Iterative Spectral Stabilization for Non-Uniform Multicollinearity in Integrated Datasets

Abstract

Large-scale integrated datasets often exhibit non-uniform multicollinearity, where dissimilar correlation structures across batches make the merged feature set unstable, creating a critical bottleneck for stable regression analysis. While conventional methods such as Principal Component Analysis (PCA) and Ridge regression provide numerical stability, their uniform treatment of the singular spectrum often results in information loss or severe global bias. This paper proposes Iterative Spectral Stabilization (ISS) to stabilize the feature matrix while maintaining the integrity of the original coordinate system. The method herein is a targeted singular value decomposition (SVD) based reconditioning algorithm to mitigate multicollinearity in integrated datasets. ISS uses an iterative spectrum correction to selectively raise the near-zero singular values to a condition number threshold while preserving the feature structure. Experimental results in diverse and ill-conditioned scenarios demonstrate that ISS achieves up to 50% reduction in Frobenius distortion compared to PCA. It also consistently yields a lower Squared Error of Coefficients (SEC) than Ridge and Elastic Net regression methods. ISS provides a controllable trade-off between numerical stability and parameter estimation accuracy by setting a target condition number. This uniquely positions ISS for heterogeneous datasets where mitigating localized multicollinearity cannot come at the expense of feature interpretability.