ABSTRACT
Laboratoire d’Informatique Fondamentale de Marseille (LIF), Aix-Marseille Universite´ - CNRS
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 9.2 Emerging Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 9.3 Representations of the Emerging Cube . . . . . . . . . . . . . . . . . . . . . . . . . . 114
9.3.1 Representations for OLAP Classification . . . . . . . . . . . . . . . 114 9.3.1.1 Borders [L;U ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 9.3.1.2 Borders ]U ;U ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.3.2 Representations for OLAP Querying . . . . . . . . . . . . . . . . . . . 117 9.3.2.1 L-Emerging Closed Cubes . . . . . . . . . . . . . . . . . 117 9.3.2.2 U -Emerging Closed Cubes . . . . . . . . . . . . . . . . 120 9.3.2.3 Reduced U -Emerging Closed Cubes . . . . . . 121
9.3.3 Representation for OLAP Navigation . . . . . . . . . . . . . . . . . . 122 Emerging Quotient Cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
9.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 9.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Decision makers are generally interested in discovering interesting trends by using a data warehouse to analyze data collected from a “population”. The data warehouse contains data concerning various measures which are observed with respect to different attributes called dimensions. More precisely, all the possible combinations of dimensions can be relevant and considered at all possible granularity levels. In order to meet decision makers’ needs, the concept of a data cube was introduced [168]. It groups the tuples according to all the dimension combinations along with their associated measures. The main interest of this structure is to support an interactive analysis of data, because all the possible trends are not yet computed. Of course, due to its
very nature (the very great volume of original data and exponential number of dimension combinations), a data cube can be very large.
