This paper further develops Aumann and Lindell's [3] proposal for a variant of association rules for which the consequent is a numeric variable. It is argued that these rules can discover useful interactions with numeric data that cannot be discovered directly using traditional association rules with discretization. Alternative measures for identifying interesting rules are proposed. Efficient algorithms are presented that enable these rules to be discovered for dense data sets for which application of Auman and Lindell's algorithm is infeasible.

Pattern discovery techniques, such as association rule discovery, explore large search spaces of potential patterns to find those that satisfy some user-specified constraints. Due to the large number of patterns considered, they suffer from an extreme risk of type-1 error, that is, of finding patterns that appear due to chance alone to satisfy the constraints on the sample data. This paper proposes techniques to overcome this problem by applying well-established statistical practices. These allow the user to enforce a strict upper limit on the risk of experimentwise error. Empirical studies demonstrate that standard pattern discovery techniques can discover numerous spurious patterns when applied to random data and when applied to real-world data result in large numbers of patterns that are rejected when subjected to sound statistical evaluation. They also reveal that a number of pragmatic choices about how such tests are performed can greatly affect their power.

Data mining algorithms produce huge sets of rules, practically impossible to analyze manually. It is thus important to develop methods for removing redundant rules from those sets. We present a solution to the problem using the Maximum Entropy approach. The problem of eciency of Maximum Entropy computations is addressed by using closed form solutions for the most frequent cases. Analytical and experimental evaluation of the proposed technique indicates that it eciently produces small sets of interesting association rules.

1 Introduction In recent years, there have been growing interests in multi-dimensional analysis of relational databases, transactional

This paper gives a survey of contrast set mining (CSM), emerging pattern mining (EPM), and subgroup discovery (SD) in a unifying framework named supervised descriptive rule discovery. While all these research areas aim at discovering patterns in the form of rules induced from labeled data, they use different terminology and task definitions, claim to have different goals, claim to use different rule learning heuristics, and use different means for selecting subsets of induced patterns. This paper contributes a novel understanding of these subareas of data mining by presenting a unified terminology, by explaining the apparent differences between the learning tasks as variants of a unique supervised descriptive rule discovery task and by exploring the apparent differences between the approaches. It also shows that various rule learning heuristics used in CSM, EPM and SD algorithms all aim at optimizing a trade off between rule coverage and precision. The commonalities (and differences) between the approaches are showcased on a selection of best known variants of CSM, EPM and SD algorithms. The paper also provides a critical survey of existing supervised descriptive rule discovery visualization methods.

Existing research on mining quantitative databases mainly focuses on mining associations. However, mining associations is too expensive to be practical in many cases. In this paper, we study mining correlations from quantitative databases and show that it is a more effective approach than mining associations. We propose a new notion of Quantitative Correlated Patterns (QCPs), which is founded on two formal concepts, mutual information and all-confidence. We first devise a normalization on mutual information and apply it to QCP mining to capture the dependency between the attributes. We further adopt all-confidence as a quality measure to control, at a finer granularity, the dependency between the attributes with specific quantitative intervals. We also propose a supervised method to combine the consecutive intervals of the quantitative attributes based on mutual information, such that the interval combining is guided by the dependency between the attributes. We develop an algorithm, QCoMine, to efficiently mine QCPs by utilizing normalized mutual information and all-confidence to perform a two-level pruning. Our experiments verify the efficiency of QCoMine and the quality of the QCPs.

We study the mining of interesting patterns in the presence of numerical attributes. Instead of the usual discretization methods, we propose the use of rank based measures to score the similarity of sets of numerical attributes. New support measures for numerical data are introduced, based on extensions of Kendall’s tau, and Spearman’s Footrule and rho. We show how these support measures are related. Furthermore, we introduce a novel type of pattern combining numerical and categorical attributes. We give efficient algorithms to find all frequent patterns for the proposed support measures, and evaluate their performance on real-life datasets.

Association rules are traditionally designed to capture statistical relationship among itemsets in a given database. To additionally capture the quantitative association knowledge, F.Korn et al recently proposed a paradigm named Ratio Rules [4] for quantifiable data mining. However, their approach is mainly based on Principle Component Analysis (PCA) and as a result, it cannot guarantee that the ratio coefficient is non-negative. This may lead to serious problems in the rules’ application. In this paper, we propose a new method, called Principal Sparse Non-Negative Matrix Factoriza-tion (PSNMF), for learning the associations between itemsets in the form of Ratio Rules. In addition, we provide a support measurement to weigh the importance of each rule for the entire dataset. 1.

This paper proposes a novel framework for mining regional colocation patterns with respect to sets of continuous variables in spatial datasets. The goal is to identify regions in which multiple continuous variables with values from the wings of their statistical distribution are co-located. A co-location mining framework is introduced that operates in the continuous domain without the need for discretization and which views regional co-location mining as a clustering problem in which an externally given fitness function has to be maximized. Interestingness of colocation patterns is assessed using products of z-scores of the relevant continuous variables. The proposed framework is evaluated by a domain expert in a case study that analyzes chemical concentrations in Texas water wells centering on colocation patterns involving Arsenic. Our approach was able to identify known and unknown regional co-location patterns, and different sets of algorithm parameters lead to the characterization of arsenic distribution at different scales. Moreover, inconsistent co-location sets were found for regions in South Texas and West Texas that can be clearly attributed to geological differences in the two regions, emphasizing the need for regional co-location mining techniques. Moreover, a novel, prototype-based region discovery algorithm named CLEVER is introduced that uses randomized hill climbing, and searches a variable number of clusters and larger neighborhood sizes. Keywords spatial data mining, regional co-location mining, regional data mining, clustering, finding associations between continuous variables. 1.

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