abstract: Today's world is seeing a rapid technological advancement in various fields, having access to faster computers and better sensing devices. With such advancements, the task of recognizing human activities has been acknowledged as an important problem, with a wide range of applications such as surveillance, health monitoring and animation. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. An alternative idea I propose is the use of descriptors of the shape of the dynamical attractor as a feature representation for quantification of nature of dynamics. The framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. Approximately 1\% of the total world population are stroke survivors, making it the most common neurological disorder. This increasing demand for rehabilitation facilities has been seen as a significant healthcare problem worldwide. The laborious and expensive process of visual monitoring by physical therapists has motivated my research to invent novel strategies to supplement therapy received in hospital in a home-setting. In this direction, I propose a general framework for tuning component-level kinematic features using therapists’ overall impressions of movement quality, in the context of a Home-based Adaptive Mixed Reality Rehabilitation (HAMRR) system. The rapid technological advancements in computing and sensing has resulted in large amounts of data which requires powerful tools to analyze. In the recent past, topological data analysis methods have been investigated in various communities, and the work by Carlsson establishes that persistent homology can be used as a powerful topological data analysis approach for effectively analyzing large datasets. I have explored suitable topological data analysis methods and propose a framework for human activity analysis utilizing the same for applications such as action recognition. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2016