ICALCC: Locally Centered Contrast Functions for FastICA with GPU Acceleration

Bounded locally centered contrasts are introduced for independent component analysis. Classical FastICA contrast functions evaluate each sample in isolation and cannot adapt to the shape of the source distribution. The locally centered mechanism replaces the pointwise nonlinearity with a pairwise statistic that averages a kernel derivative over sample differences, inheriting the outlier robustness of bounded functions while gaining sensitivity to distributional asymmetry through the pairwise structure. Two bounded kernels are proposed: LCC-tanh, based on the log-cosh kernel, and LCC-exp, based on the Gaussian kernel. LCC-exp admits an exact interpretation as maximizing Rényi entropy of order 2, connecting the method to informationtheoretic source separation. Both contrasts are implemented in the ICALCC Python package, a drop-in scikit-learn subclass that also provides polynomial locally centered contrasts of order 4, 6, and 8 for near-Gaussian regimes. A GPU-accelerated extension using PyTorch scales the pairwise computation to datasets of up to 10 6 samples, achieving 40-48× speedup over the CPU implementation.