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

Dynamic load balancing for the distributed mining of molecular structures

In molecular biology, it is often desirable to find common properties in large numbers of drug candidates. One family of methods stems from the data mining community, where algorithms to find frequent graphs have received increasing attention over the past years. However, the computational complexity of the underlying problem and the large amount of data to be explored essentially render sequential algorithms useless. In this paper, we present a distributed approach to the frequent subgraph mining problem to discover interesting patterns in molecular compounds. This problem is characterized by a highly irregular search tree, whereby no reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely, a dynamic partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiverinitiated load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer Institute’s HIV-screening data set, where we were able to show close-to linear speedup in a network of workstations. The proposed approach also allows for dynamic resource aggregation in a non dedicated computational environment. These features make it suitable for large-scale, multi-domain, heterogeneous environments, such as computational grids

Graph-based Modelling of Concurrent Sequential Patterns

Structural relation patterns have been introduced recently to extend the search for complex patterns often hidden behind large sequences of data. This has motivated a novel approach to sequential patterns post-processing and a corresponding data mining method was proposed for Concurrent Sequential Patterns (ConSP). This article refines the approach in the context of ConSP modelling, where a companion graph-based model is devised as an extension of previous work. Two new modelling methods are presented here together with a construction algorithm, to complete the transformation of concurrent sequential patterns to a ConSP-Graph representation. Customer orders data is used to demonstrate the effectiveness of ConSP mining while synthetic sample data highlights the strength of the modelling technique, illuminating the theories developed

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

Graph-based task libraries for robots: generalization and autocompletion

In this paper, we consider an autonomous robot that persists over time performing tasks and the problem of providing one additional task to the robot's task library. We present an approach to generalize tasks, represented as parameterized graphs with sequences, conditionals, and looping constructs of sensing and actuation primitives. Our approach performs graph-structure task generalization, while maintaining task ex- ecutability and parameter value distributions. We present an algorithm that, given the initial steps of a new task, proposes an autocompletion based on a recognized past similar task. Our generalization and auto- completion contributions are eective on dierent real robots. We show concrete examples of the robot primitives and task graphs, as well as results, with Baxter. In experiments with multiple tasks, we show a sig- nicant reduction in the number of new task steps to be provided

Detection of Common Subtrees with Identical Label Distribution

Frequent pattern mining is a relevant method to analyse structured data, like sequences, trees or graphs. It consists in identifying characteristic substructures of a dataset. This paper deals with a new type of patterns for tree data: common subtrees with identical label distribution. Their detection is far from obvious since the underlying isomorphism problem is graph isomorphism complete. An elaborated search algorithm is developed and analysed from both theoretical and numerical perspectives. Based on this, the enumeration of patterns is performed through a new lossless compression scheme for trees, called DAG-RW, whose complexity is investigated as well. The method shows very good properties, both in terms of computation times and analysis of real datasets from the literature. Compared to other substructures like topological subtrees and labelled subtrees for which the isomorphism problem is linear, the patterns found provide a more parsimonious representation of the data.Comment: 40 page