Training set optimization based on triple Euclidean distance and cluster-based oversampling for Noninvasive platelet Measurement.

Noninvasive spectral measurements of blood components are confronted with two fundamental challenges: interference from multiple non-measured components (M-factor) and environmental variations (N-factor). Existing sample set partitioning methods are limited in their application. Some methods ignore non-measured components (e.g., SPXY), while others suffer from poor scalability when multiple interfering components are considered (e.g., MCSD). To address these limitations, this paper proposes a Triple Euclidean Distance (TED) method grounded in the M+N theory. Unlike previous methodologies, TED constructs three independent distance spaces--measured component space, non-measured component space, and spectral space--and integrates them through normalization without mutual domination. This design prevents the overshadowing of low-concentration targets by high-concentration components, a critical limitation of MCSD. Furthermore, we identify that cluster-based oversampling alone does not ensure optimal partitioning within each cluster; to address this, we propose a KST framework that integrates TED with K-means and SMOTE, where TED functions as a post-clustering refinement mechanism. Experimental results on noninvasive platelet measurement demonstrate that KST achieves the lowest root mean square error (RMSE = 15.01 × 109/L) and highest clinical acceptability rate (100%) among all six partitioning methods evaluated. Compared to KMS (K-means + SMOTE), KST attains a 37.1% reduction in RMSE on the test set. Bootstrap confidence intervals and randomization tests confirm the robustness of these improvements, particularly in clinical acceptability. Scalability analysis further reveals that TED maintains consistent performance as the number of interfering components increases, whereas MCSD degrades significantly. This work provides a scalable and theoretically coherent solution for sample set partitioning in complex spectral measurement systems.