AdaptICA: Data-Adaptive Transformation Learning for Independent Component Analysis

2026-07-23

AI Summary

Standard independent component analysis (ICA) assumes a linear mixing structure in the observed data, an assumption often violated when applied to nonlinearly preprocessed features such as EEG band power. To address this limitation, this work proposes AdaptICA, a framework that jointly models learnable per-component transformations—applied in a grouped manner—and the demixing matrix, optimized under a contrastive mutual information criterion. Theoretically, this study establishes, for the first time, the identifiability, consistency, and asymptotic normality of the proposed joint estimator, while enabling data-driven, adaptive activation of transformations and maintaining compatibility with standard ICA. Experimental results demonstrate that AdaptICA recovers more independent and interpretable source signals when scale adjustments are necessary, and automatically reduces to standard ICA otherwise.

Abstract

Independent component analysis (ICA) is widely used to recover latent structure from signal and imaging data, but standard ICA assumes that the observed measurement scale preserves a linear mixing structure. This assumption may fail for features produced through nonlinear preprocessing, such as band-specific power in motor-imagery EEG. We propose AdaptICA, an adaptive transformation-based framework that jointly learns grouped componentwise transformations and the demixing structure using a profiled mutual-information criterion. Because the transformation and demixing parameters may compensate for one another, their joint estimation introduces new identifiability and asymptotic challenges. We establish identifiability, consistency, and asymptotic normality of the transformation estimator, together with joint strong consistency of the transformation and demixing estimators. AdaptICA selects the transformation structure data-adaptively and includes the identity transformation as a candidate, thereby reducing to standard ICA when no scale adjustment is needed. Extensive simulations support the theoretical results. Applications demonstrate that AdaptICA can recover more independent and interpretable sources when transformation is beneficial while retaining standard ICA when the original measurement scale is adequate.

Problem

• Independent Component Analysis
• nonlinear preprocessing
• measurement scale
• latent structure
• linear mixing

Innovation

• AdaptICA
• data-adaptive transformation
• independent component analysis
• mutual information
• identifiability