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In this work, we revisit fast dimension reduction approaches, as with randomprojections and random sampling. Our goal is to summarize the data to decreasecomputational costs and memory footprint of subsequent analysis. Such dimensionreduction can be very efficient when the signals of interest have a strongstructure, such as with images. We focus on this setting and investigatefeature clustering schemes for data reductions that capture this structure. Animpediment to fast dimension reduction is that good clustering comes with largealgorithmic costs. We address it by contributing a linear-time agglomerativeclustering scheme, Recursive Nearest Agglomeration (ReNA). Unlike existing fastagglomerative schemes, it avoids the creation of giant clusters. We empiricallyvalidate that it approximates the data as well as traditionalvariance-minimizing clustering schemes that have a quadratic complexity. Inaddition, we analyze signal approximation with feature clustering and show thatit can remove noise, improving subsequent analysis steps. As a consequence,data reduction by clustering features with ReNA yields very fast and accuratemodels, enabling to process large datasets on budget. Our theoretical analysisis backed by extensive experiments on publicly-available data that illustratethe computation efficiency and the denoising properties of the resultingdimension reduction scheme.

Recursive nearest agglomeration (ReNA): fast clustering for approximation of structured signals