Beyond Correlation: Learning Supervised, Sample-Distinct, and Eigenimage-Interpretable Representations

Conventional dimensionality reduction methods mainly optimize variance or correlation, leaving statistical dependence, data diversity, contrast, and interpretability under addressed. We propose three new independence criteria for designing supervised and unsupervised dimensionality reduction (DR) methods, aiming to improve feature extraction and representation quality. Our framework combines linear and nonlinear formulations and is evaluated using contrast, classification accuracy, and interpretability measures. The interpretability of eigenfaces helps to effectively summarize dominant class-specific structures and trends within representative images. Evaluated on MNIST and a Gender face dataset for classification and reconstruction, our methods achieve significant improvements in contrast (up to $+$20.1\%), accuracy (up to $+$17.4\%), and interpretability (up to $+$120.0\%) over Principal Component Analysis (PCA), t-distributed Stochastic Neighbor Embedding (t-SNE), Linear Discriminant Analysis (LDA), and Variational Autoencoder (VAE) baselines, while also improving VAE reconstruction performance by 9.5\%. These results suggest a promising direction for interpretable representation learning based on statistical dependence and independence criteria.