High dimensional data, where the number of variables is larger than the sample size, are encountered in a wide range of areas such as microarray studies, finance, engineering, biometrics and neuroimaging. This project is on pattern recognition (classification and clustering) of high dimensional data. Statistical methodology (including recognition methods) available for analyzing such data suffers from the curse of dimensionality as the enormous number of variables poses challenges to conventional methods rendering them impractical due to limited amounts of available data. A natural solution is to add a dimension reduction step before the recognition method is employed. In particular, given observations in a high dimensional space, our goal is to find a low dimensional manifold which captures the information relevant to pattern recognition for these data. One approach is writing a probability model which straddles “practically relevant” and “mathematically tractable”; defining an objective function whose arg opt (over manifolds) will act as a useful surrogate for “manifold with the most relevant information”; and finding a good approximation for the arg opt. This procedure must be accomplished in real-time in a dynamic environment to produce, e.g. an “adaptive sensor” adapting its low-dimensional view based on the pattern recognition exploitation function (rather than some far-afield surrogate such as signal-to-noise). In this project various methods are proposed to address the challenges of high-dimensional recognition by focusing on low-dimensional structures that approximate or encapsulate given high dimensional data. The main training objective of this research is to equip a European researcher with expertise about the theory and applications of high dimensional recognition, to become a competent user and trainer of this advanced methodology and to increase its availability in European research.
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