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194
A quickstart in frequent structure mining can make a difference
- In Proc. of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-2004
, 2004
"... 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 bee ..."
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Cited by 159 (5 self)
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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.
Finding frequent patterns in a large sparse graph
- SIAM Data Mining Conference
, 2004
"... 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 ..."
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Cited by 130 (4 self)
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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.
Spin: Mining maximal frequent subgraphs from graph databases
- IN KDD
, 2004
"... 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 ..."
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Cited by 99 (12 self)
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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.
Graph indexing: Tree + delta >= graph
- In VLDB
, 2007
"... Recent scientific and technological advances have witnessed an abundance of structural patterns modeled as graphs. As a result, it is of special interest to process graph containment queries effectively on large graph databases. Given a graph database G, and a query graph q, the graph containment qu ..."
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Cited by 53 (6 self)
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Recent scientific and technological advances have witnessed an abundance of structural patterns modeled as graphs. As a result, it is of special interest to process graph containment queries effectively on large graph databases. Given a graph database G, and a query graph q, the graph containment query is to retrieve all graphs in G which contain q as subgraph(s). Due to the vast number of graphs in G and the nature of complexity for subgraph isomorphism testing, it is desirable to make use of high-quality graph indexing mechanisms to reduce the overall query processing cost. In this paper, we propose a new cost-effective graph indexing method based on frequent tree-features of the graph database. We analyze the effectiveness and efficiency of tree as indexing feature from three critical aspects: feature size, feature selection cost, and pruning power. In order to achieve better pruning ability than existing graph-based indexing methods, we select, in addition to frequent tree-features (Tree), a small number of discriminative graphs (∆) on demand, without a costly graph mining process beforehand. Our study verifies that (Tree+∆) is a better choice than graph for indexing purpose, denoted (Tree+ ∆ ≥Graph), to address the graph containment query problem. It has two implications: (1) the index construction by (Tree+∆) is efficient, and (2) the graph containment query processing by (Tree+∆) is efficient. Our experimental studies demonstrate that (Tree+∆) has a compact index structure, achieves an order of magnitude better performance in index construction, and most importantly, outperforms up-to-date graphbased indexing methods: gIndex and C-Tree, in graph containment query processing. 1.
Frequent Subtree Mining - An Overview
, 2005
"... Mining frequent subtrees from databases of labeled trees is a new research field that has many practical applications in areas such as computer networks, Web mining, bioinformatics, XML document mining, etc. These applications share a requirement for the more expressive power of labeled trees to ..."
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Cited by 52 (3 self)
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Mining frequent subtrees from databases of labeled trees is a new research field that has many practical applications in areas such as computer networks, Web mining, bioinformatics, XML document mining, etc. These applications share a requirement for the more expressive power of labeled trees to capture the complex relations among data entities. Although frequent subtree mining is a more difficult task than frequent itemset mining, most existing frequent subtree mining algorithms borrow techniques from the relatively mature association rule mining area. This paper provides an overview of a broad range of tree mining algorithms. We focus on the common theoretical foundations of the current frequent subtree mining algorithms and their relationship with their counterparts in frequent itemset mining. When comparing the algorithms, we categorize them according to their problem definitions and the techniques employed for solving various subtasks of the subtree mining problem. In addition, we also present a thorough performance study for a representative family of algorithms.
Eigenspace-based Anomaly Detection in Computer Systems
- Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD
, 2004
"... We report on an automated runtime anomaly detection method at the application layer of multi-node computer systems. Although several network management systems are available in the market, none of them have sufficient capabilities to detect faults in multi-tier Web-based systems with redundancy. We ..."
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Cited by 51 (4 self)
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We report on an automated runtime anomaly detection method at the application layer of multi-node computer systems. Although several network management systems are available in the market, none of them have sufficient capabilities to detect faults in multi-tier Web-based systems with redundancy. We model a Web-based system as a weighted graph, where each node represents a “service ” and each edge represents a dependency between services. Since the edge weights vary greatly over time, the problem we address is that of anomaly detection from a time sequence of graphs. In our method, we first extract a feature vector from the adjacency matrix that represents the activities of all of the services. The heart of our method is to use the principal eigenvector of the eigenclusters of the graph. Then we derive a probability distribution for an anomaly measure defined for a time-series of directional data derived from the graph sequence. Given a critical probability, the threshold value is adaptively updated using a novel online algorithm. We demonstrate that a fault in a Web application can be automatically detected and the faulty services are identified without using detailed knowledge of the behavior of the system.
Discovering Frequent Geometric Subgraphs
- In IEEE Intl. Conference on Data Mining ’02
, 2002
"... As data mining techniques are being increasingly applied to non-traditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of these domains. An alternate way of modeling the objects in these data sets, is to use a graph to model the ..."
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Cited by 38 (1 self)
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As data mining techniques are being increasingly applied to non-traditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of these domains. An alternate way of modeling the objects in these data sets, is to use a graph to model the database objects. Within that model, the problem of finding frequent patterns becomes that of discovering subgraphs that occur frequently over the entire set of graphs. In this paper we present a computationally e#cient algorithm for finding frequent geometric subgraphs in a large collection of geometric graphs. Our algorithm is able to discover geometric subgraphs that can be rotation, scaling and translation invariant, and it can accommodate inherent errors on the coordinates of the vertices. We evaluated the performance of the algorithm using a large database of over 20,000 real two dimensional chemical structures, and our experimental results show that our algorithms requires relatively little time, can accommodate low support values, and scales linearly on the number of transactions.
Comparing Graph Representations of Protein Structure for Mining Family-Specific Residue-Based Packing Motifs
- Journal of Computational Biology
, 2005
"... We find recurring amino-acid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein three-dimensional structure. Graph nodes represent amino acids, and edges are c ..."
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Cited by 36 (5 self)
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We find recurring amino-acid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein three-dimensional structure. Graph nodes represent amino acids, and edges are chosen in one of three ways: first, using a threshold for contact distance between residues; second, using Delaunay tessellation; and third, using the recently developed almost-Delaunay edges. For a set of graphs representing a protein family from the Structural Classification of Proteins (SCOP) database, subgraph mining typically identifies several hundred common subgraphs corresponding to spatial motifs that are frequently found in proteins in the family but rarely found outside of it. We find that some of the large motifs map onto known functional regions in two protein families explored in this study, i.e., serine proteases and kinases. We find that graphs based on almost-Delaunay edges significantly reduce the number of edges in the graph representation and hence present computational advantage, yet the patterns extracted from such graphs have a biological interpretation approximately equivalent to that of those extracted from distance based graphs. Key words: protein structure motifs, frequent subgraph mining, almost-Delaunay. 1.
HybridTreeMiner: An Efficient Algorithm for Mining Frequent Rooted Trees and Free Trees Using Canonical Forms
, 2004
"... Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. In this paper, we present HybridTreeMiner, a computationally efficient algorithm that discovers all frequently occurring subtrees in a database of rooted u ..."
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Cited by 34 (4 self)
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Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. In this paper, we present HybridTreeMiner, a computationally efficient algorithm that discovers all frequently occurring subtrees in a database of rooted unordered trees. The algorithm mines frequent subtrees by traversing an enumeration tree that systematically enumerates all subtrees. The enumeration tree is defined based on a novel canonical form for rooted unordered trees -- the breadth-first canonical form (BFCF). By extending the definitions of our canonical form and enumeration tree to free trees, our algorithm can efficiently handle databases of free trees as well. We study the performance of our algorithms through extensive experiments based on both synthetic data and datasets from real applications. The experiments show that our algorithm is competitive in comparison to known rooted tree mining algorithms and is faster by one to two orders of magnitudes compared to a known algorithm for mining frequent free trees.
Mining Protein Family Specific Residue Packing Patterns from Protein Structure Graphs
- In Proc. of Research in Computational Molecular Biology
, 2004
"... Finding recurring residue packing patterns, or spatial motifs, that characterize protein structural families is an important problem in bioinformatics. To this end, we apply a novel frequent subgraph mining algorithm to three graph representations of protein threedimensional (3D) structure. In each ..."
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Cited by 31 (12 self)
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Finding recurring residue packing patterns, or spatial motifs, that characterize protein structural families is an important problem in bioinformatics. To this end, we apply a novel frequent subgraph mining algorithm to three graph representations of protein threedimensional (3D) structure. In each protein graph, a vertex represents an amino acid. Vertex-residues are connected by edges using three approaches: first, based on simple distance threshold between contact residues; second using the Delaunay tessellation from computational geometry, and third using the recently developed almost-Delaunay tessellation approach. Applying this approach to a set of graphs representing a protein family from the Structural Classification of Proteins (SCOP) database, we typically identify several hundred common subgraphs equivalent to common packing motifs found in the majority of proteins in the family. We also use the counts of motifs extracted from proteins in two different SCOP families as input variables in a binary classification experiment using Support Vector Machines. The resulting models are capable of predicting the protein family association with the accuracy exceeding 90 percent. Our results indicate that graphs based on both almost-Delaunay and Delaunay tessellations are more sparse than contact distance graph; yet the former afford similar accuracy of classification as the latter. The protein graph mining and classification approaches developed in this paper can be used for rapid and automated annotation of protein structures determined in structural genomics projects.
