The investigator and his colleagues undertake a coordinated effort to bring to bear ideas from analysis, geometry, and statistics on the problem of analysing spectroscopic data in high dimensions. A major challenge confronting the analytical chemist involves the organization and manipulation of massive amounts of data, both measured and computed. Recent work indicates that special geometric structures allow for efficient transcription and modeling of the relation between spectral measurements and material composition. The investigators develop tools to identify such structures and to automate the process of analysis and feature extraction. In particular, the investigators concentrate on near-infrared spectra of blood, with the goal being to estimate concentrations of various blood analytes from noninvasive spectrometric measurements. The multidisciplinary team undertakes a coherent approach in which various aspects of chemical analysis, blood pathology, and sensor engineering interact with mathematical analytic tools. They adapt and extend computational software to the particular geometry of chemical spectra, for which the data manifolds need to be parametrized by the concentrations of various constituent materials. To achieve such parametrizations, they exploit mathematical tools for local multiscale descriptions of data together with clustering techniques that occur naturally in the context of data analysis for expression profiles of gene arrays. Shining a light on the skin allows one to get spectral data about the blood beneath the skin and its chemical components. Hence noninvasive blood analysis is possible, if only one could make sense of the data. The investigator and his colleagues apply a range of mathematical and statistical ideas to build tools that can make sense of such data. There are important medical payoffs because of the role blood chemistry plays in health. Moreover, the underlying mathematical problem, to find efficient ways to make sense of enormous volumes of high-dimensional data, arises across science and engineering, so the potential impact of the project is even wider. The project provides interdisciplinary research and training opportunities for students and postdocs.
