Compact in‐memory representation of large graph databases for efficient mining of maximal frequent sub graphs

Frequent graph mining allows us to find useful frequent sub-graph patterns from large and complicated graph databases. In a lot of real world applications, graph patterns with relatively low supports can be used as meaningful information. However, previous methods based on a single minimum support threshold have trouble finding them. That is, they cause “rare item problem”, which means that useful sub-graphs with low supports cannot be extracted when a minimum support threshold is high, while an enormous number of patterns have to be mined to obtain these useful ones when the value is low. To overcome this problem, we propose a novel algorithm, FGM-MMS (Frequent Graph Mining based on Multiple Minimum Support constraints). After that, we demonstrate that the suggested algorithm outperforms a state-of-the-art graph mining algorithm through comprehensive performance experiments.

Graph mining is a well-established research field, and lately it has drawn in considerable research communities. It allows to process, analyze, and discover significant knowledge from graph data. In graph mining, one of the most challenging tasks is frequent subgraph mining (FSM). FSM consists of applying the data mining algorithms to extract interesting, unexpected, and useful graph patterns from the graphs. FSM has been applied to many domains, such as graphical data management and knowledge discovery, social network analysis, bioinformatics, and security. In this context, a large number of techniques have been suggested to deal with the graph data. These techniques can be classed into two primary categories: (i) a priori-based FSM approaches and (ii) pattern growth-based FSM approaches. In both of these categories, an extensive research work is available. However, FSM approaches are facing some challenges, including enormous numbers of frequent subgraph patterns (FSPs); no suitable mechanism for applying ranking at the appropriate level during the discovery process of the FSPs; extraction of repetitive and duplicate FSPs; user involvement in supplying the support threshold value; large number of subgraph candidate generation. Thus, the aim of this research is to make do with the challenges of enormous FSPs, avoid duplicate discovery of FSPs, and use the ranking for such patterns. Therefore, to address these challenges a new FSM framework A RAnked Frequent pattern-growth Framework (A-RAFF) is suggested. Consequently, A-RAFF provides an efficacious answer to these challenges through the initiation of a new ranking measure called FSP-Rank. The proposed ranking measure FSP-Rank effectively reduced the duplicate and enormous frequent patterns. The effectiveness of the techniques proposed in this study is validated by extensive experimental analysis using different benchmark and synthetic graph datasets. Our experiments have consistently demonstrated the promising empirical results, thus confirming the superiority and practical feasibility of the proposed FSM framework.

An important component of current research in big data is graph analytics on very large graphs. Of the many problems of interest in this domain, graph pattern matching is both challenging and practically important. The problem is, given a relatively small query graph, finding matching patterns in a large data graph. Algorithms to address this problem are used in large social networks and graph databases. Though fast querying is highly desirable, the scalability of pattern matching algorithms is hindered by the NP-completeness of the subgraph isomorphism problem. This paper presents a conceptually simple, memory-efficient, pruning-based algorithm for the subgraph isomorphism problem that outperforms commonly used algorithms on large graphs. The high performance is due in large part to the effectiveness of the pruning algorithm, which in many cases removes a large percentage of the vertices not found in isomorphic matches. In this paper, the runtime of the algorithm is tested alongside other algorithms on graphs of up to 10 million vertices and 250 million edges.

Retrieving graphs containing a query graph from a large graph database is a key task in many graph-based applications, including chemical compounds discovery, protein complex prediction, and structural pattern recognition. However, graph data handled by these applications is often noisy, incomplete, and inaccurate because of the way the data is produced. In this paper, we study subgraph queries over uncertain graphs. Specifically, we consider the problem of answering threshold-based probabilistic queries over a large uncertain graph database with the possible world semantics. We prove that problem is #P-complete, therefore, we adopt a filtering-and-verification strategy to speed up the search. In the filtering phase, we use a probabilistic inverted index, PIndex, based on subgraph features obtained by an optimal feature selection process. During the verification phase, we develop exact and bound algorithms to validate the remaining candidates. Extensive experimental results demonstrate the effectiveness of the proposed algorithms.

A major challenge in frequent subgraph mining is the sheer size of its mining results. In many cases, allow minimum support may generate an explosive number of frequent subgraphs, which severely restricts the usage of frequent sub graph mining. In this paper, we study anew problem of mining frequent jump patterns from graph databases. Mining frequent jump patterns can dramatically reduce the number of output graph patterns, and still capture interesting graph patterns. By integrating the operation of checking jump patterns into the well-known DFS code tree enumeration framework, we present an efficient algorithm JPMiner for this new problem. We experimentally evaluate various aspects of Jupiter using both real and synthetic datasets. Experimental results demonstrate that the number of frequent jump patterns is much smaller than that of closed frequent graph patterns, and JPMiner is efficient and scalable in mining frequent jump patterns.

Noisy graph data and pattern variations are two thorny problems faced by mining frequent subgraphs. Traditional exact-matching based methods, however, only generate patterns that have enough perfect matches in the graph database. As a result, a pattern may either remain undetected or be reported as multiple (almost identical) patterns if it manifests slightly different instances in different graphs. In this paper, we investigate the problem of approximate frequent pattern mining, with a focus on finding non-redundant representative frequent patterns that summarize the frequent patterns allowing approximate matches in a graph database. To achieve this goal, we propose the REAFUM framework which (1) first extracts a list of diverse representative graphs from the database, which may contain most approximate frequent patterns exhibited in the entire graph database; (2) then uses distinct patterns in the representative graphs as seed patterns to retrieve approximate matches in the entire graph database; (3) finally employs a consensus refinement model to derive representative approximate frequent patterns. Through a comprehensive evaluation of REAFUM on both synthetic and real datasets, we show that REAFUM is effective and efficient to find representative approximate frequent patterns and REAFUM is able to find patterns that much better resemble the ground truth in the presence of noise and errors, and are less redundant than that from any exact-matching based methods.

How can we analyze large graphs such as the Web, and social networks with hundreds of billions of vertices and edges? Although many graph mining systems have been proposed to perform various graph mining algorithms on such large graphs, they have difficulties in processing Web-scale graphs due to massive communication and I/O costs caused by communication between workers, and reading subgraphs repeatedly. In this paper, we propose FlexGraph, a scalable distributed graph mining method reducing the costs by exploiting properties of real-world graphs. FlexGraph significantly decreases the communication cost, which is the main bottleneck of distributed systems, by exploiting different edge placement policies based on types of vertices. Furthermore, we propose a flexible storage format to reduce I/O costs when reading input graph repeatedly. Experiments show that FlexGraph succeeds in processing up to 64× larger graphs than existing distributed memory-based graph mining methods, and consistently outperforms previous disk-based graph mining methods.

The subgraph searching is a fundamental operation for the analysis and exploration of graphs. Nowadays, molecular databases are nearing close to one hundred million molecules. Since finding all the data graphs in a graph database that contain the query graph using subgraph isomorphism is an NP-complete problem, indexes are built and processed. Further, to assist the formulation of the query by a user, the visual exploratory subgraph query paradigm proposes a graphical user interface and leverages exploration time to reduce query processing time. However, state-of-the-art approaches need to scale better to dynamic graph databases and suffer from efficiency problems. In addition, the existing Summarisation-based frequent subgraph mining for visual exploratory subgraph searching (SuMExplorer) is lacking implementation and evaluation study for handling visual subgraph similarity search and modify operations. In this paper, we present a novel index structure, which aids the subgraph searching using the summarised-based weighted frequent subgraph mining on data graphs. By the structure-preserving, we exploit the indexes to support similarity and modify operations. We conduct extensive performance studies on both real-world and synthetic datasets to evaluate the overall performance of the extended SuMExplorer to the recent visual exploratory FERRARI and traditional subgraph search algorithms (such as the gIndex and the GRAPES-DD). Our results showed that our indexes can query up to 3 times faster in comparison to the FERRARI while reducing the storage footprint by 2 orders of magnitude.

GraphChi is the first reported disk-based graph engine that can handle billion-scale graphs on a single PC efficiently. GraphChi is able to execute several advanced data mining, graph mining and machine learning algorithms on very large graphs. With the novel technique of parallel sliding windows (PSW) to load subgraph from disk to memory for vertices and edges updating, it can achieve data processing performance close to and even better than those of mainstream distributed graph engines. GraphChi mentioned that its memory is not effectively utilized with large dataset, which leads to suboptimal computation performances. In this paper we are motivated by the concepts of "pin " from TurboGraph and "ghost" from GraphLab to propose a new memory utilization mode for GraphChi, which is called Part-in-memory mode, to improve the GraphChi algorithm performance. The main idea is to pin a fixed part of data inside the memory during the whole computing process. Part-in-memory mode is successfully implemented with only about 40 additional lines of code to the original GraphChi engine. Extensive experiments are performed with large real datasets (including Twitter graph with 1.4 billion edges). The preliminary results show that Part-in-memory mode memory management approach effectively reduces the GraphChi running time by up to 60% in PageRank algorithm. Interestingly it is found that a larger portion of data pinned in memory does not always lead to better performance in the case that the whole dataset cannot be fitted in memory. There exists an optimal portion of data which should be kept in the memory to achieve the best computational performance.

Many studies have been conducted on seeking an efficient solution for graph similarity search over certain (deterministic) graphs due to its wide application in many fields, including bioinformatics, social network analysis, and Resource Description Framework data management. All prior work assumes that the underlying data is deterministic. However, in reality, graphs are often noisy and uncertain due to various factors, such as errors in data extraction, inconsistencies in data integration, and for privacy-preserving purposes. Therefore, in this paper, we study similarity graph containment search on large uncertain graph databases. Similarity graph containment search consists of subgraph similarity search and supergraph similarity search. Different from previous works assuming that edges in an uncertain graph are independent of each other, we study uncertain graphs where edges' occurrences are correlated. We formally prove that subgraph or supergraph similarity search over uncertain graphs is $$\#$&#P-hard; thus, we employ a filter-and-verify framework to speed up these two queries. For the subgraph similarity query, in the filtering phase, we develop tight lower and upper bounds of subgraph similarity probability based on a probabilistic matrix index (PMI). PMI is composed of discriminative subgraph features associated with tight lower and upper bounds of subgraph isomorphism probability. Based on PMI, we can filter out a large number of uncertain graphs and maximize the pruning capability. During the verification phase, we develop an efficient sampling algorithm to validate the remaining candidates. For the supergraph similarity query, in the filtering phase, we propose two pruning algorithms, one lightweight and the other strong, based on maximal common subgraphs of query graph and data graph. We run the two pruning algorithms against a probabilistic index that consists of powerful graph features. In the verification, we design an approximate algorithm based on the Horvitz---Thompson estimator to fast validate the remaining candidates. The efficiencies of our proposed solutions to the subgraph and supergraph similarity search have been verified through extensive experiments on real uncertain graph datasets.

In this paper, we propose a novel approach to exploring cross-linguistic connections, with a focus on false friends, using Large Language Model embeddings and graph databases. We achieve a classification performance on the Spanish-Portuguese false friend dataset of F1 = 83.81% using BERT and a multi-layer perceptron neural network. Furthermore, using advanced translation models to match words between vocabularies, we also construct a ground truth false friends dataset between Slovenian and Macedonian - two languages with significant historical and cultural ties. Subsequently, we construct a graph-based representation using a Neo4j database, wherein nodes correspond to words, and various types of edges capture semantic relationships between them.

Knowledge discovery in structured databases is very important nowadays. In the last years, graph-based data mining algorithms have used artificial neural networks as tools to support clustering. Several of these algorithms have obtained promising results, but they show expensive computational costs. In this work we introduce an algorithm for clustering graphs based on a SOM network, which is part of a process for discovering useful frequent patterns in large graph databases. Our algorithm is able to handle non-directed, cyclic graphs with labels in vertices and edges. An important characteristic is that it presents polynomial computational complexity, because it uses as input a feature vector built with the spectra of the Laplacian of an adjacent matrix. Such matrix contains codes representing the labels in the graph, which preserves the semantic information included in the graphs to be grouped. We tested our algorithm in a small set of graphs and in a large structured database, finding that it creates meaningful groups of graphs.

Discriminative subgraphs are widely used to define the feature space for graph classification in large graph databases. Several scalable approaches have been proposed to mine discriminative subgraphs. However, their intensive computation needs prevent them from mining large databases. We propose an efficient method GAIA for mining discriminative subgraphs for graph classification in large databases. Our method employs a novel subgraph encoding approach to support an arbitrary subgraph pattern exploration order and explores the subgraph pattern space in a process resembling biological evolution. In this manner, GAIA is able to find discriminative subgraph patterns much faster than other algorithms. Additionally, we take advantage of parallel computing to further improve the quality of resulting patterns. In the end, we employ sequential coverage to generate association rules as graph classifiers using patterns mined by GAIA. Extensive experiments have been performed to analyze the performance of GAIA and to compare it with two other state-of-the-art approaches. GAIA outperforms the other approaches both in terms of classification accuracy and runtime efficiency.

Recently, due to the rapid growth of electronic data having graph structures such as HTML and XML texts and chemical compounds, many researchers have been interested in data mining and machine learning techniques for finding useful patterns from graph-structured data (graph data). Since graph data contain a huge number of substructures and it tends to be computationally expensive to decide whether or not such data have given structural features, graph mining problems face computational difficulties. Let ${\mathcal{C}}$ be a graph class which satisfies a connected hereditary property and contains infinitely many different biconnected graphs, and for which a special kind of the graph isomorphism problem can be computed in polynomial time. In this paper, we consider learning and mining problems for ${\mathcal{C}}$ . Firstly, we define a new graph pattern, which is called a block preserving graph pattern (bp-graph pattern) for ${\mathcal{C}}$ . Secondly, we present a polynomial time algorithm for deciding whether or not a given bp-graph pattern matches a given graph in ${\mathcal{C}}$ . Thirdly, by giving refinement operators over bp-graph patterns, we present a polynomial time algorithm for finding a minimally generalized bp-graph pattern for ${\mathcal{C}}$ . Outerplanar graphs are planar graphs which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many pharmacologic chemical compounds are known to be represented by outerplanar graphs. The class of connected outerplanar graphs ${\mathcal{O}}$ satisfies the above conditions for ${\mathcal{C}}$ . Next, we propose two incremental polynomial time algorithms for enumerating all frequent bp-graph patterns with respect to a given finite set of graphs in ${\mathcal{O}}$ . Finally, by reporting experimental results obtained by applying the two graph mining algorithms to a subset of the NCI dataset, we evaluate the performance of the two graph mining algorithms.

In contrast to mining over transactional data, graph mining is done over structured data represented in the form of a graph. Data having structural relationships lends itself to graph mining. Subdue is one of the early main memory graph mining algorithms that detects the best substructure that compresses a graph using the minimum description length principle. Database approach to graph mining presented in this paper overcomes the problems – performance and scalability – inherent to main memory algorithms. The focus of this paper is the development of graph mining algorithms (specifically Subdue) using SQL and stored procedures in a Relational database environment. We have not only shown how the Subdue class of algorithms can be translated to SQL-based algorithms, but also demonstrated that scalability can be achieved without sacrificing performance.KeywordsMain MemoryExtension AttributeAssociation Rule MiningGraph MiningFrequent SubgraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.