Multiscale Fast and Distributed Data and Statistics Summarization

This work seeks to demonstrate the wide spread applicability of Geometric Multi-Resolution Analysis (GMRA) to uncover low dimensional structure in large volume and high dimensional data sets. The objective is to show that the GMRA approach applies naturally to a variety of data types and to demonstrate its practical implementation in a scalable data intensive computing environment. The GMRA approach has many beneficial characteristics including linear scaling with the number of data points, multi-resolution representation of the data, robust to noise, provable error estimates, amenable to fast algorithms, and suitability for visualization and subsequent analysis. The coarse scale representation is a form summarization where separated partitions approximate the data. In addition, the representation at fine scales encode details and provide means to zoom into particular structures of the data. We will demonstrate that GMRA provides a natural structure to perform a variety of data analysis tasks including clustering, anomaly detection, change detection and visualization.