Dimensionality Reduction Evaluation for Multivariate Quantum Data

Interdisciplinary research on high-dimensional quantum data faces significant challenges due to differing interpretive frameworks across physics, mathematics, and data science. Those differences in perspective create a communication gap that slows research progress and prevents deeper interdisciplinary discussions. This paper introduces a visual analytics framework to bridge these disciplinary divides through 2D embedding visualization, which facilitates collaborative discovery and incremental hypothesis testing. Our evaluation systematically compares PCA and UMAP using both absolute values—preserving quantum symmetries in femto scales—and standardized values. We assess the stability of UMAP in both data scenarios, which reveals corresponding class organizations equivalent to those produced by PCA. When applied to absolute values, UMAP is sensitive to the variable N, revealing intrinsic low-variance relationships within the data but sacrificing reproducibility. This often results in unique embeddings accompanied by noisy outliers. Conversely, scaling the data allows UMAP to eliminate fine-scale structures, ensuring more consistent structural convergence. Our framework formalizes these trade-offs, demonstrating how UMAP can function as a hybrid goal-driven tool. Additionally, it can benefit from PCA cross-validation to enhance interpretability, contributing to science and knowledge discovery in complex quantum data even when the ground truth is unknown.