A Novelty Detection Algorithm in the Presence of Noise

Abstract

<p indent="0mm">To address the poor performance of novelty detection in the presence of noisy samples, a method named kernel null space discriminant locality preserving projections (KNDLPP) is proposed. Firstly, the training samples are transformed into a high dimensional space through a kernel function implicitly, and different weights are assigned to these samples according to the distance weighted scheme in the kernel space, to preserve the locality while reducing the impacts of noisy samples. Then, through the kernel null space of intra-class, each class collapses to a point, which makes each known class concise efficiently. Finally, a projection matrix maximizing the distance among inter-classes can be computed based on the null space, thus after these steps a discriminative transformation matrix is got to characterize the distribution and similarity of samples. This method can grasp the underlying structure of samples, and improve the discrimination between the known classes and the unknown novelty. The comparison experiments are based on eleven public datasets, the results validate the effectiveness and robustness of proposal during the testing, and this method performs well for novelty detection. During the experiments about locality preserving on 4 UCI datasets, the whole mean AUC of KNDLPP is 90.656%. During the experiments about complex structure on Banana, Moon and 3 UCI datasets, the whole mean AUC of KNDLPP is 91.949%. During the experiments on 2 clean high dimensional datasets for novelty detection, the whole mean AUC of KNDLPP is 86.214%, which is 4 percent higher than the second best algorithm. On 4 UCI datasets with 4 different kinds of noise, the performance of KNDLPP ranks first.