Recursive nearest agglomeration (ReNA): fast clustering for approximation of structured signals
This work provides a fast and accurate dimension reduction method for processing large datasets with structured signals, such as in image analysis, though it appears incremental as it builds on existing clustering approaches.
The authors tackled the problem of fast dimension reduction for structured signals like images by introducing Recursive Nearest Agglomeration (ReNA), a linear-time clustering scheme that approximates data as well as traditional quadratic-complexity methods and removes noise to improve analysis.
In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure, such as with images. We focus on this setting and investigate feature clustering schemes for data reductions that capture this structure. An impediment to fast dimension reduction is that good clustering comes with large algorithmic costs. We address it by contributing a linear-time agglomerative clustering scheme, Recursive Nearest Agglomeration (ReNA). Unlike existing fast agglomerative schemes, it avoids the creation of giant clusters. We empirically validate that it approximates the data as well as traditional variance-minimizing clustering schemes that have a quadratic complexity. In addition, we analyze signal approximation with feature clustering and show that it can remove noise, improving subsequent analysis steps. As a consequence, data reduction by clustering features with ReNA yields very fast and accurate models, enabling to process large datasets on budget. Our theoretical analysis is backed by extensive experiments on publicly-available data that illustrate the computation efficiency and the denoising properties of the resulting dimension reduction scheme.