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Summary form only given. Computer vision (the study of extracting information from images that includes robot vision, smart video surveillance, multi-media image search, camera-based human computer interfaces, etc.) deals with very large data rates: but it generally also has to contend with high-dimensional data and incomplete data and noise. The basic tools underpinning much of contemporary computer vision research: clustering, large (and possibly incomplete) matrix factorization, regression/model fitting, manifold learning etc.; are tools common to many other branches of computing. In this article, the author draw upon examples from his own research work to outline recent advances in dealing with high-dimensional data. Illustrative applications is given from computer vision problems (with some links made to other application areas).