Constructing minimum volume surfaces using level set methods for novelty detection

A reliable novelty detector employs a model that encloses the normal dataset tightly. As nonparametric probability density function estimation methods make no assumptions about the probability distribution of a dataset, this paper applies kernel density estimation to construct the initial boundaries surrounding the normal data points. Afterwards, the level set method makes the initial boundaries shrink or expand to better fit the normal data distribution and optimize the boundary surfaces. The proposed method is able to smooth the boundary's evolution automatically while merging or splitting happens. The boundary motion is governed by partial differential equations which formulate the dynamics of the level set method. The proposed novelty detection method is compared with four representative existing methods: support vector data description, nearest neighbours data description, mixture of Gaussian and k-means. The experimental results illustrate that the proposed level set based method presents a comparable performance as mixture of Gaussian, which performs best in terms of false negative and false positive rates