Collective Spectral Density Estimation and Clustering for Spatially-Correlated Data

TL;DR

This paper introduces a novel method for estimating and clustering 2D spectral density functions of spatial data, leveraging adaptive basis functions and penalties to improve clustering accuracy and interpretability.

Contribution

The paper proposes a new spectral density estimation and clustering approach using adaptive basis functions and penalties, enhancing clustering of spatially-correlated data.

Findings

Outperforms existing methods in simulation studies

Effectively identifies homogeneous spatial clusters in soil moisture data

Provides intuitive visualizations of spectral estimation and clustering

Abstract

In this paper, we develop a method for estimating and clustering two-dimensional spectral density functions (2D-SDFs) for spatial data from multiple subregions. We use a common set of adaptive basis functions to explain the similarities among the 2D-SDFs in a low-dimensional space and estimate the basis coefficients by maximizing the Whittle likelihood with two penalties. We apply these penalties to impose the smoothness of the estimated 2D-SDFs and the spatial dependence of the spatially-correlated subregions. The proposed technique provides a score matrix, that is comprised of the estimated coefficients associated with the common set of basis functions representing the 2D-SDFs. {Instead of clustering the estimated SDFs directly, we propose to employ the score matrix for clustering purposes, taking advantage of its low-dimensional property.} In a simulation study, we demonstrate that our proposed method outperforms other competing estimation procedures used for clustering. Finally, to validate the described clustering method, we apply the procedure to soil moisture data from the Mississippi basin to produce homogeneous spatial clusters. We produce animations to dynamically show the estimation procedure, including the estimated 2D-SDFs and the score matrix, which provide an intuitive illustration of the proposed method.