SBIR-STTR Award

We propose to evaluate strategies for extracting geometric information from very large and high dimensional data sets. One aspect of the proposal will be the development of a strategy for the implementation of parallelism within the methodology already developed within the DARPA Topological Data Analysis project. This will include parallel and distributed methods for persistent homology computations, clustering, and density estimation. The second aspect will be the incorporation of the "zig-zag" methodology for assessing the consistency of clustering and consistency across sets of landmark points in witness complex constructions.

Keywords:
Point Clouds, Persistent Homology, Clustering, Density Estimation, Geometric Data Analysis

We propose to implement the ideas on parallelization of the Mapper (see [14]) visualization methodology developed under our SBIR Phase I effort. Specifically, we will use the MapReduce model, within the Hadoop framework. This development will permit the construction of Mapper outputs for very large data sets. Such methods can then be used to obtain understanding of the massive data sets coming out of the study of internet traffic and advertising, financial market time series, monitoring of consumer behavior within the retail area, and from many other settings.

Keywords:
Topology, Parallel Computing, Data Analysis, Mapping, Clustering