In this paper, we propose a general framework to learn a robust large-margin binary classifier when corrupt measurements, called anomalies, caused by sensor failure might be present in the training set. The goal is to minimize the generalization error of the classifier on non-corrupted measurements while controlling the false alarm rate associated with anomalous samples. By incorporating a non-parametric regularizer based on an empirical entropy estimator, we propose a Geometric-Entropy-Minimization regularized Maximum Entropy Discrimination (GEM-MED) method to learn to classify and detect anomalies in a joint manner. We demonstrate using simulated data and a real multimodal data set. Our GEM-MED method can yield improved performance over previous robust classification methods in terms of both classification accuracy and anomaly detection rate.

Large margin classifiers, such as the support vector machine (SVM) [1] and the maximum entropy discrimination (MED) classifier [2], have enjoyed great popularity in the signal processing and machine learning communities due to their broad applicability, robust performance, and the availability of fast software implementations. When the training data is representative of the test data, the performance of MED/SVM has theoretical guarantees that have been validated in practice [1], [3], [4]. Moreover, since the decision boundary of the MED/SVM is solely defined by a few support vectors, the algorithm can tolerate random feature distortions and perturbations. However, in many real applications, anomalous measurements are inherent to the data set due to strong environmental noise or possible sensor failures. Such anomalies arise in industrial process monitoring, video surveillance, tactical multi-modal sensing, and, more generally, any application that involves unattended sensors in difficult environments (Figure 1).