Novelty detection using level set methods

Abstract

Novelty detection refers to the process of identifying unforeseen anomalies that deviate from normal behaviours. It can be described by constructing an optimal decision boundary around the given normal data and how the surface area within the boundary is minimised in order to reduce the chance of accepting abnormal data.
This thesis proposes a new novelty detection approach using level set methods (LSM). The LSM approach can construct a nonlinear decision boundary directly in the input space using an implicit level set function (LSF), which evolves the boundary to better fit the data distribution and smoothes the change of the boundary shape (e.g. boundary merging and splitting). The boundary evolution is fully data-driven and the LSM approach does not require any assumptions on data distribution (a nonparametric approach).
In terms of implementation, the Laplacian of kernel density estimations on given data is first used to construct an LSF and an initial boundary. Two algorithms are proposed for global boundary evolution: one based on the surface normal vectors of the boundary and the other on the sign of the LSF at the given data. An evolution termination is also proposed to stop the boundary motion that is governed by partial differential equations. In order to make the boundary better fit the data distribution, a novel locally adaptive boundary evolution scheme is also proposed and its performance is compared against the global boundary evolution scheme. Three distinct algorithms are proposed to determine the boundary segments to be locally evolved. These are based on the zero level set of the boundary, the exterior points lying outside the boundary, and finally the best approximate zero level set of the boundary, respectively. Extensive experimental evaluation demonstrated that the proposed LSM based novelty detection approaches outperform a selection of four representative traditional methods through the overall and relative performance analyses.

Date of Award	Feb 2014
Original language	English
Sponsors	VCRS
Supervisor	Yuhua Li (Supervisor), Ammar Belatreche (Supervisor) & Liam Maguire (Supervisor)