Στρατηγικές μείωσης των διαστάσεων σε κύβους δεδομένων με ανεξάρτητες “φέτες”

Abstract

Data cubes are p-dimensional data structures, where p≥3. The application of traditional dimensionality reduction methods depends on the scientific field, the objectives of the study, the type of data cube and the observed data. Therefore, it is considered wiser to apply different analysis strategies. In this study, the application of different dimensionality reduction strategies based on PCA was investigated. Some strategies were based on the idea of decomposing the total variability (inertia) of the cube into between-“slices” and within-“slices” variability. Other strategies either initially ignored the effect of “slices” on the variability structure and introduced it at a second level or ignored it entirely, while other strategies took into account the effect of “slices” on the overall data cube structure by coding the variable of “slices” differently. The aim was to propose some new insights into dimensionality reduction strategies on data cubes with independent “slices”. For the implementation and comparison of the proposed strategies, the “ADONUT” dataset was used (42,061×13×3 data cube with three independent “slices” and an unequal number of objects/“slice”), which comes from a Panhellenic study on the nutritional habits of adolescents, during 2010-2012, by the Department of Nutritional Sciences and Dietetics, IHU. The weekly consumption frequencies of 13 food groups constituted the quantitative variables, while the adolescents drawn from three geographic areas that represented the independent “slices”. The proposed strategies highlighted the importance of applying different dimensionality reduction strategies according to the research objectives.