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.

Mining frequent trees is very useful in domains like bioinformatics, web mining, mining semi-structured data, and so on. We formulate the problem of mining (embedded) subtrees in a forest of rooted, labeled, and ordered trees. We present TreeMiner, a novel algorithm to discover all frequent subtrees in a forest, using a new data structure called scope-list. We contrast TreeMiner with a pattern matching tree mining algorithm (PatternMatcher). We conduct detailed experiments to test the performance and scalability of these methods. We find that TreeMiner outperforms the pattern matching approach by a factor of 4 to 20, and has good scaleup properties. We also present an application of tree mining to analyze real web logs for usage patterns.

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. Di#erent 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 an elegant solution to the graph indexing problem, but also demonstrates how database indexing and query processing can benefit from data mining, especially frequent pattern mining. Furthermore, the concepts developed here can be applied to indexing sequences, trees, and other complicated structures as well.

Sequential pattern mining is an important data mining problem with broad applications. However, it is also a difficult problem since the mining may have to generate or examine a combinatorially explosive number of intermediate subsequences. Most of the previously developed sequential pattern mining methods, such as GSP, explore a candidate generation-and-test approach [1] to reduce the number of candidates to be examined. However, this approach may not be efficient in mining large sequence databases having numerous patterns and/or long patterns. In this paper, we propose a projection-based, sequential pattern-growth approach for efficient mining of sequential patterns. In this approach, a sequence database is recursively projected into a set of smaller projected databases, and sequential patterns are grown in each projected database by exploring only locally frequent fragments. Based on an initial study of the pattern growth-based sequential pattern mining, FreeSpan [8], we propose a more efficient method, called PSP, which offers ordered growth and reduced projected databases. To further improve the performance, a pseudoprojection technique is developed in PrefixSpan. A comprehensive performance study shows that PrefixSpan, in most cases, outperforms the a priori-based algorithm GSP, FreeSpan, and SPADE [29] (a sequential pattern mining algorithm that adopts vertical data format), and PrefixSpan integrated with pseudoprojection is the fastest among all the tested algorithms. Furthermore, this mining methodology can be extended to mining sequential patterns with user-specified constraints. The high promise of the pattern-growth approach may lead to its further extension toward efficient mining of other kinds of frequent patterns, such as frequent substructures.

Frequent subgraph mining is an active research topic in the data mining community. A graph is a general model to represent data and has been used in many domains like cheminformatics and bioinformatics. Mining patterns from graph databases is challenging since graph related operations, such as subgraph testing, generally have higher time complexity than the corresponding operations on itemsets, sequences, and trees, which have been studied extensively. In this paper, we propose a novel frequent subgraph mining algorithm: FFSM, which employs a vertical search scheme within an algebraic graphical framework we have developed to reduce the number of redundant candidates proposed. Our empirical study on synthetic and real datasets demonstrates that FFSM achieves a substantial performance gain over the current start-of-the-art subgraph mining algorithm gSpan.

Given a database, structure mining algorithms search for substructures that satisfy constraints such as minimum fre-quency, minimum confidence, minimum interest and maxi-mum frequency. Examples of substructures include graphs, trees and paths. For these substructures many mining al-gorithms have been proposed. In order to make graph min-ing more efficient, we investigate the use of the “quickstart principle”, which is based on the fact that these classes of structures are contained in each other, thus allowing for the development of structure mining algorithms that split the search into steps of increasing complexity. We introduce the GrAph/Sequence/Tree extractiON (Gaston) algorithm that implements this idea by searching first for frequent paths, then frequent free trees and finally cyclic graphs. We investigate two alternatives for computing the frequency of structures and present experimental results to relate these alternatives.

In this paper we study the problem of classifying chemical compound datasets. We present a sub-structure-based classification algorithm that decouples the sub-structure discovery process from the classification model construction and uses frequent subgraph discovery algorithms to find all topological and geometric sub-structures present in the dataset. The advantage of our approach is that during classification model construction, all relevant sub-structures are available allowing the classifier to intelligently select the most discriminating ones. The computational scalability is ensured by the use of highly efficient frequent subgraph discovery algorithms coupled with aggressive feature selection. Our experimental evaluation on eight different classification problems shows that our approach is computationally scalable and outperforms existing schemes by 10% to 35%, on the average.

This paper presents two algorithms based on the horizontal and vertical pattern discovery paradigms that find the connected subgraphs that have a sufficient number of edge-disjoint embeddings in a single large undirected labeled sparse graph. These algorithms use three different methods to determine the number of the edge-disjoint embeddings of a subgraph that are based on approximate and exact maximum independent set computations and use it to prune infrequent subgraphs. Experimental evaluation on real datasets from various domains show that both algorithms achieve good performance, scale well to sparse input graphs with more than 100,000 vertices, and significantly outperform a previously developed algorithm.

Although frequent-pattern mining has been widely studied and used, it is challenging to extend it to data streams. Compared to mining from a static transaction data set, the streaming case has far more information to track and far greater complexity to manage. Infrequent items can become frequent later on and hence cannot be ignored. The storage structure needs to be dynamically adjusted to reflect the evolution of itemset frequencies over time.

How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: “How can we generate synthetic but realistic graphs? ” To answer this, we must first understand what patterns are common in real-world graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.