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

TL;DR

ReNA is a fast, linear-time agglomerative clustering method designed for structured signals like images, enabling efficient data reduction, noise removal, and accurate modeling for large datasets.

Contribution

We introduce ReNA, a novel linear-time clustering algorithm that approximates data effectively while avoiding large clusters, improving speed and accuracy in structured signal analysis.

Findings

ReNA achieves comparable data approximation to quadratic algorithms.

It effectively removes noise, enhancing analysis accuracy.

ReNA enables processing large datasets efficiently.

Abstract

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.