Browsing by Author "Zheng, Xiaojun"

With remarkable advances in sensing and experimental technologies, scientists and engineers now have access to massive datasets with complex forms for decision-making, and the ability to efficiently process and analyze high-dimensional datasets in real time is more critical than ever. Anomaly detection and change point detection are pivotal in various applications, from video surveillance to solar activity monitoring, enabling timely responses to dynamic changes and aberrant behaviors within the data.

This dissertation offers three main contributions to the field. In Chapter 1, we introduce a novel persistence diagram-based method for change point detection, and the key component is to leverage the embedded topological structured from topological data analysis. In Chapter 2, we extend the Robust Principal Component Analysis to accommodate Exponential Family distributions. This extension enables the decomposition of data into low-rank and sparse matrices, where the sparse matrix effectively captures anomalies essential for process monitoring and diagnosis. In Chapter 3, we propose a Bayesian change-point detection framework, which incorporates image and spatial features learned from Gaussian Markov random fields. We investigate the effectiveness of our proposed methods through extensive numerical experiments, and demonstrate their applicability in diverse fields such as engineering, physics, and computer vision.