Accelerating Effect of Attribute Variations: Accelerated Gradual Itemsets Extraction

Abstract

Abstract. Gradual itemsets of the form "the more/less A, the more/less B" summarize data through the description of their internal tendencies, identified as correlation between attribute values. This paper proposes to enrich such gradual itemsets by taking into account an acceleration effect, leading to a new type of gradual itemset of the form "the more/less A increases, the more quickly B increases". It proposes an interpretation as convexity constraint imposed on the relation between A and B and a formalization of these accelerated gradual itemsets, as well as evaluation criteria. It illustrates the relevance of the proposed approach on real data.

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

“…Accelerated gradual itemsets aim at extracting information in the form of correlations between attribute values by focusing on how fast the values of some attributes vary as compared to others [22]. This section briefly recalls their principle, formalization and the evaluation criterion of the acceleration effect.…”

“…The principle of acceleration is naturally understood as speed variation increase, which can be translated as a convexity constraint on the underlying function associating the considered attributes. This constraint can be modeled as an additional co-variation constraint, leading to the definition of a criterion called accelerated support to assess the validity of such accelerated gradual itemsets [22]. It is added to the evaluation of the gradual itemset through the classical gradual support defined in Equation 1.…”

“…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]". The second one is defined as accelerated gradual itemsets [22]. It can be illustrated by an example such as "the more the US closing price increases, the more quickly the Brazilian closing price increases", where "quickly" provides additional knowledge about the relation between considered attributes.…”