes less memory than the algorithms of the state-of-the-art concise representations of FIs, while the accuracy of MineTCFI is only slightly lower than that of CFI2TCFI.

Correlated pattern mining in quantitative databases

We study mining correlations from quantitative databases and show that this is a more effective approach than mining associations to discover useful patterns. We propose the novel notion of quantitative correlated pattern (QCP), which is founded on two formal concepts, mutual information and all-confidence. We first devise a normalization on mutual information and apply it to the problem of QCP mining to capture the dependency between the attributes. We further adopt all-confidence as a quality measure to ensure, at a finer granularity, the dependency between the attributes with specific quantitative intervals. We also propose an effective supervised method that combines the consecutive intervals of the quantitative attributes based on mutual information, such that the interval-combining is guided by the dependency between the attributes. We develop an algorithm, QCoMine, to mine QCPs efficiently by utilizing normalized mutual information and all-confidence to perform bilevel pruning. We also identify the redundancy existing in the set of QCPs and propose effective techniques to eliminate the redundancy. Our extensive experiments on both real and synthetic datasets verify the efficiency of QCoMine and the quality of the QCPs. The experimental results also justify the effectiveness of our proposed techniques for redundancy elimination. To further demonstrate the usefulness and the quality of QCPs, we study an application of QCPs to classification. We demonstrate that the classifier built on the QCPs achieves higher classification accuracy than the state-of-the-art classifiers built on association rules.

Maintaining frequent closed itemsets over a sliding window

In this paper, we study the incremental update of Frequent Closed Itemsets (FCIs) over a sliding window in a high-speed data stream. We propose the notion of semi-FCIs, which is to progressively increase the minimum support threshold for an itemset as it is retained longer in the window, thereby drastically reducing the number of itemsets that need to be maintained and processed. We explore the properties of semi-FCIs and observe that a majority of the subsets of a semi-FCI are not semi-FCIs and need not be updated. This finding allows us to devise an efficient algorithm, IncMine, that incrementally updates the set of semi-FCIs over a sliding window. We also develop an inverted index to facilitate the update process. Our empirical results show that IncMine achieves significantly higher throughput and consumes less memory than the state-of-the-art streaming algorithms for mining FCIs and FIs. IncMine also attains high accuracy of 100% precision and over 93% recall.