论文标题
通过稀疏凸小波群集同时进行分组和降解
Simultaneous Grouping and Denoising via Sparse Convex Wavelet Clustering
论文作者
论文摘要
聚类是数据科学和信号处理中的无处不在的问题。在我们观察到嘈杂信号的许多应用程序中，首先使用小波降解，然后应用群集算法是普遍做法。在本文中，我们开发了一种稀疏的凸小波群集方法，同时降解和发现群体。我们的方法利用凸融合惩罚来实现集聚和小组范围的惩罚，以通过小波域中的稀疏性来降级。与当时簇的常见实践相反，我们的方法是一种同时执行的统一的凸方法。我们的方法产生了deNo的（小波）群集质心，既可以改善解释性和数据压缩。我们证明了我们的合成示例和NMR光谱应用的方法。
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.
