I am interested in using topological methods to understand data. I am currently interested in analyzing dimensionality reduction techniques, and proving guarantees for finite samples and noisy data points. I am also working on a project from molecular dynamics where we are working on using machine learning techniques to create fast approximate molecule simulators learned from data obtained from slow simulations.

David McClure

My research is related to image/video analysis, specifically object tracking. Our goal is to determine a simple, yet adequate and generalizable representation of an object in video and construct a probabilistic framework to describe how that can change over time (including motion, scale, rotation, occlusions, etc.). We aim for it to be accurate and efficient enough to take an object specified at time 0 and predict its position using incoming video data with high fidelity in close to real time.

I am interested in using topological methods to understand data. Lately, I have been working in the area of probabilistic sensor network coverage. I have been investigating the use of a homological criterion to tell when the sensor network no longer covers a given domain. I am also working on creating a model using topological methods to understand baboon and chimpanzee community fission/fusion dynamics using data from Gombe Stream National Park in Tanzania.

I'm a first year PhD statistics student studying for my qualifying exams. My research interests include shape analysis, specifically relating to protein structures.

I try to develop algebraic and topological tools for application in a wide variety of scientific areas, particularly the analysis of complex and high-dimensional datasets, and to build useful bridges between computational topology, diffusion geometry, and statistical methodology.

Data from many physical experiments arise as time series, which often contain long-range dependencies over time. Using tools from dynamical systems and ergodic theory, I seek to understand the statistical properties of such data. In particular, I would like to understand the extent to which Conley index theory may be used to make inferences about the dynamical processes generating the data.

My main research interest is algebraic topology and its applications to the analysis of point cloud data. Other topics that interest me are computer vision and computational biology.

My current research focuses on both mathematical and practical aspects of signal processing, specifically sparse approximation and compressed sensing. I work on developing and analyzing algorithms for finding sparse representations of signals and for signal reconstruction from compressed sensing measurements. My current work also includes quantization of redundant representations and quantization of compressed sensing measurements.

I research techniques and algorithms for high dimensional data analysis. I primarily study mathematical methods in machine learning, manifold learning, geometry and topology, and Bayesian statistics. Applications to data summarization, navigation, and visualization are my primary motivations.

Topological data analysis, multi-scale topology

Graph theory, multi-scale geometry

Wavelets, harmonic analysis

Geometry and topology for stochastic modeling

Statistical shape analysis, probability, computational biology

Information theory, coding theory

Scientific computing, multi-scale geometry

Stochastic processes, statistical computation, environmental science

Spatial statistics, random fields

Computational geometry, spatial statistics

Bayesian statistics, compressed sensing, very high-dimensional data

Inference for point processes, medical imaging, social networks