Xifeng Yan

gSpan: graph-based substructure pattern mining

We investigate new approaches for frequent graph-based pattern mining in graph datasets and propose a novel algorithm called gSpan (graph-based substructure pattern mining), which discovers frequent substructures without candidate generation. gSpan builds a new lexicographic order among graphs, and maps each graph to a unique minimum DFS code as its canonical label. Based on this lexicographic order gSpan adopts the depth-first search strategy to mine frequent connected subgraphs efficiently. Our performance study shows that gSpan substantially outperforms previous algorithms, sometimes by an order of magnitude.

Frequent pattern mining: current status and future directions

Frequent pattern mining has been a focused theme in data mining research for over a decade. Abundant literature has been dedicated to this research and tremendous progress has been made, ranging from efficient and scalable algorithms for frequent itemset mining in transaction databases to numerous research frontiers, such as sequential pattern mining, structured pattern mining, correlation mining, associative classification, and frequent pattern-based clustering, as well as their broad applications. In this article, we provide a brief overview of the current status of frequent pattern mining and discuss a few promising research directions. We believe that frequent pattern mining research has substantially broadened the scope of data analysis and will have deep impact on data mining methodologies and applications in the long run. However, there are still some challenging research issues that need to be solved before frequent pattern mining can claim a cornerstone approach in data mining applications.

CloseGraph: mining closed frequent graph patterns

Recent research on pattern discovery has progressed form mining frequent itemsets and sequences to mining structured patterns including trees, lattices, and graphs. As a general data structure, graph can model complicated relations among data with wide applications in bioinformatics, Web exploration, and etc. However, mining large graph patterns in challenging due to the presence of an exponential number of frequent subgraphs. Instead of mining all the subgraphs, we propose to mine closed frequent graph patterns. A graph g is closed in a database if there exists no proper supergraph of g that has the same support as g. A closed graph pattern mining algorithm, CloseGraph, is developed by exploring several interesting pruning methods. Our performance study shows that CloseGraph not only dramatically reduces unnecessary subgraphs to be generated but also substantially increases the efficiency of mining, especially in the presence of large graph patterns.

Graph indexing: a frequent structure-based approach

Graph has become increasingly important in modelling complicated structures and schemaless data such as proteins, chemical compounds, and XML documents. Given a graph query, it is desirable to retrieve graphs quickly from a large database via graph-based indices. In this paper, we investigate the issues of indexing graphs and propose a novel solution by applying a graph mining technique. Different from the existing path-based methods, our approach, called gIndex, makes use of frequent substructure as the basic indexing feature. Frequent substructures are ideal candidates since they explore the intrinsic characteristics of the data and are relatively stable to database updates. To reduce the size of index structure, two techniques, size-increasing support constraint and discriminative fragments, are introduced. Our performance study shows that gIndex has 10 times smaller index size, but achieves 3--10 times better performance in comparison with a typical path-based method, GraphGrep. The gIndex approach not only provides and elegant solution to the graph indexing problem, but also demonstrates how database indexing and query processing can benefit form data mining, especially frequent pattern mining. Furthermore, the concepts developed here can be applied to indexing sequences, trees, and other complicated structures as well.

Discriminative Frequent Pattern Analysis for Effective Classification

The application of frequent patterns in classification appeared in sporadic studies and achieved initial success in the classification of relational data, text documents and graphs. In this paper, we conduct a systematic exploration of frequent pattern-based classification, and provide solid reasons supporting this methodology. It was well known that feature combinations (patterns) could capture more underlying semantics than single features. However, inclusion of infrequent patterns may not significantly improve the accuracy due to their limited predictive power. By building a connection between pattern frequency and discriminative measures such as information gain and Fisher score, we develop a strategy to set minimum support in frequent pattern mining for generating useful patterns. Based on this strategy, coupled with a proposed feature selection algorithm, discriminative frequent patterns can be generated for building high quality classifiers. We demonstrate that the frequent pattern-based classification framework can achieve good scalability and high accuracy in classifying large datasets. Empirical studies indicate that significant improvement in classification accuracy is achieved (up to 12% in UCI datasets) using the so-selected discriminative frequent patterns.

Mining coherent dense subgraphs across massive biological networks for functional discovery

MOTIVATION The rapid accumulation of biological network data translates into an urgent need for computational methods for graph pattern mining. One important problem is to identify recurrent patterns across multiple networks to discover biological modules. However, existing algorithms for frequent pattern mining become very costly in time and space as the pattern sizes and network numbers increase. Currently, no efficient algorithm is available for mining recurrent patterns across large collections of genome-wide networks. RESULTS We developed a novel algorithm, CODENSE, to efficiently mine frequent coherent dense subgraphs across large numbers of massive graphs. Compared with previous methods, our approach is scalable in the number and size of the input graphs and adjustable in terms of exact or approximate pattern mining. Applying CODENSE to 39 co-expression networks derived from microarray datasets, we discovered a large number of functionally homogeneous clusters and made functional predictions for 169 uncharacterized yeast genes. AVAILABILITY http://zhoulab.usc.edu/CODENSE/

Substructure similarity search in graph databases

Advanced database systems face a great challenge raised by the emergence of massive, complex structural data in bioinformatics, chem-informatics, and many other applications. The most fundamental support needed in these applications is the efficient search of complex structured data. Since exact matching is often too restrictive, similarity search of complex structures becomes a vital operation that must be supported efficiently.In this paper, we investigate the issues of substructure similarity search using indexed features in graph databases. By transforming the edge relaxation ratio of a query graph into the maximum allowed missing features, our structural filtering algorithm, called Grafil, can filter many graphs without performing pairwise similarity computations. It is further shown that using either too few or too many features can result in poor filtering performance. Thus the challenge is to design an effective feature set selection strategy for filtering. By examining the effect of different feature selection mechanisms, we develop a multi-filter composition strategy, where each filter uses a distinct and complementary subset of the features. We identify the criteria to form effective feature sets for filtering, and demonstrate that combining features with similar size and selectivity can improve the filtering and search performance significantly. Moreover, the concept presented in Grafil can be applied to searching approximate non-consecutive sequences, trees, and other complicated structures as well.

Mining significant graph patterns by leap search

With ever-increasing amounts of graph data from disparate sources, there has been a strong need for exploiting significant graph patterns with user-specified objective functions. Most objective functions are not antimonotonic, which could fail all of frequency-centric graph mining algorithms. In this paper, we give the first comprehensive study on general mining method aiming to find most significant patterns directly. Our new mining framework, called LEAP (Descending Leap Mine), is developed to exploit the correlation between structural similarity and significance similarity in a way that the most significant pattern could be identified quickly by searching dissimilar graph patterns. Two novel concepts, structural leap search and frequency descending mining, are proposed to support leap search in graph pattern space. Our new mining method revealed that the widely adopted branch-and-bound search in data mining literature is indeed not the best, thus sketching a new picture on scalable graph pattern discovery. Empirical results show that LEAP achieves orders of magnitude speedup in comparison with the state-of-the-art method. Furthermore, graph classifiers built on mined patterns outperform the up-to-date graph kernel method in terms of efficiency and accuracy, demonstrating the high promise of such patterns.

IncSpan: incremental mining of sequential patterns in large database

Many real life sequence databases grow incrementally. It is undesirable to mine sequential patterns from scratch each time when a small set of sequences grow, or when some new sequences are added into the database. Incremental algorithm should be developed for sequential pattern mining so that mining can be adapted to incremental database updates. However, it is nontrivial to mine sequential patterns incrementally, especially when the existing sequences grow incrementally because such growth may lead to the generation of many new patterns due to the interactions of the growing subsequences with the original ones. In this study, we develop an efficient algorithm, IncSpan, for incremental mining of sequential patterns, by exploring some interesting properties. Our performance study shows that IncSpan outperforms some previously proposed incremental algorithms as well as a non-incremental one with a wide margin.

Summarizing itemset patterns: a profile-based approach

Frequent-pattern mining has been studied extensively on scalable methods for mining various kinds of patterns including itemsets, sequences, and graphs. However, the bottleneck of frequent-pattern mining is not at the efficiency but at the interpretability, due to the huge number of patterns generated by the mining process.In this paper, we examine how to summarize a collection of itemset patterns using only K representatives, a small number of patterns that a user can handle easily. The K representatives should not only cover most of the frequent patterns but also approximate their supports. A generative model is built to extract and profile these representatives, under which the supports of the patterns can be easily recovered without consulting the original dataset. Based on the restoration error, we propose a quality measure function to determine the optimal value of parameter K. Polynomial time algorithms are developed together with several optimization heuristics for efficiency improvement. Empirical studies indicate that we can obtain compact summarization in real datasets.