Theses and Dissertations
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- All Subjects: manifolds
- All Subjects: vernacular
- Creators: Turaga, Pavan
Description
The data explosion in the past decade is in part due to the widespread use of rich sensors that measure various physical phenomenon -- gyroscopes that measure orientation in phones and fitness devices, the Microsoft Kinect which measures depth information, etc. A typical application requires inferring the underlying physical phenomenon from data, which is done using machine learning. A fundamental assumption in training models is that the data is Euclidean, i.e. the metric is the standard Euclidean distance governed by the L-2 norm. However in many cases this assumption is violated, when the data lies on non Euclidean spaces such as Riemannian manifolds. While the underlying geometry accounts for the non-linearity, accurate analysis of human activity also requires temporal information to be taken into account. Human movement has a natural interpretation as a trajectory on the underlying feature manifold, as it evolves smoothly in time. A commonly occurring theme in many emerging problems is the need to \emph{represent, compare, and manipulate} such trajectories in a manner that respects the geometric constraints. This dissertation is a comprehensive treatise on modeling Riemannian trajectories to understand and exploit their statistical and dynamical properties. Such properties allow us to formulate novel representations for Riemannian trajectories. For example, the physical constraints on human movement are rarely considered, which results in an unnecessarily large space of features, making search, classification and other applications more complicated. Exploiting statistical properties can help us understand the \emph{true} space of such trajectories. In applications such as stroke rehabilitation where there is a need to differentiate between very similar kinds of movement, dynamical properties can be much more effective. In this regard, we propose a generalization to the Lyapunov exponent to Riemannian manifolds and show its effectiveness for human activity analysis. The theory developed in this thesis naturally leads to several benefits in areas such as data mining, compression, dimensionality reduction, classification, and regression.
ContributorsAnirudh, Rushil (Author) / Turaga, Pavan (Thesis advisor) / Cochran, Douglas (Committee member) / Runger, George C. (Committee member) / Taylor, Thomas (Committee member) / Arizona State University (Publisher)
Created2016
Description
This thesis aims to explore the language of different bodies in the field of dance by analyzing
the habitual patterns of dancers from different backgrounds and vernaculars. Contextually,
the term habitual patterns is defined as the postures or poses that tend to re-appear,
often unintentionally, as the dancer performs improvisational dance. The focus lies in exposing
the movement vocabulary of a dancer to reveal his/her unique fingerprint.
The proposed approach for uncovering these movement patterns is to use a clustering
technique; mainly k-means. In addition to a static method of analysis, this paper uses
an online method of clustering using a streaming variant of k-means that integrates into
the flow of components that can be used in a real-time interactive dance performance. The
computational system is trained by the dancer to discover identifying patterns and therefore
it enables a feedback loop resulting in a rich exchange between dancer and machine. This
can help break a dancer’s tendency to create similar postures, explore larger kinespheric
space and invent movement beyond their current capabilities.
This paper describes a project that distinguishes itself in that it uses a custom database
that is curated for the purpose of highlighting the similarities and differences between various
movement forms. It puts particular emphasis on the process of choosing source movement
qualitatively, before the technological capture process begins.
the habitual patterns of dancers from different backgrounds and vernaculars. Contextually,
the term habitual patterns is defined as the postures or poses that tend to re-appear,
often unintentionally, as the dancer performs improvisational dance. The focus lies in exposing
the movement vocabulary of a dancer to reveal his/her unique fingerprint.
The proposed approach for uncovering these movement patterns is to use a clustering
technique; mainly k-means. In addition to a static method of analysis, this paper uses
an online method of clustering using a streaming variant of k-means that integrates into
the flow of components that can be used in a real-time interactive dance performance. The
computational system is trained by the dancer to discover identifying patterns and therefore
it enables a feedback loop resulting in a rich exchange between dancer and machine. This
can help break a dancer’s tendency to create similar postures, explore larger kinespheric
space and invent movement beyond their current capabilities.
This paper describes a project that distinguishes itself in that it uses a custom database
that is curated for the purpose of highlighting the similarities and differences between various
movement forms. It puts particular emphasis on the process of choosing source movement
qualitatively, before the technological capture process begins.
ContributorsIyengar, Varsha (Author) / Xin Wei, Sha (Thesis advisor) / Turaga, Pavan (Committee member) / Coleman, Grisha (Committee member) / Arizona State University (Publisher)
Created2016