Structural phase transitions in solid materials often follow a Minimum Energy Path (MEP), which represents the most probable trajectory from the initial to the final state. However, as the MEP resides in a high-dimensional structural space, direct modeling remains highly challenging. To address this issue, we propose a data-driven framework that employs Singular Value Decomposition (SVD) to extract the principal directions of the high-dimensional MEP, together with a singular value–based error estimation scheme to quantitatively assess the reliability of low-dimensional approximations. Numerical studies on pure Fe crystals and Fe systems with carbon impurities demonstrate that, in the ideal case, the Bain path aligns well with the principal directions of the MEP, confirming its physical validity, whereas in defect-containing systems the Bain path fails, even though the MEP still exhibits robust low-dimensional characteristics. Finally, we provide a physical interpretation of the extracted features.