The TWC Sigma Model: A Nonlinear Correlation and Neural Network Approach for Spatial Source Detection

The TWC Sigma model, part of the Topological Weighted Centroid (TWC) family, is introduced as a spatial framework for source localization in systems where network information is incomplete or unavailable. Its architecture relies on two alternative approaches: one based on nonlinear correlation, capable of capturing complex spatial dependencies among observed signals, and another based on supervised neural networks, which use adaptive learning on a discretized spatial grid to estimate the probability of hidden source localization. In both cases, TWC Sigma provides a robust and consistent mechanism to estimate the probable positions of hidden sources using only spatial coordinates and signal intensity. Applications on both synthetic and real-world datasets—such as those collected by Minna-no Data Site on post-Fukushima radiocesium contamination—confirm the model’s ability to identify both primary and secondary emission zones with strong spatial coherence. These results highlight TWC Sigma as an efficient and interpretable model that can be used both independently and as a complementary tool to more complex network-based frameworks, offering rapid and reliable localization even in the presence of sparse, noisy, or heterogeneous data.