Simultaneous Grouping and Denoising via Sparse Convex Wavelet Clustering

TL;DR

This paper introduces a unified convex method that simultaneously denoises and clusters noisy signals in the wavelet domain, improving interpretability and data compression.

Contribution

It develops a novel sparse convex wavelet clustering approach that combines denoising and clustering into a single convex optimization framework.

Findings

Method outperforms traditional two-step approaches in synthetic tests.

Produces interpretable, wavelet-sparse cluster centroids.

Effective in NMR spectroscopy data analysis.

Abstract

Clustering is a ubiquitous problem in data science and signal processing. In many applications where we observe noisy signals, it is common practice to first denoise the data, perhaps using wavelet denoising, and then to apply a clustering algorithm. In this paper, we develop a sparse convex wavelet clustering approach that simultaneously denoises and discovers groups. Our approach utilizes convex fusion penalties to achieve agglomeration and group-sparse penalties to denoise through sparsity in the wavelet domain. In contrast to common practice which denoises then clusters, our method is a unified, convex approach that performs both simultaneously. Our method yields denoised (wavelet-sparse) cluster centroids that both improve interpretability and data compression. We demonstrate our method on synthetic examples and in an application to NMR spectroscopy.