L1 norm based KPCA for novelty detection

Novelty detection is a one class classification problem, and it builds up the model with only normal samples, based on which the novelty is detected. Though conventional KPCA is an effective method of building one class classification models, it is prone to being affected by the presence of outliers due to its inherent properties of L2 norm. In this paper, we propose a new optimization problem, L1 norm based KPCA, which is robust to outliers. Correspondingly, we present the algorithm and the measure of novelty. The proposed method is applied to novelty detection and performs well on the simulation data sets.

► We propose L1 norm based KPCA problem in an optimization way.
► A new L1-KPCA algorithm is presented to solve the L1 norm based KPCA problem.
► We prove the convergence to a local maximum point of the algorithm.
► By giving the measure of novelty, we apply the L1-KPCA into novelty detection.