Department of Mathematics
503 Boston Avenue
Medford, MA 02155
Email @tufts.edu: kye.taylor
High-dimensional, geometric and statistical processing of datasets.
Mankind's collection of data is increasingly expanding. For example, in
2009, American drones flying over Afghanistan returned over 24 years' worth
of video. To extract meaningful patterns or information from the large
amounts of (high-dimensional, nonlinear) data, transformations are
performed to identify and emphasize such features.
My research interest regards transformations of datasets that rely on
graph-based metrics. In this setting, data points associated with vertices
of the graphs. Relationships extracted from (dis)similarities in the
data's features are associated with edges of the graph. The resulting
graph creates a new geometry on which to define metrics, which can
ultimately be used to embed the dataset in a new space. In addition to
interpreting the embedding, another challenge that interests me is
efficiently calculating the embedding via decomposition of a "data matrix,"
using techniques such as random SVD and multilevel eigensolvers.