Mathematical methods for visualization and anomaly detection in telemetry datasets

Recent developments in both biological data acquisition and analysis provide new opportunities for data-driven modelling of the health state of an organism. In this paper, we explore the evolution of temperature patterns generated by telemetry data collected from healthy and infected mice. We investigate several techniques to visualize and identify anomalies in temperature time series as temperature relates to the onset of infectious disease. Visualization tools such as Laplacian Eigenmaps and Multidimensional Scaling allow one to gain an understanding of a dataset as a whole. Anomaly detection tools for nonlinear time series modelling, such as Radial Basis Functions and Multivariate State Estimation Technique, allow one to build models representing a healthy state in individuals. We illustrate these methods on an experimental dataset of 306 Collaborative Cross mice challenged with Salmonella typhimurium and show how interruption in circadian patterns and severity of infection can be revealed directly from these time series within 3 days of the infection event.