New applications of data mining, such as in biology, bioinformatics, or sociology, are faced with large datasets structured as graphs. We introduce a novel class of tree-shaped patterns called tree queries, and present algorithms for mining tree queries and tree-query associations in a large data graph. Novel about our class of patterns is that they can contain constants, and can contain existential nodes which are not counted when determining the number of occurrences of the pattern in the data graph. Our algorithms have a number of provable optimality properties, which are based on the theory of conjunctive database queries. We propose a practical, database-oriented implementation in SQL, and show that the approach works in practice through experiments on data about food webs, protein interactions, and citation analysis.
Approaches to graph mining, especially mining for frequent patterns or association rules, can be divided in two major categories which are not to be confused. In transactional graph mining, e.g., @cite_8 @cite_19 @cite_24 @cite_32 @cite_26 @cite_5 @cite_39 , the dataset consists of many small data graphs which we call transactions, and the task is to discover patterns that occur at least once in a sufficient number of transactions. (Approaches from machine learning or inductive logic programming usually call the small data graphs examples'' instead of transactions.) In single-graph mining the dataset is a single large data graph, and the task is to discover patterns that occur sufficiently often in the dataset.
@cite_26 @cite_8 @cite_32 @cite_39 @cite_24 @cite_19 @cite_5
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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 nontraditional domains, existing frequent pattern discovery approaches cannot be used. This is because the transaction framework that is assumed by these algorithms cannot be used to effectively model the data sets in these domains. An alternate way of modeling the objects in these data sets is to represent them using graphs. Within that model, one way of formulating the frequent pattern discovery problem is that of discovering subgraphs that occur frequently over the entire set of graphs. We present a computationally efficient algorithm, called FSG, for finding all frequent subgraphs in large graph data sets. We experimentally evaluate the performance of FSG using a variety of real and synthetic data sets. Our results show that despite the underlying complexity associated with frequent subgraph discovery, FSG is effective in finding all frequently occurring subgraphs in data sets containing more than 200,000 graph transactions and scales linearly with respect to the size of the data set. Discovery of frequent patterns has been studied in a variety of data mining settings. In its simplest form, known from association rule mining, the task is to discover all frequent itemsets, i.e., all combinations of items that are found in a sufficient number of examples. The fundamental task of association rule and frequent set discovery has been extended in various directions, allowing more useful patterns to be discovered with special purpose algorithms. We present WARMR, a general purpose inductive logic programming algorithm that addresses frequent query discovery: a very general DATALOG formulation of the frequent pattern discovery problem. The motivation for this novel approach is twofold. First, exploratory data mining is well supported: WARMR offers the flexibility required to experiment with standard and in particular novel settings not supported by special purpose algorithms. Also, application prototypes based on WARMR can be used as benchmarks in the comparison and evaluation of new special purpose algorithms. Second, the unified representation gives insight to the blurred picture of the frequent pattern discovery domain. Within the DATALOG formulation a number of dimensions appear that relink diverged settings. We demonstrate the frequent query approach and its use on two applications, one in alarm analysis, and one in a chemical toxicology domain. The derivation of frequent subgraphs from a dataset of labeled graphs has high computational complexity because the hard problems of isomorphism and subgraph isomorphism have to be solved as part of this derivation. To deal with this computational complexity, all previous approaches have focused on one particular kind of graph. In this paper, we propose an approach to conduct a complete search for various classes of frequent subgraphs in a massive dataset of labeled graphs within a practical time. The power of our approach comes from the algebraic representation of graphs, its associated operations and well-organized bias constraints to limit the search space efficiently. The performance has been evaluated using real world datasets, and the high scalability and flexibility of our approach have been confirmed with respect to the amount of data and the computation time. 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. 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. In recent years there has been an increased interest in algorithms that can perform frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it becomes intractable for arbitrary graph databases. Existing approaches have therefore resorted to various heuristic strategies and restrictions of the search space, but have not identified a practically relevant tractable graph class beyond trees. In this paper, we define the class of so called tenuous outerplanar graphs, a strict generalization of trees, develop a frequent subgraph mining algorithm for tenuous outerplanar graphs that works in incremental polynomial time, and evaluate the algorithm empirically on the NCI molecular graph dataset. 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.