Comparative evaluation of linear and nonlinear dimensionality reduction techniques for breast cancer diagnosis

Dimensionality reduction plays a crucial role in improving the interpretability and structural visualization of machine learning configurations applied to high-dimensional biomedical data. This study presents an exploratory comparative evaluation of four widely used techniques: Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), Linear Discriminant Analysis (LDA), and Self-Organizing Maps (SOM), mapping cytological breast cancer features derived from fine-needle aspirate (FNA) measurements in the Breast Cancer Wisconsin (Diagnostic) dataset. Each method was assessed according to its ability to preserve underlying geometric data distribution and enhance class separability margins within the reduced two-dimensional feature spaces. Experimental results demonstrate that the supervised projection layout of LDA achieves the highest class-separability, yielding an out-of-fold logistic-regression proxy accuracy of 98.83% and a Silhouette Score of 0.6776. We note that this accuracy figure is computed after fitting each projection on the full dataset (see Section 5.1) and should therefore be interpreted as a measure of class-consistent latent geometry rather than a leakage-free estimate of clinical predictive performance. PCA provides a stable representation of global data variance but exhibits overlapping boundaries across categories. t-SNE effectively captures local manifold structure to produce informative cluster visualizations; however, its resulting classification proxy score remains lower (95.32%). In contrast, SOM shows weaker topological grouping performance, reflecting the challenges of accommodating complex cytological distributions within rigid low-dimensional grids. Statistical validation using paired t-tests and Wilcoxon signed-rank tests confirms that the observed structural differences among the evaluated low-dimensional layouts are statistically significant across validation partitions. Rather than asserting clinical predictive readiness, these findings provide critical architectural insights into selecting appropriate dimensionality reduction techniques for the exploratory characterization of cytological features, establishing an essential geometric baseline for biomedical feature space mapping.