Condition monitoring schemes are essential for increasing the reliability and ensuring the equipment efficiency in industrial processes. The feature extraction and dimensionality reduction are useful preprocessing steps to obtain high performance in condition monitoring schemes. To address this issue, this work presents a novel diagnosis methodology based on high-dimensional feature reduction applied to detect multiple faults in an induction motor linked to a kinematic chain. The proposed methodology involves a hybrid feature reduction that ensures a good processing of the acquired vibration signals. The method is performed sequentially. First, signal decomposition is carried out by means of empirical mode decomposition. Second, statistical-time-based features are estimated from the resulting decompositions. Third, a feature optimization is performed to preserve the data variance by a genetic algorithm in conjunction with the principal component analysis. Fourth, a feature selection is done by means of Fisher score analysis. Fifth, a feature extraction is performed through linear discriminant analysis. And, finally, sixth, the different considered faults are diagnosed by a Neural Network-based classifier. The performance and the effectiveness of the proposed diagnosis methodology is validated experimentally and compared with classical feature reduction strategies, making the proposed methodology suitable for industry applications.