Galois Connections and Data Mining

Dana Cristofor; Laurentiu Cristofor; Dan Simovici

doi:10.3217/jucs-006-01-0060

JUCS - Journal of Universal Computer Science 6(1): 60-73, doi: 10.3217/jucs-006-01-0060

Galois Connections and Data Mining

Dana Cristofor^‡, Laurentiu Cristofor^‡, Dan Simovici^§

‡ University of Massachusetts at Boston, Department of Mathematics and Computer Science, Boston, Massachusetts, United States of America§ University of Massachusetts Boston, Boston, United States of America

Corresponding author: Dana Cristofor ( dana@cs.umb.edu )

This article is freely available under the J.UCS Open Content License.

Citation: Cristofor D, Cristofor L, Simovici D (2000) Galois Connections and Data Mining. JUCS - Journal of Universal Computer Science 6(1): 60-73. https://doi.org/10.3217/jucs-006-01-0060

Abstract

We investigate the application of Galois connections to the identification of frequent item sets, a central problem in data mining. Starting from the notion of closure generated by a Galois connection, we define the notion of extended closure, and we use these notions to improve the classical Apriori algorithm. Our experimental study shows that in certain situations, the algorithms that we describe outperform the Apriori algorithm. Also, these algorithms scale up linearly. 1 C.S.Calude and G.Stefanescu (eds.). Automata, Logic, and Computability. Special issue dedicated to Professor Sergiu Rudeanu Festschrift.

Keywords

Galois connection, closure, extended closure, support, frequent set of items