Normed principal components analysis: A new approach to data warehouse fragmentation

In this paper, we present a state of the art on the principal components analysis (PCA) and the possibility of its use for horizontal and vertical fragmentation of data warehouses (DW), in order to reduce the time of query execution. We focus on the study of correlation matrices, the impact of the eigenvalues evolution on the determination of suitable situations to achieve the PCA, and a study of criteria for extracting principal components. Then, we proceed to the projection of individuals on the first principal plane, and the 3D vector space generated by the first three principal components. We try to determine graphically homogeneous groups of individuals and therefore, a horizontal fragmentation schema for the studied data table. The study of correlations between the original variables and the principal components allow us to draw the circle of correlations and define graphically, under some conditions, candidate variables to be collected in vertical fragments. To satisfy a maximum of decision queries OLAP, our approach is independent from any set of queries, and seeks to exploit the graphical representations provided by the PCA. We conclude our study by an experiment on a data warehouse which shows the interest and the originality of our approach.