Galois Connections, T-CUBES, and P2P Data Mining

Abstract

Galois connections are bread and butter of the formal concept analysis. They concern objects with properties, represented typically as a single-valued (.true or null) binary attributes. The closed sets and Galois lattices are the most studied connections. We generalize them to the relational database universe with the multi-valued domains. We show interesting queries that appear from, hard or impossible with SQL at present. As remedy, we generalize CUBE to a new operator we call θ-CUBE, writing T-CUBE It calculates the groups according to all the values of the θ operator popular with the relational joins. We show also the utility of new aggregate functions LIST and T-GROUP. In this context We finally discuss scalable distributed algorithms in P2P or grid environment for T-CUBE queries Our proposals should benefit to both: the data mining and the concept analysis over many objects.