A Probabilistic Collaborative Representation based Approach for Pattern Classification

Conventional representation based classifiers, ranging from the classical nearest neighbor classifier and nearest subspace classifier to the recently developed sparse representation based classifier (SRC) and collaborative representation based classifier (CRC), are essentially distance based classifiers. Though SRC and CRC have shown interesting classification results, their intrinsic classification mechanism remains unclear. In this paper we propose a probabilistic collaborative representation framework, where the probability that a test sample belongs to the collaborative subspace of all classes can be well defined and computed. Consequently, we present a probabilistic collaborative representation based classifier (ProCRC), which jointly maximizes the likelihood that a test sample belongs to each of the multiple classes. The final classification is performed by checking which class has the maximum likelihood. The proposed ProCRC has a clear probabilistic interpretation, and it shows superior performance to many popular classifiers, including SRC, CRC and SVM. Coupled with the CNN features, it also leads to state-of-the-art classification results on a variety of challenging visual datasets.