Kernel null space methods for novelty detection

Detecting samples from previously unknown classes is a crucial task in object recognition, especially when deal-ing with real-world applications where the closed-world as-sumption does not hold. We present how to apply a null space method for novelty detection, which maps all training samples of one class to a single point. Beside the possibil-ity of modeling a single class, we are able to treat multi-ple known classes jointly and to detect novelties for a set of classes with a single model. In contrast to modeling the support of each known class individually, our approach makes use of a projection in a joint subspace where training samples of all known classes have zero intra-class variance. This subspace is called the null space of the training data. To decide about novelty of a test sample, our null space ap-proach allows for solely relying on a distance measure in-stead of performing density estimation directly. Therefore, we derive a simple yet powerful method for multi-class nov-elty detection, an important problem not studied sufficiently so far. Our novelty detection approach is assessed in com-prehensive multi-class experiments using the publicly avail-able datasets Caltech-256 and ImageNet. The analysis re-veals that our null space approach is perfectly suited for multi-class novelty detection since it outperforms all other methods. 1