Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

Detecting drift from event streams of unpredictable business processes

Existing business process drift detection methods do not work with event streams. As such, they are designed to detect inter-trace drifts only, i.e. drifts that occur between complete process executions (traces), as recorded in event logs. However, process drift may also occur during the execution of a process, and may impact ongoing executions. Existing methods either do not detect such intra-trace drifts, or detect them with a long delay. Moreover, they do not perform well with unpredictable processes, i.e. processes whose logs exhibit a high number of distinct executions to the total number of executions. We address these two issues by proposing a fully automated and scalable method for online detection of process drift from event streams. We perform statistical tests over distributions of behavioral relations between events, as observed in two adjacent windows of adaptive size, sliding along with the stream. An extensive evaluation on synthetic and real-life logs shows that our method is fast and accurate in the detection of typical change patterns, and performs significantly better than the state of the art.