In this paper, we present a robust feature extraction framework based on information-theoretic learning. Its formulated objective aims at dual targets, motivated by the Renyi’s quadratic entropy of the features and the Renyi’s cross entropy between features and class labels, respectively. This objective function reaps the advantages in robustness from both redescending M-estimator and manifold regularization, and can be efficiently optimized via half-quadratic optimization in an iterative manner. In addition, the popular algorithms LPP, SRDA and LapRLS for feature extraction are all justified to be the special cases within this framework. Extensive comparison experiments on several real-world data sets, with contaminated features or labels, well validate the encouraging gain in algorithmic robustness from this proposed framework.