Graph aware adaptive tracking-error optimization with wavelet-principal component analysis features and proportional-integral control (GATE-WPCA-PI)

We introduced GATE-WPCA-PI—geometry-aware, tracking-error-controlled allocation with wavelet principle component analysis features and a proportional-integral controller—a practical portfolio construction framework that linked multi-scale market geometry to explicit, out-of-sample risk targeting. At each rebalance, the daily returns were embedded in a multi-resolution wavelet feature space and compressed via principal component analysis to form a similarity kernel. A simple discriminative-power score gated the optimizer: when the cross section was heterogeneous, the feature geometry was activated; when it was homogeneous, the method reverted to a correlation-only view. Allocations were obtained from an implementable mean–variance surrogate with (ⅰ) a geometry penalty that discouraged concentration in highly similar assets, (ⅱ) quadratic and absolute turnover costs, (ⅲ) an entropy floor, and (ⅳ) standard long-only, budget, and sleeve caps. A proportional-integral (PI) law treated the tracking error (TE) as a controllable state and steered realized TE toward a feasible band under trading frictions.