Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules

Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association rules are parameterized by a lower bound on their confidence, which is the empirical conditional probability of their consequent given the antecedent, and/or by some other parameter bounds such as "support" or deviation from independence. We study here notions of redundancy among association rules from a fundamental perspective. We see each transaction in a dataset as an interpretation (or model) in the propositional logic sense, and consider existing notions of redundancy, that is, of logical entailment, among association rules, of the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant". We discuss several existing alternative definitions of redundancy between association rules and provide new characterizations and relationships among them. We show that the main alternatives we discuss correspond actually to just two variants, which differ in the treatment of full-confidence implications. For each of these two notions of redundancy, we provide a sound and complete deduction calculus, and we show how to construct complete bases (that is, axiomatizations) of absolutely minimum size in terms of the number of rules. We explore finally an approach to redundancy with respect to several association rules, and fully characterize its simplest case of two partial premises.Comment: LMCS accepted pape

Discovering Implicational Knowledge in Wikidata

Knowledge graphs have recently become the state-of-the-art tool for representing the diverse and complex knowledge of the world. Examples include the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or Microsoft, but also freely available ones such as YAGO, DBpedia, and Wikidata. A distinguishing feature of Wikidata is that the knowledge is collaboratively edited and curated. While this greatly enhances the scope of Wikidata, it also makes it impossible for a single individual to grasp complex connections between properties or understand the global impact of edits in the graph. We apply Formal Concept Analysis to efficiently identify comprehensible implications that are implicitly present in the data. Although the complex structure of data modelling in Wikidata is not amenable to a direct approach, we overcome this limitation by extracting contextual representations of parts of Wikidata in a systematic fashion. We demonstrate the practical feasibility of our approach through several experiments and show that the results may lead to the discovery of interesting implicational knowledge. Besides providing a method for obtaining large real-world data sets for FCA, we sketch potential applications in offering semantic assistance for editing and curating Wikidata

Problem-Solving Knowledge Mining from Users’\ud Actions in an Intelligent Tutoring System

In an intelligent tutoring system (ITS), the domain expert should provide\ud relevant domain knowledge to the tutor so that it will be able to guide the\ud learner during problem solving. However, in several domains, this knowledge is\ud not predetermined and should be captured or learned from expert users as well as\ud intermediate and novice users. Our hypothesis is that, knowledge discovery (KD)\ud techniques can help to build this domain intelligence in ITS. This paper proposes\ud a framework to capture problem-solving knowledge using a promising approach\ud of data and knowledge discovery based on a combination of sequential pattern\ud mining and association rules discovery techniques. The framework has been implemented\ud and is used to discover new meta knowledge and rules in a given domain\ud which then extend domain knowledge and serve as problem space allowing\ud the intelligent tutoring system to guide learners in problem-solving situations.\ud Preliminary experiments have been conducted using the framework as an alternative\ud to a path-planning problem solver in CanadarmTutor