ABSTRACT: Dimensionality reduction (DR) simplifies complex data from genomics, imaging, sensors, and language into interpretable forms that support visualization, clustering, and modeling. Yet widely used methods like principal component analysis, t-distributed stochastic neighbor embedding, uniform manifold approximation and projection, and autoencoders are often applied as "black boxes," neglecting interpretability, fairness, stability, and privacy. This review introduces a unified classification-linear, nonlinear, hybrid, and ensemble approaches-and assesses them against eight core challenges: dimensionality selection, overfitting, instability, noise sensitivity, bias, scalability, privacy risks, and ethical compliance. We outline solutions such as intrinsic dimensionality estimation, robust neig
