Discovering Geometry in Data Arrays

Modern technologies produce a deluge of complicated data. In neuroscience, for example, minimally invasive experimental methods can take recordings of large populations of neurons at high resolution under a multitude of conditions. Such data arrays possess non-trivial interdependencies along each of their axes. Insights into these data arrays may lay the foundations of advanced treatments for nervous system disorders. The potential impacts of such data, however, will not be fully realized unless the techniques for analyzing them keep pace. Specifically, there is an urgent, growing need for methods for estimating the low-dimensional structure and geometry in big and noisy data arrays. This article reviews a framework for identifying complicated underlying patterns in such data and also recounts the key role that the Department of Energy Computational Sciences Graduate Fellowship played in setting the stage for this work to be done by the author.