Human physiological responses to external stimuli are generally categorized into three types—Active coping, Passive coping, and No coping—each exhibiting characteristic variations in hemodynamic indices such as mean blood pressure, cardiac output, and total peripheral resistance. Understanding these physiological patterns is essential for developing non-invasive monitoring techniques that can assess individual stress responses in real time. In this study, we aimed to discriminate these coping styles based on facial imaging data using two wavelength bands: Thermal Facial Imaging (TFI) and Near-Infrared Facial Imaging (NIFI). Three dimensionality reduction methods—Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), and Uniform Manifold Approximation and Projection (UMAP)—were applied to visualize latent stress-related dynamics. To compensate for physiological response latency, time-delay correction was incorporated prior to analysis. Furthermore, k-means clustering and F1-score analysis were conducted to quantitatively evaluate the separability among coping states. Results demonstrated that TFI, which reflects surface temperature changes associated with blood flow and heat conduction, exhibited higher robustness and clearer separability than NIFI, which captures subsurface vascular signals. Nonlinear methods (t-SNE and UMAP) outperformed the linear PCA, effectively visualizing smooth temporal transitions of physiological adaptation and residual thermal responses after task completion. These findings indicate that TFI features represent slow physiological processes modulated by vascular and thermal mechanisms, and that dimensionality reduction serves as an effective framework for revealing latent stress-response structures in facial imaging data.