Locally Centered Cyclic Kernels for Higher-Order Independent Component Analysis

Independent component analysis algorithms such as FastICA rely on higher-order cumulant estimation to separate non-Gaussian sources. The standard sample-cumulant estimator is asymptotically inconsistent: the bias between the estimated and true cumulants does not vanish with sample size, and the cumulative distortion is bounded by the Itakura-Saito divergence between the source density and its Gaussian proxy. A locally centered cyclic (LCC) kernel is proposed as a drop-in replacement that preserves full cumulant information at every expansion order through a nondegenerate V-statistic. An asymptotic relative efficiency (ARE) analysis identifies the operating regime: LCC outperforms FastICA on super-Gaussian sources of moderate kurtosis, where cubic nonlinearity provides insufficient contrast gradient, while extreme kurtosis marks the boundary where estimator variance overtakes the bias reduction from higher orders. Experiments on synthetic sources, grayscale image unmixing, and MUSDB18 music stem separation confirm both the predicted gains and their limits.