Mining Frequent Itemsets in Evidential Database

Abstract

Mining frequent patterns is widely used to discover knowledge from a database. It was originally applied on Market Basket Analysis (MBA) problem which represents the Boolean databases. In those databases, only the existence of an article (item) in a transaction is defined. However, in real-world application, the gathered information generally suffer from imperfections. In fact, a piece of information may contain two types of imperfection: imprecision and uncertainty. Recently, a new database representing and integrating those two types of imperfection were introduced: Evidential Database. Only few works have tackled those databases from a data mining point of view. In this work, we aim to discuss evidential itemset's support. We improve the complexity of state of art methods for support's estimation. We also introduce a new support measure gathering fastness and precision. The proposed methods are tested on several constructed evidential databases showing performance improvement.

Evidential data mining: precise support and confidence

“…Two different itemsets can be related via the inclusion or intersection operator. Indeed, the inclusion operator [4,27] for itemsets is defined as follows, let X and Y are two itemsets:…”

“…where x i and y j are the i th and the j th elements of respectively X and Y . For the same itemsets X and Y , the intersection operator [27] is defined as follows:…”

Classification with Evidential Associative Rules

“…In a previous work [10], we introduced a new metric for support estimation providing more accuracy and overcoming several limits of using the belief function. The Precise support P r is defined by:…”

“…In the following, we propose a new metric for the confidence estimation based on our Precise support measure [10] and probability assumption:…”

“…This asset makes from the evidential database more informative but more complex than the usual binary database. In [10], we have shown the significant number of generated frequent patterns that may be drawn even from small databases. Indeed, from a frequent itemset, of size k, 2 k − 2 potential rules are generated.…”