FLAT: Fused Lasso Regression with Adaptive Minimum Spanning Tree with Applications on Thermohaline Circulation

TL;DR

This paper presents FLAT, a novel fused lasso regression method utilizing an adaptive minimum spanning tree to detect spatial heterogeneity and boundaries, with applications in oceanography and thermohaline circulation analysis.

Contribution

It introduces a new adaptive minimum spanning tree guided by spatial and coefficient dissimilarity, combined with fused and LASSO regularizations for spatial heterogeneity detection.

Findings

Effective in estimation and heterogeneity detection in simulations

Identified new temperature-salinity surfaces in Atlantic Ocean data

Demonstrated practical utility in oceanographic applications

Abstract

This article introduces a new methodology model both discrete and continuous spatial heterogeneity simultaneously with an application in detection of hyper-plain in thermohaline circulation. To enable the data-driven detection of spatial boundaries with heterogeneity, we constructs an adaptive minimum spanning tree guided by both spatial proximity and coefficient dissimilarity, and combines both a spatial fused regularization and LASSO-type regularization to estimate the spatial coefficients under the framework of spatial regression. Numerical simulations demonstrate the effectiveness of proposed method in both estimation and heterogeneity detection. The usefulness of the approach is further illustrated via an analysis of oceanic data that provides new empirical finds about Atlantic with detected surfaces in temperature-salinity relationship.