Statistical strategies for pruning all the uninteresting association rules

We propose a general framework to describe formally the problem of capturing the intensity of implication for association rules through statistical metrics. In this framework we present properties that influence the interestingness of a rule, analyze the conditions that lead a measure to perform a perfect prune at a time, and define a final proper order to sort the surviving rules. We will discuss why none of the currently employed measures can capture objective interestingness, and just the combination of some of them, in a multi-step fashion, can be reliable. In contrast, we propose a new simple modification of the Pearson coefficient that will meet all the necessary requirements. We statistically infer the convenient cut-off threshold for this new metric by empirically describing its distribution function through simulation. Final experiments serve to show the ability of our proposal.Postprint (published version

Towards improving solution dominance with incomparability conditions : a case-study using Generator Itemset Mining

Funding: EPSRC (EP/P015638/1).Finding interesting patterns is a challenging task in data mining. Constraint based mining is a well-known approach to this, and one for which constraint programming has been shown to be a well-suited and generic framework. Dominance programming has been proposed as an extension that can capture an even wider class of constraint-based mining problems, by allowing to compare relations between patterns. In this paper, in addition to specifying a dominance relation, we introduce the ability to specify an incomparability condition. Using these two concepts we devise a generic framework that can do a batch-wise search that avoids checking incomparable solutions. We extend the ESSENCE language and underlying modelling pipeline to support this. We use generator itemset mining problem as a test case and give a declarative specification for that. We also present preliminary experimental results on this specific problem class with a CP solver backend to show that using the incomparability condition during search can improve the efficiency of dominance programming and reduces the need for post-processing to filter dominated solutions.Publisher PD

In-Network Outlier Detection in Wireless Sensor Networks

To address the problem of unsupervised outlier detection in wireless sensor networks, we develop an approach that (1) is flexible with respect to the outlier definition, (2) computes the result in-network to reduce both bandwidth and energy usage,(3) only uses single hop communication thus permitting very simple node failure detection and message reliability assurance mechanisms (e.g., carrier-sense), and (4) seamlessly accommodates dynamic updates to data. We examine performance using simulation with real sensor data streams. Our results demonstrate that our approach is accurate and imposes a reasonable communication load and level of power consumption.Comment: Extended version of a paper appearing in the Int'l Conference on Distributed Computing Systems 200

High-level efficient constraint dominance programming for pattern mining problems

Pattern mining is a sub-field of data mining that focuses on discovering patterns in data to extract knowledge. There are various techniques to identify different types of patterns in a dataset. Constraint-based mining is a well-known approach to this where additional constraints are introduced to retrieve only interesting patterns. However, in these systems, there are limitations on imposing complex constraints. Constraint programming is a declarative methodology where the problem is modelled using constraints. Generic solvers can operate on a model to find the solutions. Constraint programming has been shown to be a well-suited and generic framework for various pattern mining problems with a selection of constraints and their combinations. However, a system that handles arbitrary constraints in a generic way has been missing in this field. In this thesis, we propose a declarative framework where the pattern mining models can be represented in high-level constraint specifications with arbitrary additional constraints. These models can be efficiently solved using underlying optimisations. The first contribution of this thesis is to determine the key aspects of solving pattern mining problems by creating an ad-hoc solver system. We investigate this further and create Constraint Dominance Programming (CDP) to be able to capture certain behaviours of pattern mining problems in an abstract way. To that end, we integrate CDP into the high-level \essence pipeline. Early empirical evaluation presents that CDP is already competitive with current existing techniques. The second contribution of this thesis is to exploit an additional behaviour, the incomparability, in pattern mining problems. By including the incomparability condition to CDP, we create CDP+I, a more explicit and even more efficient framework to represent these problems. We also prototype an automated system to deduct the optimal incomparability information for a given modelled problem. The third contribution of this thesis is to focus on the underlying solving of CDP+I to bring further efficiency. By creating the Solver Interactive Interface (SII) on SAT and SMT back-ends, we highly optimise not only CDP+I but any iterative modelling and solving, such as optimisation problems. The final contribution of this thesis is to investigate creating an automated configuration selection system to determine the best performing solving methodologies of CDP+I and introduce a portfolio of configurations that can perform better than any single best solver. In summary, this thesis presents a highly efficient, high-level declarative framework to tackle pattern mining problems

A COLLABORATIVE FILTERING APPROACH TO PREDICT WEB PAGES OF INTEREST FROMNAVIGATION PATTERNS OF PAST USERS WITHIN AN ACADEMIC WEBSITE

This dissertation is a simulation study of factors and techniques involved in designing hyperlink recommender systems that recommend to users, web pages that past users with similar navigation behaviors found interesting. The methodology involves identification of pertinent factors or techniques, and for each one, addresses the following questions: (a) room for improvement; (b) better approach, if any; and (c) performance characteristics of the technique in environments that hyperlink recommender systems operate in. The following four problems are addressed:Web Page Classification. A new metric (PageRank × Inverse Links-to-Word count ratio) is proposed for classifying web pages as content or navigation, to help in the discovery of user navigation behaviors from web user access logs. Results of a small user study suggest that this metric leads to desirable results.Data Mining. A new apriori algorithm for mining association rules from large databases is proposed. The new algorithm addresses the problem of scaling of the classical apriori algorithm by eliminating an expensive joinstep, and applying the apriori property to every row of the database. In this study, association rules show the correlation relationships between user navigation behaviors and web pages they find interesting. The new algorithm has better space complexity than the classical one, and better time efficiency under some conditionsand comparable time efficiency under other conditions.Prediction Models for User Interests. We demonstrate that association rules that show the correlation relationships between user navigation patterns and web pages they find interesting can be transformed intocollaborative filtering data. We investigate collaborative filtering prediction models based on two approaches for computing prediction scores: using simple averages and weighted averages. Our findings suggest that theweighted averages scheme more accurately computes predictions of user interests than the simple averages scheme does.Clustering. Clustering techniques are frequently applied in the design of personalization systems. We studied the performance of the CLARANS clustering algorithm in high dimensional space in relation to the PAM and CLARA clustering algorithms. While CLARA had the best time performance, CLARANS resulted in clusterswith the lowest intra-cluster dissimilarities, and so was most effective in this regard

Proceedings of the 2022 XCSP3 Competition

This document represents the proceedings of the 2022 XCSP3 Competition. The results of this competition of constraint solvers were presented at FLOC (Federated Logic Conference) 2022 Olympic Games, held in Haifa, Israel from 31th July 2022 to 7th August, 2022.Comment: arXiv admin note: text overlap with arXiv:1901.0183

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc

Generalised Interaction Mining: Probabilistic, Statistical and Vectorised Methods in High Dimensional or Uncertain Databases

Knowledge Discovery in Databases (KDD) is the non-trivial process of identifying valid, novel, useful and ultimately understandable patterns in data. The core step of the KDD process is the application of Data Mining (DM) algorithms to efficiently find interesting patterns in large databases. This thesis concerns itself with three inter-related themes: Generalised interaction and rule mining; the incorporation of statistics into novel data mining approaches; and probabilistic frequent pattern mining in uncertain databases. An interaction describes an effect that variables have -- or appear to have -- on each other. Interaction mining is the process of mining structures on variables describing their interaction patterns -- usually represented as sets, graphs or rules. Interactions may be complex, represent both positive and negative relationships, and the presence of interactions can influence another interaction or variable in interesting ways. Finding interactions is useful in domains ranging from social network analysis, marketing, the sciences, e-commerce, to statistics and finance. Many data mining tasks may be considered as mining interactions, such as clustering; frequent itemset mining; association rule mining; classification rules; graph mining; flock mining; etc. Interaction mining problems can have very different semantics, pattern definitions, interestingness measures and data types. Solving a wide range of interaction mining problems at the abstract level, and doing so efficiently -- ideally more efficiently than with specialised approaches, is a challenging problem. This thesis introduces and solves the Generalised Interaction Mining (GIM) and Generalised Rule Mining (GRM) problems. GIM and GRM use an efficient and intuitive computational model based purely on vector valued functions. The semantics of the interactions, their interestingness measures and the type of data considered are flexible components of vectorised frameworks. By separating the semantics of a problem from the algorithm used to mine it, the frameworks allow both to vary independently of each other. This makes it easier to develop new methods by focusing purely on a problem's semantics and removing the burden of designing an efficient algorithm. By encoding interactions as vectors in the space (or a sub-space) of samples, they provide an intuitive geometric interpretation that inspires novel methods. By operating in time linear in the number of interesting interactions that need to be examined, the GIM and GRM algorithms are optimal. The use of GRM or GIM provides efficient solutions to a range of problems in this thesis, including graph mining, counting based methods, itemset mining, clique mining, a clustering problem, complex pattern mining, negative pattern mining, solving an optimisation problem, spatial data mining, probabilistic itemset mining, probabilistic association rule mining, feature selection and generation, classification and multiplication rule mining. Data mining is a hypothesis generating endeavour, examining large databases for patterns suggesting novel and useful knowledge to the user. Since the database is a sample, the patterns found should describe hypotheses about the underlying process generating the data. In searching for these patterns, a DM algorithm makes additional hypothesis when it prunes the search space. Natural questions to ask then, are: "Does the algorithm find patterns that are statistically significant?" and "Did the algorithm make significant decisions during its search?". Such questions address the quality of patterns found though data mining and the confidence that a user can have in utilising them. Finally, statistics has a range of useful tools and measures that are applicable in data mining. In this context, this thesis incorporates statistical techniques -- in particular, non-parametric significance tests and correlation -- directly into novel data mining approaches. This idea is applied to statistically significant and relatively class correlated rule based classification of imbalanced data sets; significant frequent itemset mining; mining complex correlation structures between variables for feature selection; mining correlated multiplication rules for interaction mining and feature generation; and conjunctive correlation rules for classification. The application of GIM or GRM to these problems lead to efficient and intuitive solutions. Frequent itemset mining (FIM) is a fundamental problem in data mining. While it is usually assumed that the items occurring in a transaction are known for certain, in many applications the data is inherently noisy or probabilistic; such as adding noise in privacy preserving data mining applications, aggregation or grouping of records leading to estimated purchase probabilities, and databases capturing naturally uncertain phenomena. The consideration of existential uncertainty of item(sets) makes traditional techniques inapplicable. Prior to the work in this thesis, itemsets were mined if their expected support is high. This returns only an estimate, ignores the probability distribution of support, provides no confidence in the results, and can lead to scenarios where itemsets are labeled frequent even if they are more likely to be infrequent. Clearly, this is undesirable. This thesis proposes and solves the Probabilistic Frequent Itemset Mining (PFIM) problem, where itemsets are considered interesting if the probability that they are frequent is high. The problem is solved under the possible worlds model and a proposed probabilistic framework for PFIM. Novel and efficient methods are developed for computing an itemset's exact support probability distribution and frequentness probability, using the Poisson binomial recurrence, generating functions, or a Normal approximation. Incremental methods are proposed to answer queries such as finding the top-k probabilistic frequent itemsets. A number of specialised PFIM algorithms are developed, with each being more efficient than the last: ProApriori is the first solution to PFIM and is based on candidate generation and testing. ProFP-Growth is the first probabilistic FP-Growth type algorithm and uses a proposed probabilistic frequent pattern tree (Pro-FPTree) to avoid candidate generation. Finally, the application of GIM leads to GIM-PFIM; the fastest known algorithm for solving the PFIM problem. It achieves orders of magnitude improvements in space and time usage, and leads to an intuitive subspace and probability-vector based interpretation of PFIM.Knowledge Discovery in Datenbanken (KDD) ist der nicht-triviale Prozess, gültiges, neues, potentiell nützliches und letztendlich verständliches Wissen aus großen Datensätzen zu extrahieren. Der wichtigste Schritt im KDD Prozess ist die Anwendung effizienter Data Mining (DM) Algorithmen um interessante Muster ("Patterns") in Datensätzen zu finden. Diese Dissertation beschäftigt sich mit drei verwandten Themen: Generalised Interaction und Rule Mining, die Einbindung von statistischen Methoden in neue DM Algorithmen und Probabilistic Frequent Itemset Mining (PFIM) in unsicheren Daten. Eine Interaktion ("Interaction") beschreibt den Einfluss, den Variablen aufeinander haben. Interaktionsmining ist der Prozess, Strukturen zwischen Variablen zu finden, die Interaktionsmuster beschreiben. Diese werden gewöhnlicherweise als Mengen, Graphen oder Regeln repräsentiert. Interaktionen können komplex sein und sowohl positive als auch negative Beziehungen repräsentieren. Außerdem kann das Vorhandensein von Interaktionen andere Interaktionen oder Variablen beeinflussen. Interaktionen stellen in Bereichen wie Soziale Netzwerk Analyse, Marketing, Wissenschaft, E-commerce, Statistik und Finanz wertvolle Information dar. Viele DM Methoden können als Interaktionsmining betrachtet werden: Zum Beispiel Clustering, Frequent Itemset Mining, Assoziationsregeln, Klassifikationsregeln, Graph Mining, Flock Mining, usw. Interaktionsmining-Probleme können sehr unterschiedliche Semantik, Musterdefinitionen, Interessantheitsmaße und Datentypen erfordern. Interaktionsmining-Probleme auf breiter und abstrakter Basis effizient -- und im Idealfall effizienter als mit spezialisierten Methoden -- zu lösen, ist ein herausforderndes Problem. Diese Dissertation führt das Generalised Interaction Mining (GIM) und das Generalised Rule Mining (GRM) Problem ein und beschreibt Lösungen für diese. GIM und GRM benutzen ein effizientes und intuitives Berechnungsmodell, das einzig und allein auf vektorbasierten Funktionen beruht. Die Semantik der Interaktionen, ihre Interessantheitsmaße und die Datenarten, sind Komponenten in vektorisierten Frameworks. Die Frameworks ermöglichen die Trennung der Problemsemantik vom Algorithmus, so dass beide unabhängig voneinander geändert werden können. Die Entwicklung neuer Methoden wird dadurch erleichtert, da man sich völlig auf die Problemsemantik fokussieren kann und sich nicht mit der Entwicklung problemspezifischer Algorithmen befassen muss. Die Kodierung der Interaktionen als Vektoren im gesamten Raum (oder Teilraum) der Stichproben stellt eine intuitive geometrische Interpretation dar, die neuartige Methoden inspiriert. Die GRM- und GIM- Algorithmen haben lineare Laufzeit in der Anzahl der Interaktionen die geprüft werden müssen und sind somit optimal. Die Anwendung von GRM oder GIM in dieser Dissertation ermöglicht effiziente Lösungen für eine Reihe von Problemen, wie zum Beispiel Graph Mining, Aufzählungsmethoden, Itemset Mining, Clique Mining, ein Clusteringproblem, das Finden von komplexen und negativen Mustern, die Lösung von Optimierungsproblemen, Spatial Data Mining, probabilistisches Itemset Mining, probabilistisches Mining von Assoziationsregel, Selektion und Erzeugung von Features, Mining von Klassifikations- und Multiplikationsregel, u.v.m. Data Mining ist ein Verfahren, das Hypothesen produziert, indem es in großen Datensätzen Muster findet und damit für den Anwender neues und nützliches Wissen vorschlägt. Da die untersuchte Datenbank ein Resultat des datenerzeugenden Prozesses ist, sollten die gefundenen Muster Erkenntnisse über diesen Prozess liefern. Bei der Suche nach diesen Mustern macht ein DM Algorithmus zusätzliche Hypothesen, wenn Teile des Suchraums ausgeschlossen werden. Die folgenden Fragen sind dabei wichtig: "Findet der Algorithmus statistisch signifikante Muster?" und "Hat der Algorithmus während des Suchprozesses signifikante Entscheidungen getroffen?". Diese Fragen beeinflussen die Qualität der Muster und die Sicherheit die der Anwender in ihrer Benutzung haben kann. Da die Statistik auch eine Reihe von nützlichen Methoden bereitstellt, die für DM anwendbar sind, kombiniert diese Dissertation einige statistische Methoden mit neuen DM Algorithmen, insbesondere nicht-parametrische Signifikanztests und Korrelation. Diese Idee wird für die folgenden Probleme angewandt: Signifikante und "relatively class correlated" regelbasierte Klassifikation in unsymmetrischen Datensätzen, signifikantes Frequent Itemset Mining, Mining von komplizierten Korrelationsstrukturen zwischen Variablen zum Zweck der Featureselektion, Mining von korrelierten Multiplikationsregeln zum Zwecke des Interaktionsminings und Featureerzeugung und konjunktive Korrelationsregeln für die Klassifikation. Die Anwendung von GIM und GRM auf diese Probleme führt zu effizienten und intuitiven Lösungen. Frequent Itemset Mining (FIM) ist ein fundamentales Problem im Data Mining. Obwohl allgemein die Annahme gilt, dass in einer Transaktion enthaltene Items bekannt sind, sind die Daten in vielen Anwendungen unsicher oder probabilistisch. Beispiele sind das Hinzufügen von Rauschen zu Datenschutzzwecken, die Gruppierung von Datensätzen die zu geschätzten Kaufwahrscheinlichkeiten führen und Datensätze deren Herkunft von Natur aus unsicher sind. Die Berücksichtigung von unsicheren Datensätzen verhindert die Anwendung von traditionellen Methoden. Vor der Arbeit in dieser Dissertation wurden Itemsets gesucht, deren erwartetes Vorkommen hoch ist. Diese Methode produziert jedoch nur Schätzwerte, vernachlässigt die Wahrscheinlichkeitsverteilung der Vorkommen, bietet keine Sicherheit für die Genauigkeit der Ergebnisse und kann zu Szenarien führen in denen das Vorkommen als häufig eingestuft wird, obwohl die Wahrscheinlichkeit höher ist, dass sie nur selten vorkommen. Solche Ergebnisse sind natürlich unerwünscht. Diese Dissertation führt das Probabilistic Frequent Itemset Mining (PFIM) ein. Diese Lösung betrachtet Itemsets als interessant, wenn die Wahrscheinlichkeit groß ist, dass sie häufig vorkommen. Die Problemlösung besteht aus der Anwendung des Possible Worlds Models und dem vorgeschlagenen probabilistisches Framework für PFIM. Es werden neue und effiziente Methoden entwickelt um die Wahrscheinlichkeitsverteilung des Vorkommens und die Häufigkeitsverteilung eines Itemsets zu berechnen. Dazu werden die Poisson Binomial Recurrence, Generating Functions, oder eine normalverteilte Annäherung verwendet. Inkrementelle Methoden werden vorgeschlagen um Fragen wie "Finde die top-k Probabilistic Frequent Itemsets" zu beantworten. Mehrere PFIM Algorithmen werden entwickelt, wobei die Effizienz von Algorithmus zu Algorithmus steigt: ProApriori ist die erste Lösung für PFIM und basiert auf erzeugen und testen von Kandidaten. ProFP-Growth ist der erste probabilistische FP-Growth Algorithmus. Er schlägt einen Probabilistic Frequent Pattern Tree (Pro-FPTree) vor, der Kandidatenerzeugung überflüssig macht. Die Anwendung von GIM führt schließlich zu GIM-PFIM, dem schnellsten bekannten Algorithmus zur Lösung des PFIM Problems. Dieser Algorithmus resultiert in einem um Größenordnungen besseren Zeit- und Speicherbedarf, und führt zu einer intuitiven Interpretation von PFIM, basierend auf Unterräumen und Wahrscheinlichkeitsvektoren