Maximal Frequent Subgraphs Research Articles

Isomorphic Graph Embedding for Progressive Maximal Frequent Subgraph Mining

Maximal frequent subgraph mining (MFSM) is the task of mining only maximal frequent subgraphs, i.e., subgraphs that are not a part of other frequent subgraphs. Although many intelligent systems require MFSM, MFSM is challenging compared to frequent subgraph mining (FSM), as maximal frequent subgraphs lie in the middle of graph lattice, and FSM algorithms must explore an exponential space and an NP-hard subroutine of frequency counting. Different from prior research, which primarily focused on optimal solutions, we introduce pmMine, a progressive graph neural framework designed for MFSM in a single large graph to attain an approximate solution. The framework combines isomorphic graph embedding, non-parametric partitioning, and an efficiently top-down pattern searching strategy. The critical insight that makes pmMine work is to define the concepts of rooted subgraph and isomorphic graph embedding, in which the costly isomorphism subroutine can be efficiently performed using similarity estimation in embedding space. In addition, pmMine returns the patterns identified during the mining process in a progressive manner. We validate the efficiency and effectiveness of our technique through extensive experiments on a variety of datasets spanning various domains.

Scalable maximal subgraph mining with backbone-preserving graph convolutions

Maximal subgraph mining is increasingly important in various domains, including bioinformatics, genomics, and chemistry, as it helps identify common characteristics among a set of graphs and enables their classification into different categories. Existing approaches for identifying maximal subgraphs typically rely on traversing a graph lattice. However, in practice, these approaches are limited to relatively small subgraphs due to the exponential growth of the search space and the NP-completeness of the underlying subgraph isomorphism test. In this work, we propose SCAMA, an approach that addresses these limitations by adopting a divide-and-conquer strategy for efficient mining of maximal subgraphs. Our approach involves initially partitioning a graph database into equivalence classes using bootstrapped backbones, which are tree-shaped frequent subgraphs. We then introduce a learning process based on a novel graph convolutional network (GCN) to extract maximal backbones for each equivalence class. A critical insight of our approach is that by estimating each maximal backbone directly in the embedding space, we can avoid the exponential traversal of the graph lattice. From the extracted maximal backbones, we construct the maximal frequent subgraphs. Furthermore, we outline how SCAMA can be extended to perform top-k largest frequent subgraph mining and how the discovered patterns facilitate graph classification. Our experimental results demonstrate the effectiveness of SCAMA in identifying almost perfectly maximal frequent subgraphs, while exhibiting approximately 10 times faster performance compared to the best baseline technique.

RASMA: a reverse search algorithm for mining maximal frequent subgraphs

BackgroundGiven a collection of coexpression networks over a set of genes, identifying subnetworks that appear frequently is an important research problem known as mining frequent subgraphs. Maximal frequent subgraphs are a representative set of frequent subgraphs; A frequent subgraph is maximal if it does not have a super-graph that is frequent. In the bioinformatics discipline, methodologies for mining frequent and/or maximal frequent subgraphs can be used to discover interesting network motifs that elucidate complex interactions among genes, reflected through the edges of the frequent subnetworks. Further study of frequent coexpression subnetworks enhances the discovery of biological modules and biological signatures for gene expression and disease classification.ResultsWe propose a reverse search algorithm, called RASMA, for mining frequent and maximal frequent subgraphs in a given collection of graphs. A key innovation in RASMA is a connected subgraph enumerator that uses a reverse-search strategy to enumerate connected subgraphs of an undirected graph. Using this enumeration strategy, RASMA obtains all maximal frequent subgraphs very efficiently. To overcome the computationally prohibitive task of enumerating all frequent subgraphs while mining for the maximal frequent subgraphs, RASMA employs several pruning strategies that substantially improve its overall runtime performance. Experimental results show that on large gene coexpression networks, the proposed algorithm efficiently mines biologically relevant maximal frequent subgraphs.ConclusionExtracting recurrent gene coexpression subnetworks from multiple gene expression experiments enables the discovery of functional modules and subnetwork biomarkers. We have proposed a reverse search algorithm for mining maximal frequent subnetworks. Enrichment analysis of the extracted maximal frequent subnetworks reveals that subnetworks that are frequent are highly enriched with known biological ontologies.

Generic visual data mining-based framework for revealing abnormal operation patterns in building energy systems

The abnormal operation patterns in building energy systems can be revealed by analyzing their historical operational data. In practice, the amount of data is so tremendous that manual data analysis is challenging. Visual data mining is a promising solution to this problem. This study proposes a generic visual data mining-based framework for extracting abnormal operation patterns in building energy systems from their historical operational data. The framework consists of three steps. First, a kernel density estimation-based approach is utilized to preprocess the raw data. Then, a decision tree-based approach is adopted to identify the system operation conditions. Finally, a maximal frequent subgraph mining-based approach is developed to reveal the system operation patterns. The framework is applied to analyze the one-year operational data of a chiller plant. This study proves that the framework can appropriately interpret the data mining results, and can make the analysis of the results more convenient.

Uncertain maximal frequent subgraph mining algorithm based on adjacency matrix and weight

How to mine many interesting subgraphs in uncertain graph has become an important research field in data mining. In this paper, a novel algorithm Uncertain Maximal Frequent Subgraph Mining Algorithm Based on Adjacency Matrix and Weight (UMFGAMW) is proposed. The definition of the adjacency matrix and the standard matrix coding for uncertain graph are presented. The correspondence between the adjacency matrix and uncertain graph is established. A new vertex ordering policy for computing the standard coding of uncertain graph adjacency matrix is designed. The complexity of uncertain graph standard coding is reduced, and the matching speed of uncertain subgraph standard coding is improved. The definition of the weight of uncertain graph and the mean weight of uncertain edge is proposed. The importance of the uncertain subgraphs that meet the minimum support threshold in the graph dataset is fully considered. Finally, a depth-first search weighted uncertain maximal frequent subgraph mining algorithm is discussed. According to the limiting condition of the uncertain maximum frequent subgraph and weighed uncertain edge, the number of mining results is reduced effectively. Experimental results demonstrate that the UMFGAMW algorithm has higher efficiency and better scalability.

Object Discovery: Soft Attributed Graph Mining.

We categorize this research in terms of its contribution to both graph theory and computer vision. From the theoretical perspective, this study can be considered as the first attempt to formulate the idea of mining maximal frequent subgraphs in the challenging domain of messy visual data, and as a conceptual extension to the unsupervised learning of graph matching. We define a soft attributed pattern (SAP) to represent the common subgraph pattern among a set of attributed relational graphs (ARGs), considering both their structure and attributes. Regarding the differences between ARGs with fuzzy attributes and conventional labeled graphs, we propose a new mining strategy that directly extracts the SAP with the maximal graph size without applying node enumeration. Given an initial graph template and a number of ARGs, we develop an unsupervised method to modify the graph template into the maximal-size SAP. From a practical perspective, this research develops a general platform for learning the category model (i.e., the SAP) from cluttered visual data (i.e., the ARGs) without labeling "what is where," thereby opening the possibility for a series of applications in the era of big visual data. Experiments demonstrate the superior performance of the proposed method on RGB/RGB-D images and videos.

The Complexity of Mining Maximal Frequent Subgraphs

A frequent subgraph of a given collection of graphs is a graph that is isomorphic to a subgraph of at least as many graphs in the collection as a given threshold. Frequent subgraphs generalize frequent itemsets and arise in various contexts, from bioinformatics to the Web. Since the space of frequent subgraphs is typically extremely large, research in graph mining has focused on special types of frequent subgraphs that can be orders of magnitude smaller in number, yet encapsulate the space of all frequent subgraphs. Maximal frequent subgraphs (i.e., the ones not properly contained in any frequent subgraph) constitute the most useful such type. In this article, we embark on a comprehensive investigation of the computational complexity of mining maximal frequent subgraphs. Our study is carried out by considering the effect of three different parameters: possible restrictions on the class of graphs; a fixed bound on the threshold; and a fixed bound on the number of desired answers. We focus on specific classes of connected graphs: general graphs, planar graphs, graphs of bounded degree, and graphs of bounded treewidth (trees being a special case). Moreover, each class has two variants: that in which the nodes are unlabeled, and that in which they are uniquely labeled. We delineate the complexity of the enumeration problem for each of these variants by determining when it is solvable in (total or incremental) polynomial time and when it is NP-hard. Specifically, for the labeled classes, we show that bounding the threshold yields tractability but, in most cases, bounding the number of answers does not, unless P=NP; an exception is the case of labeled trees, where bounding either of these two parameters yields tractability. The state of affairs turns out to be quite different for the unlabeled classes. The main (and most challenging to prove) result concerns unlabeled trees: we show NP-hardness, even if the input consists of two trees and both the threshold and the number of desired answers are equal to just two. In other words, we establish that the following problem is NP-complete: given two unlabeled trees, do they have more than one maximal subtree in common?

NIBBS-Search for Fast and Accurate Prediction of Phenotype-Biased Metabolic Systems

Understanding of genotype-phenotype associations is important not only for furthering our knowledge on internal cellular processes, but also essential for providing the foundation necessary for genetic engineering of microorganisms for industrial use (e.g., production of bioenergy or biofuels). However, genotype-phenotype associations alone do not provide enough information to alter an organism's genome to either suppress or exhibit a phenotype. It is important to look at the phenotype-related genes in the context of the genome-scale network to understand how the genes interact with other genes in the organism. Identification of metabolic subsystems involved in the expression of the phenotype is one way of placing the phenotype-related genes in the context of the entire network. A metabolic system refers to a metabolic network subgraph; nodes are compounds and edges labels are the enzymes that catalyze the reaction. The metabolic subsystem could be part of a single metabolic pathway or span parts of multiple pathways. Arguably, comparative genome-scale metabolic network analysis is a promising strategy to identify these phenotype-related metabolic subsystems. Network Instance-Based Biased Subgraph Search (NIBBS) is a graph-theoretic method for genome-scale metabolic network comparative analysis that can identify metabolic systems that are statistically biased toward phenotype-expressing organismal networks. We set up experiments with target phenotypes like hydrogen production, TCA expression, and acid-tolerance. We show via extensive literature search that some of the resulting metabolic subsystems are indeed phenotype-related and formulate hypotheses for other systems in terms of their role in phenotype expression. NIBBS is also orders of magnitude faster than MULE, one of the most efficient maximal frequent subgraph mining algorithms that could be adjusted for this problem. Also, the set of phenotype-biased metabolic systems output by NIBBS comes very close to the set of phenotype-biased subgraphs output by an exact maximally-biased subgraph enumeration algorithm ( MBS-Enum ). The code (NIBBS and the module to visualize the identified subsystems) is available at http://freescience.org/cs/NIBBS.

Top-Down Algorithm for Mining Maximal Frequent Subgraph

In order to solution the problem of mining maximal frequent subgraph is very hard we proposed new algorithm Top-Down. The process of this algorithm is using decision tree to count support then firstly judge the biggest graph whether frequent and gradually reduce the graph which used to judge until can not mining maximal frequent subgraph, at the same time this algorithm is proposed a theorem and two principles these are improved the mining efficiency.

MFC: Mining Maximal Frequent Dense Subgraphs without Candidate Maintenance in Imbalanced PPI Networks

The prediction of protein function is one of the most challenging problems in bioinformatics. Several studies have shown that the prediction using PPI is promising. However, the PPI data generated from high-throughput experiments are very noisy, which renders great challenges to the existing methods. In this paper, we propose an algorithm, MFC , to efficiently mine maximal frequent dense subgraphs without candidate maintenance in PPI networks. Instead of using summary graph, MFC produces frequent dense patterns by extending vertices. It adopts several techniques to achieve efficient mining. Due to the imbalance character of PPI network, we also propose to generate frequent patterns using relative support. We evaluate our approach on four PPI data sets. The experimental results show that our approach has good performance in terms of efficiency. With the help of relative support, more frequent dense functional interaction patterns in the PPI networks can be identified.

MARGIN

The exponential number of possible subgraphs makes the problem of frequent subgraph mining a challenge. The set of maximal frequent subgraphs is much smaller to that of the set of frequent subgraphs providing ample scope for pruning. MARGIN is a maximal subgraph mining algorithm that moves among promising nodes of the search space along the “border” of the infrequent and frequent subgraphs. This drastically reduces the number of candidate patterns in the search space. The proof of correctness of the algorithm is presented. Experimental results validate the efficiency and utility of the technique proposed.

Efficiently mining δ-tolerance closed frequent subgraphs

The output of frequent pattern mining is a huge number of frequent patterns, which are very redundant, causing a serious problem in understandability. We focus on mining frequent subgraphs for which well-considered approaches to reduce the redundancy are limited because of the complex nature of graphs. Two known, standard solutions are closed and maximal frequent subgraphs, but closed frequent subgraphs are still redundant and maximal frequent subgraphs are too specific. A more promising solution is ?-tolerance closed frequent subgraphs, which decrease monotonically in ?, being equal to maximal frequent subgraphs and closed frequent subgraphs for ?=0 and 1, respectively. However, the current algorithm for mining ?-tolerance closed frequent subgraphs is a naive, two-step approach in which frequent subgraphs are all enumerated and then sifted according to ?-tolerance closedness. We propose an efficient algorithm based on the idea of reverse-search by which the completeness of enumeration is guaranteed and for which new pruning conditions are incorporated. We empirically demonstrate that our approach significantly reduced the amount of real computation time of two compared algorithms for mining ?-tolerance closed frequent subgraphs, being pronounced more for practical settings.

Mining Top-K Graph Patterns that Jointly Maximize Some Significance Measure

Most of graph pattern mining algorithms focus on finding frequent subgraphs and its compact representations, such as closed frequent subgraphs and maximal frequent subgraphs. However, little attention has been paid to mining graph patterns with user-specified significance measure. In this paper, we study a new problem of mining top-k graph patterns that jointly maximize some significance measure from graph databases. Exploiting entropy and information gain, we give two problem formulation s , E M and IG M. We first prove them to be NP-hard and then propose two efficient algorithms, PP-TopK and DM-TopK, to solve them . PP-TopK greedily selects top-k graph patterns among frequent sub graph s. DM-TopK integrates the pruning techniques into the mining framework, and directly mines top-k graph patterns from graph databases. Empirical results demonstrate the quality of our top-k graph patterns, and validate the efficiency and scalability of our algorithms.

Discovering Neglected Conditions in Software by Mining Dependence Graphs

Neglected conditions are an important but difficult-to-find class of software defects. This paper presents a novel approach to revealing neglected conditions that integrates static program analysis and advanced data mining techniques to discover implicit conditional rules in a code base and to discover rule violations that indicate neglected conditions. The approach requires the user to indicate minimal constraints on the context of the rules to be sought, rather than specific rule templates. To permit this generality, rules are modeled as graph minors of enhanced procedure dependence graphs (EPDGs), in which control and data dependence edges are augmented by edges representing shared data dependences. A heuristic maximal frequent subgraph mining algorithm is used to extract candidate rules from EPDGs, and a heuristic graph matching algorithm is used to identify rule violations. We also report the results of an empirical study in which the approach was applied to four open source projects (openssl, make, procmail, amaya). These results indicate that the approach is effective and reasonably efficient.