Approximation of Frequency Queries by Means of Free-Sets

Abstract

Abstract.Given a large collection of transactions containing items, a basic common data mining problem is to extract the so-called frequent itemsets (i.e., set of items appearing in at least a given number of transactions). In this paper, we propose a structure called free-sets, from which we can approximate any itemset support (i.e., the number of transactions containing the itemset) and we formalize this notion in the framework of -adequate representation [10].We show that frequent free-sets can be efficiently extracted using pruning strategies developed for frequent itemset discovery, and that they can be used to approximate the support of any frequent itemset. Experiments run on real dense data sets show a significant reduction of the size of the output when compared with standard frequent itemsets extraction. Furthermore, the experiments show that the extraction of frequent free-sets is still possible when the extraction of frequent itemsets becomes intractable. Finally, we show that the error made when approximating frequent itemset support remains very low in practice.

Efficient Mining of Association Rules Based on Formal Concept Analysis

“…One of them are δ-free sets [11], where an itemset is called δ-free if there are 'almost no dependencies' between its attributes. 3 They lead to almost closures [10], where an attribute m is in the almost-closure of an itemset X iff the supports of X and X ∪ {m} differ not more than a given threshold.…”

Feature Construction Based on Closedness Properties Is Not That Simple

“…In this paper, we consider closure equivalence classes, i.e., frequent closed sets and their generators [11]. Furthermore, when considering the δ-free itemsets with δ > 0 [12,13], we can consider a "near equivalence" perspective and thus, roughly speaking, the concept of almost-closed itemsets. We want to contribute to difficult classification tasks by using a method based on: (1) the efficient extraction of set patterns that satisfy given constraints, (2) the encoding of the original data into a new data set by using extracted patterns as new features.…”

“…The relevancy of such a minimality property is also discussed in terms of "near equivalence" in [19]. In [2], we have considered preliminary results on feature construction based on δ-freeness [12,13]. Feature construction approaches based on closedness properties differ in two main aspects: (i) mining can be performed on the whole database or per class, and (ii) we can mine with or without the class labels.…”

Using Condensed Representations for Interactive Association Rule Mining

“…This property is used in the following algorithms: To compute the closed sets, the algorithms mine the free itemsets and then output their closures. Let us note that free sets are special cases of δ-free sets [5] and have been independently formalized as key patterns in [3].…”

“…frequency queries [11] is useful. Several researchers have studied the efficient computation of condensed representations of (frequent) itemsets like the closed sets [17,4,20], the free sets [5] or the disjunct free sets [7].…”