Mining subjectively interesting attributed subgraphs

Community detection in graphs, data clustering, and local pattern mining are three mature fields of data mining and machine learning. In recent years, attributed subgraph mining is emerging as a new powerful data mining task in the intersection of these areas. Given a graph and a set of attributes for each vertex, attributed subgraph mining aims to find cohesive subgraphs for which (a subset of) the attribute values has exceptional values in some sense. While research on this task can borrow from the three abovementioned fields, the principled integration of graph and attribute data poses two challenges: the definition of a pattern language that is intuitive and lends itself to efficient search strategies, and the formalization of the interestingness of such patterns. We propose an integrated solution to both of these challenges. The proposed pattern language improves upon prior work in being both highly flexible and intuitive. We show how an effective and principled algorithm can enumerate patterns of this language. The proposed approach for quantifying interestingness of patterns of this language is rooted in information theory, and is able to account for prior knowledge on the data. Prior work typically quantifies interestingness based on the cohesion of the subgraph and for the exceptionality of its attributes separately, combining these in a parameterized trade-off. Instead, in our proposal this trade-off is implicitly handled in a principled, parameter-free manner. Extensive empirical results confirm the proposed pattern syntax is intuitive, and the interestingness measure aligns well with actual subjective interestingness

DEvIANT: Discovering Significant Exceptional (Dis-)Agreement Within Groups

We strive to find contexts (i.e., subgroups of entities) under which exceptional (dis-)agreement occurs among a group of individuals , in any type of data featuring individuals (e.g., parliamentarians , customers) performing observable actions (e.g., votes, ratings) on entities (e.g., legislative procedures, movies). To this end, we introduce the problem of discovering statistically significant exceptional contextual intra-group agreement patterns. To handle the sparsity inherent to voting and rating data, we use Krippendorff's Alpha measure for assessing the agreement among individuals. We devise a branch-and-bound algorithm , named DEvIANT, to discover such patterns. DEvIANT exploits both closure operators and tight optimistic estimates. We derive analytic approximations for the confidence intervals (CIs) associated with patterns for a computationally efficient significance assessment. We prove that these approximate CIs are nested along specialization of patterns. This allows to incorporate pruning properties in DEvIANT to quickly discard non-significant patterns. Empirical study on several datasets demonstrates the efficiency and the usefulness of DEvIANT. Technical Report Associated with the ECML/PKDD 2019 Paper entitled: "DEvIANT: Discovering Significant Exceptional (Dis-)Agreement Within Groups"

Programação orientada a objectos na determinação das bases dum sistema de fecho

Dissertação de Mestrado em Estatística Matemática e Computação apresentada à Universidade AbertaO objectivo desta dissertação foi a criação de uma ferramenta informática capaz de determinar as bases de um sistema de fecho. Para tal foram criadas diferentes implementações de três algoritmos, o de Tietze, o de Tietze- SA e o SA, utilizando o paradigma da programação orientada a objectos e escolhida como implementação para a construção da ferramenta a que resultava num menor número de chamadas a um oráculo. O oráculo utilizado foi a aplicação Prover9/Mace4 da autoria de William McCune composto pelo demonstrador automático de teoremas Prover9 e o construtor de modelos finitos Mace4. As aplicações resultantes executam nos sistemas operativos Windows XP, Vista e 7 (32 e 64 bits).The aim of this thesis is to provide a software tool capable of determining the basis of a closure system. To this end, we created different implementations of three algorithms, the algorithm Tietze,the algorithm Tietze-SA and the SA algorithm using the paradigm of object-oriented programming, and selected the one that could reach the goal in a minimal number of calls to an oracle. The oracle was Prover9/Mace4 authored by William McCune consisted by the automated deduction tool Prover9 and the finite model builder Mace4. The resulting applications are executable under Windows XP, Vista and 7 (32 and 64 bits), determining the bases with an exponential time complexity

The Efficient Discovery of Interesting Closed Pattern Collections

Enumerating closed sets that are frequent in a given database is a fundamental data mining technique that is used, e.g., in the context of market basket analysis, fraud detection, or Web personalization. There are two complementing reasons for the importance of closed sets---one semantical and one algorithmic: closed sets provide a condensed basis for non-redundant collections of interesting local patterns, and they can be enumerated efficiently. For many databases, however, even the closed set collection can be way too large for further usage and correspondingly its computation time can be infeasibly long. In such cases, it is inevitable to focus on smaller collections of closed sets, and it is essential that these collections retain both: controlled semantics reflecting some notion of interestingness as well as efficient enumerability. This thesis discusses three different approaches to achieve this: constraint-based closed set extraction, pruning by quantifying the degree or strength of closedness, and controlled random generation of closed sets instead of exhaustive enumeration. For the original closed set family, efficient enumerability results from the fact that there is an inducing efficiently computable closure operator and that its fixpoints can be enumerated by an amortized polynomial number of closure computations. Perhaps surprisingly, it turns out that this connection does not generally hold for other constraint combinations, as the restricted domains induced by additional constraints can cause two things to happen: the fixpoints of the closure operator cannot be enumerated efficiently or an inducing closure operator does not even exist. This thesis gives, for the first time, a formal axiomatic characterization of constraint classes that allow to efficiently enumerate fixpoints of arbitrary closure operators as well as of constraint classes that guarantee the existence of a closure operator inducing the closed sets. As a complementary approach, the thesis generalizes the notion of closedness by quantifying its strength, i.e., the difference in supporting database records between a closed set and all its supersets. This gives rise to a measure of interestingness that is able to select long and thus particularly informative closed sets that are robust against noise and dynamic changes. Moreover, this measure is algorithmically sound because all closed sets with a minimum strength again form a closure system that can be enumerated efficiently and that directly ties into the results on constraint-based closed sets. In fact both approaches can easily be combined. In some applications, however, the resulting set of constrained closed sets is still intractably large or it is too difficult to find meaningful hard constraints at all (including values for their parameters). Therefore, the last part of this thesis presents an alternative algorithmic paradigm to the extraction of closed sets: instead of exhaustively listing a potentially exponential number of sets, randomly generate exactly the desired amount of them. By using the Markov chain Monte Carlo method, this generation can be performed according to any desired probability distribution that favors interesting patterns. This novel randomized approach complements traditional enumeration techniques (including those mentioned above): On the one hand, it is only applicable in scenarios that do not require deterministic guarantees for the output such as exploratory data analysis or global model construction. On the other hand, random closed set generation provides complete control over the number as well as the distribution of the produced sets.Das Aufzählen abgeschlossener Mengen (closed sets), die häufig in einer gegebenen Datenbank vorkommen, ist eine algorithmische Grundaufgabe im Data Mining, die z.B. in Warenkorbanalyse, Betrugserkennung oder Web-Personalisierung auftritt. Die Wichtigkeit abgeschlossener Mengen ist semantisch als auch algorithmisch begründet: Sie bilden eine nicht-redundante Basis zur Erzeugung von lokalen Mustern und können gleichzeitig effizient aufgezählt werden. Allerdings kann die Anzahl aller abgeschlossenen Mengen, und damit ihre Auflistungszeit, das Maß des effektiv handhabbaren oft deutlich übersteigen. In diesem Fall ist es unvermeidlich, kleinere Ausgabefamilien zu betrachten, und es ist essenziell, dass dabei beide o.g. Eigenschaften erhalten bleiben: eine kontrollierte Semantik im Sinne eines passenden Interessantheitsbegriffes sowie effiziente Aufzählbarkeit. Diese Arbeit stellt dazu drei Ansätze vor: das Einführen zusätzlicher Constraints, die Quantifizierung der Abgeschlossenheit und die kontrollierte zufällige Erzeugung einzelner Mengen anstelle von vollständiger Aufzählung. Die effiziente Aufzählbarkeit der ursprünglichen Familie abgeschlossener Mengen rührt daher, dass sie durch einen effizient berechenbaren Abschlussoperator erzeugt wird und dass desweiteren dessen Fixpunkte durch eine amortisiert polynomiell beschränkte Anzahl von Abschlussberechnungen aufgezählt werden können. Wie sich herausstellt ist dieser Zusammenhang im Allgemeinen nicht mehr gegeben, wenn die Funktionsdomäne durch Constraints einschränkt wird, d.h., dass die effiziente Aufzählung der Fixpunkte nicht mehr möglich ist oder ein erzeugender Abschlussoperator unter Umständen gar nicht existiert. Diese Arbeit gibt erstmalig eine axiomatische Charakterisierung von Constraint-Klassen, die die effiziente Fixpunktaufzählung von beliebigen Abschlussoperatoren erlauben, sowie von Constraint-Klassen, die die Existenz eines erzeugenden Abschlussoperators garantieren. Als ergänzenden Ansatz stellt die Dissertation eine Generalisierung bzw. Quantifizierung des Abgeschlossenheitsbegriffs vor, der auf der Differenz zwischen den Datenbankvorkommen einer Menge zu den Vorkommen all seiner Obermengen basiert. Mengen, die bezüglich dieses Begriffes stark abgeschlossen sind, weisen eine bestimmte Robustheit gegen Veränderungen der Eingabedaten auf. Desweiteren wird die gewünschte effiziente Aufzählbarkeit wiederum durch die Existenz eines effizient berechenbaren erzeugenden Abschlussoperators sichergestellt. Zusätzlich zu dieser algorithmischen Parallele zum Constraint-basierten Vorgehen, können beide Ansätze auch inhaltlich kombiniert werden. In manchen Anwendungen ist die Familie der abgeschlossenen Mengen, zu denen die beiden oben genannten Ansätze führen, allerdings immer noch zu groß bzw. ist es nicht möglich, sinnvolle harte Constraints und zugehörige Parameterwerte zu finden. Daher diskutiert diese Arbeit schließlich noch ein völlig anderes Paradigma zur Erzeugung abgeschlossener Mengen als vollständige Auflistung, nämlich die randomisierte Generierung einer Anzahl von Mengen, die exakt den gewünschten Vorgaben entspricht. Durch den Einsatz der Markov-Ketten-Monte-Carlo-Methode ist es möglich die Verteilung dieser Zufallserzeugung so zu steuern, dass das Ziehen interessanter Mengen begünstigt wird. Dieser neue Ansatz bildet eine sinnvolle Ergänzung zu herkömmlichen Techniken (einschließlich der oben genannten): Er ist zwar nur anwendbar, wenn keine deterministischen Garantien erforderlich sind, erlaubt aber andererseits eine vollständige Kontrolle über Anzahl und Verteilung der produzierten Mengen