Frequent Subgraph Mining in Outerplanar Graphs

In recent years there has been an increased interest in 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

Frequent Subgraph Mining in Outerplanar Graphs

In recent years there has been an increased interest in 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

Inductive queries for a drug designing robot scientist

It is increasingly clear that machine learning algorithms need to be integrated in an iterative scientific discovery loop, in which data is queried repeatedly by means of inductive queries and where the computer provides guidance to the experiments that are being performed. In this chapter, we summarise several key challenges in achieving this integration of machine learning and data mining algorithms in methods for the discovery of Quantitative Structure Activity Relationships (QSARs). We introduce the concept of a robot scientist, in which all steps of the discovery process are automated; we discuss the representation of molecular data such that knowledge discovery tools can analyse it, and we discuss the adaptation of machine learning and data mining algorithms to guide QSAR experiments

A Polynomial Algorithm for Subisomorphism of Open Plane Graphs

International audienceWe address the problem of searching for a pattern in a plane graph, that is, a planar drawing of a planar graph. We define plane subgraph isomorphism and give a polynomial algorithm for this problem. We show that this algorithm may be used even when the pattern graph has holes

FS^3: A Sampling based method for top-k Frequent Subgraph Mining

Mining labeled subgraph is a popular research task in data mining because of its potential application in many different scientific domains. All the existing methods for this task explicitly or implicitly solve the subgraph isomorphism task which is computationally expensive, so they suffer from the lack of scalability problem when the graphs in the input database are large. In this work, we propose FS^3, which is a sampling based method. It mines a small collection of subgraphs that are most frequent in the probabilistic sense. FS^3 performs a Markov Chain Monte Carlo (MCMC) sampling over the space of a fixed-size subgraphs such that the potentially frequent subgraphs are sampled more often. Besides, FS^3 is equipped with an innovative queue manager. It stores the sampled subgraph in a finite queue over the course of mining in such a manner that the top-k positions in the queue contain the most frequent subgraphs. Our experiments on database of large graphs show that FS^3 is efficient, and it obtains subgraphs that are the most frequent amongst the subgraphs of a given size

Efficient Frequent Subtree Mining Beyond Forests

A common paradigm in distance-based learning is to embed the instance space into some appropriately chosen feature space equipped with a metric and to define the dissimilarity between instances by the distance of their images in the feature space. If the instances are graphs, then frequent connected subgraphs are a well-suited pattern language to define such feature spaces. Identifying the set of frequent connected subgraphs and subsequently computing embeddings for graph instances, however, is computationally intractable. As a result, existing frequent subgraph mining algorithms either restrict the structural complexity of the instance graphs or require exponential delay between the output of subsequent patterns. Hence distance-based learners lack an efficient way to operate on arbitrary graph data. To resolve this problem, in this thesis we present a mining system that gives up the demand on the completeness of the pattern set to instead guarantee a polynomial delay between subsequent patterns. Complementing this, we devise efficient methods to compute the embedding of arbitrary graphs into the Hamming space spanned by our pattern set. As a result, we present a system that allows to efficiently apply distance-based learning methods to arbitrary graph databases. To overcome the computational intractability of the mining step, we consider only frequent subtrees for arbitrary graph databases. This restriction alone, however, does not suffice to make the problem tractable. We reduce the mining problem from arbitrary graphs to forests by replacing each graph by a polynomially sized forest obtained from a random sample of its spanning trees. This results in an incomplete mining algorithm. However, we prove that the probability of missing a frequent subtree pattern is low. We show empirically that this is true in practice even for very small sized forests. As a result, our algorithm is able to mine frequent subtrees in a range of graph databases where state-of-the-art exact frequent subgraph mining systems fail to produce patterns in reasonable time or even at all. Furthermore, the predictive performance of our patterns is comparable to that of exact frequent connected subgraphs, where available. The above method considers polynomially many spanning trees for the forest, while many graphs have exponentially many spanning trees. The number of patterns found by our mining algorithm can be negatively influenced by this exponential gap. We hence propose a method that can (implicitly) consider forests of exponential size, while remaining computationally tractable. This results in a higher recall for our incomplete mining algorithm. Furthermore, the methods extend the known positive results on the tractability of exact frequent subtree mining to a novel class of transaction graphs. We conjecture that the next natural extension of our results to a larger transaction graph class is at least as difficult as proving whether P = NP, or not. Regarding the graph embedding step, we apply a similar strategy as in the mining step. We represent a novel graph by a forest of its spanning trees and decide whether the frequent trees from the mining step are subgraph isomorphic to this forest. As a result, the embedding computation has one-sided error with respect to the exact subgraph isomorphism test but is computationally tractable. Furthermore, we show that we can leverage a partial order on the pattern set. This structure can be used to reduce the runtime of the embedding computation dramatically. For the special case of Jaccard-similarity between graph embeddings, a further substantial reduction of runtime can be achieved using min-hashing. The Jaccard-distance can be approximated using small sketch vectors that can be computed fast, again using the partial order on the tree patterns

Expert System for Crop Disease based on Graph Pattern Matching: A proposal

Para la agroindustria, las enfermedades en cultivos constituyen uno de los problemas más frecuentes que generan grandes pérdidas económicas y baja calidad en la producción. Por otro lado, desde las ciencias de la computación, han surgido diferentes herramientas cuya finalidad es mejorar la prevención y el tratamiento de estas enfermedades. En este sentido, investigaciones recientes proponen el desarrollo de sistemas expertos para resolver este problema haciendo uso de técnicas de minería de datos e inteligencia artificial, como inferencia basada en reglas, árboles de decisión, redes bayesianas, entre otras. Además, los grafos pueden ser usados para el almacenamiento de los diferentes tipos de variables que se encuentran presentes en un ambiente de cultivos, permitiendo la aplicación de técnicas de minería de datos en grafos, como el emparejamiento de patrones en los mismos. En este artículo presentamos una visión general de las temáticas mencionadas y una propuesta de un sistema experto para enfermedades en cultivos, basado en emparejamiento de patrones en grafos.For agroindustry, crop diseases constitute one of the most common problems that generate large economic losses and low production quality. On the other hand, from computer science, several tools have emerged in order to improve the prevention and treatment of these diseases. In this sense, recent research proposes the development of expert systems to solve this problem, making use of data mining and artificial intelligence techniques like rule-based inference, decision trees, Bayesian network, among others. Furthermore, graphs can be used for storage of different types of variables that are present in an environment of crops, allowing the application of graph data mining techniques like graph pattern matching. Therefore, in this paper we present an overview of the above issues and a proposal of an expert system for crop disease based on graph pattern matching

A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification