Unsupervised kernel learning for abnormal events detection

In this paper, we propose a method to detect abnormal events using a novel unsupervised kernel learning algorithm. The key of our method is to learn a suitable feature space and the associated kernel function of the training samples. By considering the self-similarity property of training samples, we assume that the training samples will show the distinctly clustering property in the obtained feature space. Non-negative matrix factorization (NMF) is used to learn the feature space, and the support vector data description (SVDD) method is adopted to measure the clustering degree of instances in the feature space. We append the clustering constraints in the process of learning the feature space and use the bases produced by NMF as the projection matrix to construct the kernel function in SVDD. In other words, we incorporate the minimal enclosing sphere constraints within the NMF formulation. In the process of feature space learning, instances in the obtained feature space will be described better and better by an hypersphere. Our algorithm converges to a local optimal solution by applying an alternating optimization approach. Experimental results on three public datasets and the comparison to the state-of-the-art methods show that our method is effective in detecting and locating unknown abnormal behaviors.