Medical and biological data often come in the form of digitized signals and images; for example, magnetic resonance images, electrocardiogram traces and even the folding paths of proteins. As instrumental data acquisition becomes routine, sequences of such images, signals or paths are collected, often along with other covariate measurements, resulting in datasets where the basic unit of measurement, or response, is a high-dimensional object. The project continues to focus on developing techniques for modelling and understanding such data that explicitly take into account, and indeed exploit inherent spatial or temporal correlation, and when appropriate, relate it to covariate or class label information. To study covariance structure, the project proposes "sparse" forms of principal components and discriminant analysis that may be more sensitive to either local phenomena of not necessarily smooth form or that are more adapted to irregularly observed data. Corresponding quadratically regularized methods in appropriate bases form a natural foil for comparison, and will also be developed in certain applications. For estimation of means, the project will examine sparse empirical Bayes methods for estimating non smooth local phenomena. Much of this work will be carried out in existing and new collaborations with researchers in medical imaging, cardiology and other specialties, working for example on cancer, heart disease and brain mapping.
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