Data sparsity, particularly the partial loss of diagnostic data caused by sensor failures, transmission errors, or missed inspections, frequently occurs in practical power transformer operations and significantly degrades the accuracy and reliability of health index (HI) assessments. In this study, a machine learning-based HI evaluation framework is developed using key diagnostic input parameters systematically derived from failure mode and effect analysis (FMEA) and established transformer diagnostic practices. To compensate for missing data, an unsupervised autoencoder (AE)-based imputation method is introduced and benchmarked against conventional statistical supplementation techniques, namely mean and mode imputation. The experimental results, obtained using real inspection-based transformer diagnostic records, demonstrate that the AE-based approach effectively preserves inter-variable correlations and latent data structures by learning nonlinear feature relationships. As a result, the proposed method maintains robust and consistent HI classification performance under varying missing-data conditions. Furthermore, validation using confirmed transformer failure cases shows that the AE method more accurately reconstructs missing dissolved gas analysis indicators and improves the identification of high-risk equipment compared with statistical imputation. Overall, the proposed approach provides decision-consistent HI evaluations even when diagnostic data are incomplete, thereby reducing uncertainty in maintenance planning and minimizing the need for additional follow-up inspections solely to compensate for missing information.