Efficient Discovery of Interesting Patterns Based on Strong Closedness

Abstract

Finding patterns that are interesting to a user in a certain application context is one of the central goals of Data Mining research. Regarding all patterns above a certain frequency threshold as interesting is one way of defining interestingness. In this paper, however, we argue that in many applications, a different notion of interestingness is required in order to be able to capture "long", and thus particularly informative, patterns that are correspondingly of low frequency. To identify such patterns, our proposed measure of interestingness is based on the degree or strength of closedness of the patterns. We show that (a) indeed this definition selects long interesting patterns that are difficult to identify with frequency-based approaches, and (b) that it selects patterns that are robust against noise and/or dynamic changes. We prove that the family of interesting patterns proposed here forms a closure system and use the corresponding closure operator to design a mining algorithm listing these patterns in amortized quadratic time. In particular, for non-sparse datasets its time complexity is O(nm) per pattern, where n denotes the number of items and m the size of the database. This is equal to the best known time bound for listing ordinary closed frequent sets, which is a special case of our problem. We also report empirical results with realworld datasets.

A novel meta-analytic approach: Mining frequent co-activation patterns in neuroimaging databases

“…In data-mining, closedness is a measure of the interestingness of patterns, which is defined as the difference between the support of a pattern and the support of its most supported direct super-pattern (Boley et al, 2009). Hence, closedness indicates the number of experiments that activate a specific pattern, but do not show any further activated brain regions.…”

△-Closure Structure for Studying Data Distribution

“…If ∆ = 1, then the itemset is just closed w.r.t. object counting [2], [11]. In [2] it was also shown that Δ-closedness is associated with a closure operator that we call Δ-closure and that works as follows.…”

“…Following the research directions discussed in [2] and [10], we are interested in discovering closed and stable patterns together with their related equivalence classes and minimum generators (passkeys). As in [2], we introduce a ∆ parameter for studying ∆-closure and the robustness of the discovered patterns against noise, and as well the stability of the associated equivalence classes and their characteristic elements such as passkeys. Moreover, as in [10] are also interested in investigating the data distribution through the closure structure.…”

“…For dealing with large amounts of closed itemsets, it is possible to evaluate itemsets thanks to quality metrics [9], [17]. For example ∆-closedness evaluates the robustness of patterns and the corresponding closure operation [2]. Roughly speaking, a ∆-closed set cannot be augmented by any further item without decreasing its support by at least ∆.…”