This article presents a data-driven approach for the classification of faults in induction machines. The designed scheme involves newly engineered features extracted from the line current signals, which provides an improved fault discrimination. For this purpose, a topological-based fast projection technique (curvilinear component analysis) is used as a tool to reduce the dimensionality of the data and interpret the feature behavior. Consequently, a shallow convolutional neural network has been designed to classify the three-phase stator current signals. Experimental tests at different operating conditions have assessed the procedure, confirming its effectiveness and suitability for online and real-time diagnostics.