Accurate dimensionality recovery is a fundamental challenge in Multidimensional Item Response Theory (MIRT). While recent machine learning (ML) approaches outperform traditional statistical methods, their reliance on supervised training data limits generalizability to empirical data with unforeseen structural anomalies. This study introduces a novel unsupervised dimensionality selection method integrating Constrained Joint Maximum Likelihood Estimation (CJMLE) with elementwise cross-validation. The performance of this approach, using both prediction accuracy and the area under the curve (AUC) as selection criteria, was benchmarked against supervised ML classifiers (XGBoost, Random Forest) and traditional techniques (MAP, PA, VSS-C2, EGA) across 7,200 simulated datasets varying in sample size, factor correlation, and structural complexity. Additionally, the methods were applied to empirical data from the Narcissistic Personality Inventory (NPI-40). Simulation results indicated that MAP and XGBoost achieved the highest recovery rates. Contrary to previous recommendations in collaborative filtering literature, JML-ACC consistently outperformed JML-AUC. Although the CJMLE-based method fell short of ML performance in simulated conditions, its independence from training data assumptions suggests greater potential robustness for applied settings. Empirical application supported a parsimonious two- to three-dimensional structure for the NPI-40, challenging the originally reported seven-factor solution. These findings highlight the trade-off between the predictive power of feature-engineered ML models and the distributional independence of cross-validation techniques in psychometric research.