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This work provides a systematic cross-domain analysis of Kernelized Linear Principal Component Discriminant Analysis (KLPCDA) to resolve representation instability in high-dimensional, small-sample-size (SSS) regimes. By evaluating seven modular configurations across medical imaging, face recognition, and fault diagnosis benchmarks, the authors characterize the precise interplay among global variance preservation, between-class divergence, and within-class compactness. The resulting empirical taxonomy establishes actionable selection heuristics for tabular and spatial SSS tasks, delivering robust classification under severe label scarcity and noise at minimal computational cost.
High-dimensional small-sample learning can achieve robust classification without parameter-heavy deep networks simply by systematically balancing kernel variance, margin, and compactness.
The small-sample-size (SSS) problem remains a fundamental challenge in machine learning when labeled data are scarce due to cost, accessibility, or ethical constraints. While numerous approaches have been proposed, existing methods often struggle to maintain stable and discriminative representations under high-dimensional and limited-data conditions. Kernelized Linear Principal Component Discriminant Analysis (KLPCDA), a recently proposed modular framework, integrates variance preservation, inter-class separability, and intra-class compactness within a unified kernel space. Although its formulation has shown promising initial results, a systematic understanding of how its components interact across diverse SSS scenarios remains lacking. In this paper, we present a systematic cross-domain study of KLPCDA to characterize the interaction mechanisms among its core objectives. We analyze the behavior of its seven variants across multiple real-world SSS tasks, including hyperspectral image classification, mechanical fault diagnosis, medical diagnosis, and face recognition. Through extensive experiments and ablation studies, we investigate how different objective combinations influence performance under varying conditions such as noise, class imbalance, and high dimensionality. Our analysis reveals consistent patterns in the interaction of the three core objectives variance, between-class, and within-class terms, providing a unified and interpretable understanding of their roles in stabilizing representations and enhancing discrimination in SSS settings. Based on these findings, we further derive practical guidelines for selecting appropriate KLPCDA variants under different data characteristics. Experimental results demonstrate that KLPCDA achieves strong and robust performance across domains, while maintaining low computational complexity suitable for resource-constrained environments.
