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 graph 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.

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.

Abstract — Over the years, frequent itemset discovery algorithms have been used to find interesting patterns in various application areas. However, as data mining techniques are being increasingly applied to non-traditional domains, existing frequent pattern discovery approach cannot be used. This is because the transaction framework that is assumed by these algorithms cannot be used to effectively model the datasets in these domains. An alternate way of modeling the objects in these datasets is to represent them using graphs. Within that model, one way of formulating the frequent pattern discovery problem is as that of discovering subgraphs that occur frequently over the entire set of graphs. In this paper we present a computationally efficient algorithm, called FSG, for finding all frequent subgraphs in large graph datasets. We experimentally evaluate the performance of FSG using a variety of real and synthetic datasets. Our results show that despite the underlying complexity associated with frequent subgraph discovery, FSG is effective in finding all frequently occurring subgraphs in datasets containing over 200,000 graph transactions and scales linearly with respect to the size of the dataset. Index Terms — Data mining, scientific datasets, frequent pattern discovery, chemical compound datasets.

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.

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.

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.

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. 1.

Information cascades are phenomena in which individuals adopt a new action or idea due to influence by others. As such a process spreads through an underlying social network, it can result in widespread adoption overall. We consider information cascades in the context of recommendations, and in particular study the patterns of cascading recommendations that arise in large social networks. We investigate a large person-to-person recommendation network, consisting of four million people who made sixteen million recommendations on half a million products. Such a dataset allows us to pose a number of fundamental questions: What kinds of cascades arise frequently in real life? What features distinguish them? We enumerate and count cascade subgraphs on large directed graphs; as one component of this, we develop a novel efficient heuristic based on graph isomorphism testing that scales to large datasets. We discover novel patterns: the distribution of cascade sizes is approximately heavy-tailed; cascades tend to be shallow, but occasional large bursts of propagation can occur. The relative abundance of di#erent cascade subgraphs suggests subtle properties of the underlying social network and recommendation process.

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.

One fundamental challenge for mining recurring subgraphs from semi-structured data sets is the overwhelming abundance of such patterns. In large graph databases, the total number of frequent subgraphs can become too large to allow a full enumeration using reasonable computational resources. In this paper, we propose a new algorithm that mines only maximal frequent subgraphs, i.e. subgraphs that are not a part of any other frequent subgraphs. This may exponentially decrease the size of the output set in the best case; in our experiments on practical data sets, mining maximal frequent subgraphs reduces the total number of mined patterns by two to three orders of magnitude. Our method first mines all frequent trees from a general graph database and then reconstructs all maximal subgraphs from the mined trees. Using two chemical structure benchmarks and a set of synthetic graph data sets, we demonstrate that, in addition to decreasing the output size, our algorithm can achieve a five-fold speed up over the current state-of-the-art subgraph mining algorithms.