Björn Bringmann

Mining graph evolution rules

In this paper we introduce graph-evolution rules , a novel type of frequency-based pattern that describe the evolution of large networks over time, at a local level. Given a sequence of snapshots of an evolving graph, we aim at discovering rules describing the local changes occurring in it. Adopting a definition of support based on minimum image we study the problem of extracting patterns whose frequency is larger than a minimum support threshold. Then, similar to the classical association rules framework, we derive graph-evolution rules from frequent patterns that satisfy a given minimum confidence constraint. We discuss merits and limits of alternative definitions of support and confidence, justifying the chosen framework. To evaluate our approach we devise GERM (Graph Evolution Rule Miner), an algorithm to mine all graph-evolution rules whose support and confidence are greater than given thresholds. The algorithm is applied to analyze four large real-world networks (i.e., two social networks, and two co-authorship networks from bibliographic data), using different time granularities. Our extensive experimentation confirms the feasibility and utility of the presented approach. It further shows that different kinds of networks exhibit different evolution rules, suggesting the usage of these local patterns to globally discriminate different kind of networks.

The Chosen Few: On Identifying Valuable Patterns

Constrained pattern mining extracts patterns based on their individual merit. Usually this results in far more patterns than a human expert or a machine learning technique could make use of. Often different patterns or combinations of patterns cover a similar subset of the examples, thus being redundant and not carrying any new information. To remove the redundant information contained in such pattern sets, we propose a general heuristic approach for selecting a small subset of patterns. We identify several selection techniques for use in this general algorithm and evaluate those on several data sets. The results show that the technique succeeds in severely reducing the number of patterns, while at the same time apparently retaining much of the original information. Additionally the experiments show that reducing the pattern set indeed improves the quality of classification results. Both results show that the approach is very well suited for the goals we aim at.

Don't be afraid of simpler patterns

This paper investigates the trade-off between the expressiveness of the pattern language and the performance of the pattern miner in structured data mining. This trade-off is investigated in the context of correlated pattern mining, which is concerned with finding the k-best patterns according to a convex criterion, for the pattern languages of itemsets, multi-itemsets, sequences, trees and graphs. The criteria used in our investigation are the typical ones in data mining: computational cost and predictive accuracy and the domain is that of mining molecular graph databases. More specifically, we provide empirical answers to the following questions: how does the expressive power of the language affect the computational cost? and what is the trade-off between expressiveness of the pattern language and the predictive accuracy of the learned model? While answering the first question, we also introduce a novel stepwise approach to correlated pattern mining in which the results of mining a simpler pattern language are employed as a starting point for mining in a more complex one. This stepwise approach typically leads to significant speed-ups (up to a factor 1000) for mining graphs.

Tree 2 : decision trees for tree structured data

We present Tree2, a new approach to structural classification. This integrated approach induces decision trees that test for pattern occurrence in the inner nodes. It combines state-of-the-art tree mining with sophisticated pruning techniques to find the most discriminative pattern in each node. In contrast to existing methods, Tree2 uses no heuristics and only a single, statistically well founded parameter has to be chosen by the user. The experiments show that Tree2 classifiers achieve good accuracies while the induced models are smaller than those of existing approaches, facilitating better comprehensibility.

One in a million: picking the right patterns

Constrained pattern mining extracts patterns based on their individual merit. Usually this results in far more patterns than a human expert or a machine leaning technique could make use of. Often different patterns or combinations of patterns cover a similar subset of the examples, thus being redundant and not carrying any new information. To remove the redundant information contained in such pattern sets, we propose two general heuristic algorithms—Bouncer and Picker—for selecting a small subset of patterns. We identify several selection techniques for use in this general algorithm and evaluate those on several data sets. The results show that both techniques succeed in severely reducing the number of patterns, while at the same time apparently retaining much of the original information. Additionally, the experiments show that reducing the pattern set indeed improves the quality of classification results. Both results show that the developed solutions are very well suited for the goals we aim at.

Frequent Hypergraph Mining

The class of frequent hypergraph mining problems is introduced which includes the frequent graph mining problem class and contains also the frequent itemset mining problem. We study the computational properties of different problems belonging to this class. In particular, besides negative results, we present practically relevant problems that can be solved in incremental-polynomial time. Some of our practical algorithms are obtained by reductions to frequent graph mining and itemset mining problems. Our experimental results in the domain of citation analysis show the potential of the framework on problems that have no natural representation as an ordinary graph.

CTC - correlating tree patterns for classification

We present CTC, a new approach to structural classification. It uses the predictive power of tree patterns correlating with the class values, combining state-of-the-art tree mining with sophisticated pruning techniques to find the k most discriminative pattern in a dataset. In contrast to existing methods, CTC uses no heuristics and the only parameters to be chosen by the user are the maximum size of the rule set and a single, statistically well founded cut-off value. The experiments show that CTC classifiers achieve good accuracies while the induced models are smaller than those of existing approaches, facilitating comprehensibility.

Matching in frequent tree discovery

Various definitions and frameworks for discovering frequent trees in forests have been developed. At the heart of these frameworks lies the notion of matching, which determines when a pattern tree matches a tree in a data set. We introduce a notion of tree matching for use in frequent tree mining and we show that it generalizes the framework of Zaki while still being more specific than that of Termier et al. Furthermore, we show how Zakis TreeMinerV algorithm can be adapted towards our notion of tree matching. Experiments show the promise of the approach.

Fast, effective molecular feature mining by local optimization

In structure-activity-relationships (SAR) one aims at finding classifiers that predict the biological or chemical activity of a compound from its molecular graph. Many approaches to SAR use sets of binary substructure features, which test for the occurrence of certain substructures in the molecular graph. As an alternative to enumerating very large sets of frequent patterns, numerous pattern set mining and pattern set selection techniques have been proposed. Existing approaches can be broadly classified into those that focus on minimizing correspondences, that is, the number of pairs of training instances from different classes with identical encodings and those that focus on maximizing the number of equivalence classes, that is, unique encodings in the training data. In this paper we evaluate a number of techniques to investigate which criterion is a better indicator of predictive accuracy. We find that minimizing correspondences is a necessary but not sufficient condition for good predictive accuracy, that equivalence classes are a better indicator of success and that it is important to have a good match between training set and pattern set size. Based on these results we propose a new, improved algorithm which performs local minimization of correspondences, yet evaluates the effect of patterns on equivalence classes globally. Empirical experiments demonstrate its efficacy and its superior run time behavior.

From local patterns to classification models

Using pattern mining techniques for building a predictive model is currently a popular topic of research. The aim of these techniques is to obtain classifiers of better predictive performance as compared to greedily constructed models, as well as to allow the construction of predictive models for data not represented in attribute-value vectors. In this chapter we provide an overview of recent techniques we developed for integrating pattern mining and classification tasks. The range of techniques spans the entire range from approaches that select relevant patterns from a previously mined set for propositionalization of the data, over inducing patternbased rule sets, to algorithms that integrate pattern mining and model construction. We provide an overview of the algorithms which are most closely related to our approaches in order to put our techniques in a context.