Sequential multiple change point detection concerns the identification of multiple points in time where the systematic behavior of a statistical process changes. A special case of this problem, called online anomaly detection, occurs when the goal is to detect the first change and then signal an alert to an analyst for further investigation. This dissertation concerns the use of methods based on kernel functions and support vectors to detect changes. A variety of support vector-based methods are considered, but the primary focus concerns Least Squares Support Vector Data Description (LS-SVDD). LS-SVDD constructs a hypersphere in a kernel space to bound a set of multivariate vectors using a closed-form solution. The mathematical tractability of the LS-SVDD facilitates closed-form updates for the LS-SVDD Lagrange multipliers. The update formulae concern either adding or removing a block of observations from an existing LS-SVDD description, respectively, and thus LS-SVDD can be constructed or updated sequentially which makes it attractive for online problems with sequential data streams. LS-SVDD is applied to a variety of scenarios including online anomaly detection and sequential multiple change point detection
