Characterisation of gradual itemsets based on mathematical morphology tools

Abstract

Gradual itemsets of the form "the more/less A, the more/less B" summarise data through the description of their internal tendencies, identified as correlation between attribute values. This paper proposes to characterise gradual itemsets, enriching them with an additional clause introduced by the linguistic expression "especially if": they are of the form "the more/less A, the more/less B, especially if J ∈ R", where J is a set of attributes occurring in A ∪ B and R is a set of intervals defined for each attribute in J. The method proposed to automatically extract characterised gradual itemsets is based on appropriate mathematical morphology tools. The paper illustrates the relevance of the proposed approach on a real data set.

Mining Emerging Gradual Patterns

“…It can be noted that the notions of emerging patterns and contrast sets are related to that of characterised gradual patterns [23]: the latter automatically extract data subsets on which the support of a gradual pattern is greater than on the whole data. Two differences must be underlined: first it is specific to the interpretation of gradual patterns in terms of ranking compliant data subsets [2].…”

Analysis of the emission of American Depositary Receipts of Brazilian companies through the extraction of linguistic summaries

“…Two types of enriched gradual itemsets are considered in the paper. The first type, called characterized gradual itemset, linguistically introduced by the expression "especially if " [21]. It can be exemplified with "the more the US closing price increases, the more the Brazilian closing price increases, especially if it belongs to the interval [1,10]".…”

Accelerating Effect of Attribute Variations: Accelerated Gradual Itemsets Extraction

“…Two enrichment types for gradual itemsets have been proposed, namely through characterization [10] and strengthening [9]. Both are based on a principle of increased validity when the data are restricted to a subset: the gradual support of the considered itemset must increase when it is computed on the data subset only.…”

“…Both are based on a principle of increased validity when the data are restricted to a subset: the gradual support of the considered itemset must increase when it is computed on the data subset only. More precisely, in the case of characterization [10], the restriction is defined as a set of intervals: characterized gradual itemsets are linguistically of the form "the more/less A, the more/less B, especially if J ∈ R", where J is a set of attributes belonging to A∪B and R is a set of intervals defined for each attribute in J. R defines the data subset, it applies only in the case of numerical data.…”

“…They can be illustrated by an example such as "the closer the wall, the harder the brakes are applied, all the more the higher the speed ". For numerical data, an enrichment by characterization clauses [10] adds a clause linguistically introduced by the expression "especially if": characterized gradual itemsets can be illustrated Fig. 1: Two data sets, leading to "the more A, the more B" where an acceleration effect is observed for the right data set and not for the left one.…”