Sensing physical and social environments are ubiquitous in modern mobile phones,
IoT devices, and infrastructure-based settings. Information engraved in such
data, especially the time and location attributes have unprecedented potential
to characterize individual and crowd behaviour, natural and technological processes.
However, it is challenging to extract abstract knowledge from the data
due to its massive size, sequential structure, asynchronous operation, noisy characteristics,
privacy concerns, and real time analysis requirements. Therefore, the
primary goal of this thesis is to propose theoretically grounded and practically
useful algorithms to learn from location and time stamps in sensor data. The
proposed methods are inspired by tools from geometry, topology, and statistics.
They leverage structures in the temporal and spatial data by probabilistically
modeling noise, exploring topological structures embedded, and utilizing statistical
structure to protect personal information and simultaneously learn aggregate
information. Proposed algorithms are geared towards streaming and distributed
operation for efficiency. The usefulness of the methods is argued using mathematical
analysis and empirical experiments on real and artificial datasets
