Michael Fauß, Michael Muma and Abdelhak M. Zoubir
Princeton University, TU Darmstadt
With rapid developments in signal processing and data analytics, driven by technological advances towards a more intelligent networked world, there is an ever-increasing need for reliable and robust information extraction and processing. Robust statistical methods account for the fact that the postulated models for the data are fulfilled only approximately and not exactly. In contrast to classical parametric procedures, robust methods are not significantly affected by small changes in the data, such as outliers or minor model departures. In practice, many engineering applications involve measurements that are not Gaussian and that may contain corrupted measurements and outliers, which cause the data distributions to be heavy-tailed. This leads to a breakdown in performance of traditional signal processing techniques that are based on Gaussian models.
The focus of this tutorial is on recent advances in the related areas of robust detection and robust cluster analysis for unsupervised learning. This tutorial is organized into two parts. In the first part, we discuss robust detection for a given number of hypotheses. In the second part, we move to robust cluster analysis with a focus on recent advances in robust cluster enumeration.