Density-based Adaptive Mode Decomposition

Abstract

Variational Mode Decomposition (VMD) requires manual specification of mode numbers and center frequencies, limiting its practical applicability for non-stationary signals. This paper introduces Density-based Adaptive Mode Decomposition (DAMD), which addresses these limitations through three key innovations. First, we establish mathematical equivalence between VMD optimization and density-based clustering, enabling automatic mode detection through meanshift clustering with adaptive bandwidth estimation. Second, we develop Direct Mode Extraction that replaces iterative optimization with efficient clustering, and Hybrid Variational Refinement for selective precision enhancement. Third, we extend the framework to diverse time-frequency representations including wavelets and synchrosqueezed transforms. Experimental validation across biomedical signals, gravitational waves, mechanical faults, and speech data demonstrates significant computational improvements while maintaining perfect reconstruction. DAMD eliminates manual parameter tuning and enables automated adaptive signal decomposition for complex non-stationary signals.