Dimensionality Reduction Strategy on Four-Dimensional Data Cubes with Independent Slices and Hyper-Slices Focusing on Variability Structure and Components

Abstract

Data cubes are p-dimensional data structures (p ≥ 3). In most biological sciences, the key point of statistical data analysis is the study of variability, focusing on its structure and components. The proposed strategy was based on principal component analysis (PCA) and the idea of decomposing the total variability of a four-dimensional cube (p = 4) into variability between and within the cube’s slices and hyper-slices. The aim of this study was to propose new insights into the dimensionality reduction of four-dimensional cubes with independent slices and hyper-slices and equal or unequal number of experimental units per slice within each hyper-slice. As an example, the simulated dataset “Basil” from the field of agriculture was used. The fourth dimension consisted of three irrigation levels (hyper-slices). The third dimension consisted of five basil varieties (slices). The second dimension consisted of seven quantitative traits-variables, and the first dimension consisted of different plants. The proposed strategy allowed for a detailed examination of the effect of slices and hyper-slices on the overall data cube structure by highlighting the dominant influence of irrigation levels. Also, the study highlighted the controversial case of the variability decomposition on unbalanced four-dimensional cubes. For future research, various clustering strategies could be applied, in terms of the distance metric and the linkage method, either to the initial cubes or to the PCA components’ scores from each variability data matrix. The proposed strategy could also be applied to data cubes with greater imbalance, in terms of sample size, between slices, and hyper-slices.

Received: 28 November 2025 | Revised: 3 June 2026 | Accepted: 11 September 2026

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data are available from Professor Christos Dordas (co-author) upon reasonable request.

Author Contribution Statement

Zacharenia Kyrana: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization. Nikolaos Papafilippou: Writing – review & editing. Emmanouil D. Pratsinakis: Writing – review & editing. Alexandra-Maria Michaelidou: Writing – review & editing. Christos Dordas: Validation, Investigation, Resources, Data curation, Writing – review & editing. Angelos Markos: Methodology, Writing – review & editing. George C. Menexes: Conceptualization, Methodology, Validation, Investigation, Data curation, Writing – review & editing, Supervision, Project administration.