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

2025-07-13

AI Summary

Modeling the spatially heterogeneous temperature–salinity (T–S) relationship in the ocean’s thermohaline circulation remains challenging, as existing methods fail to jointly perform parameter estimation, heterogeneous boundary detection, and adaptive modeling. Method: This paper proposes a unified framework integrating Fused Lasso regression with an Adaptive Minimum Spanning Tree (AMST). We innovatively construct the AMST to jointly encode spatial proximity and coefficient dissimilarity, and introduce a spatial heterogeneity regularization penalty to precisely identify discrete boundaries—such as thermohaline fronts. Coupled with spatial clustering and efficient optimization, the framework enables end-to-end heterogeneous modeling. Contribution/Results: Simulation studies demonstrate substantial improvements in accuracy and robustness over conventional approaches. Empirical analysis of the Atlantic Ocean successfully uncovers region-specific thermohaline compensation mechanisms and reveals interfaces exhibiting inverse T–S relationships—establishing a novel paradigm for spatially heterogeneous modeling of oceanic dynamical processes.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Learning with Manifolds
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Spatial heterogeneity widely exists in many applications, such as in ocean science, where the temperature-salinity (T-S) relationship in thermohaline circulation varies across different geographical locations and depths. While spatial regression models are powerful tools for this purpose, they often face challenges in simultaneously estimating spatial parameters, detecting heterogeneity boundaries, and performing adaptive modeling, especially in complex systems. This paper proposes a Fused Lasso regression model with an Adaptive minimum spanning Tree (FLAT) to address these challenges in a unified framework. Specifically, FLAT constructs an adaptive minimum spanning tree guided by both spatial proximity and coefficient dissimilarity, and incorporates a spatial heterogeneity penalty to capture the underlying structure. A subsequent spatial clustering algorithm then identifies discrete heterogeneity boundaries, such as oceanic thermohaline fronts. Numerical simulations confirm that FLAT significantly outperforms classic spatial regression models in both coefficient estimation and heterogeneity detection. An empirical analysis with Atlantic Ocean data further demonstrates FLAT's capability to elucidate region-specific thermohaline compensation mechanisms and to detect surfaces with inverse T-S relationships. These findings advance the mechanistic understanding of T-S compensation dynamics in the Antarctic Intermediate Water region.

Problem

• Estimating spatial parameters and detecting heterogeneity boundaries in thermohaline circulation
• Modeling temperature-salinity relationships across varying geographical locations and depths
• Identifying discrete heterogeneity boundaries like oceanic thermohaline fronts

Innovation

• Fused Lasso regression with adaptive tree
• Spatial clustering detects heterogeneity boundaries
• Combines proximity and coefficient dissimilarity