Dimensionality Reduction via Hierarchical Analysis of Partially Ordered Structures: LAPOS

Abstract

Domains such as artificial intelligence, statistical modeling, and signal interpretation. This method aims to retain the core characteristics of datasets while minimizing their dimensional scope, which contributes to improving the efficiency of algorithms and enhancing data understanding. The proposed framework relies on the principle of Level Analysis of Partially Ordered Sets (LAPOS). Instead of treating dimensions as independent entities or searching for linear projections, this method considers the ordinal relationships between different dimensions. A partial order structure is constructed that reflects the correlations and interactions between data attributes, allowing for a more accurate identification of the most influential and frequently occurring dimensions. LAPOS can reveal nonlinear relationships, better interpretability, and flexibility in dimension selection. Preliminary results have shown that this method surpasses traditional dimensionality reduction approaches in maintaining data integrity and minimizing information loss in subsequent tasks (such as classification and clustering). LAPOS, Principal Component Analysis (PCA), and Factor Analysis (FA) achieve 92.59, 86.1, and 81.02 accuracy respectively, when employing the Support Vector Machine (SVM) algorithm. This research opens new avenues for using partially ordered set theory to manage the complications arising from high-dimensional feature spaces.