This paper proposes a novel data mapping technique to develop a fault diagnosis method. The data mapping technique takes advantage of rising empirical mode decomposition and non-negative matrix factorization to transform nonlinear and non-stationary signals into characteristic power spectral density (PSD) bases with physical interpretations. A number of mapped PSD basis vectors not only bear more distinctive features compared to the original data form, but also fuse separate features into an integrated one. Feature recognition quantifies the degree of similarity between different PSD bases to achieve fault recognition and classification. A simulated mechanical vibration signal is presented to illustrate that adopting PSD basis as a data feature yields better diagnostic performances than those obtained from other feature forms. Real faulted bearing data are also analyzed in different experiments to give a comprehensive verification of the proposed fault diagnosis method.