Hierarchical Probabilistic Model for Blind Source Separation via Legendre Transformation
This addresses the problem of separating mixed signals in fields like signal processing or data analysis, but appears incremental as it builds on existing BSS methods with a new hierarchical formulation.
The authors tackled blind source separation by proposing a hierarchical probabilistic model based on information geometry, which uniquely recovers source signals by minimizing KL divergence, and demonstrated superior performance on images and time series data compared to established techniques.
We present a novel blind source separation (BSS) method, called information geometric blind source separation (IGBSS). Our formulation is based on the log-linear model equipped with a hierarchically structured sample space, which has theoretical guarantees to uniquely recover a set of source signals by minimizing the KL divergence from a set of mixed signals. Source signals, received signals, and mixing matrices are realized as different layers in our hierarchical sample space. Our empirical results have demonstrated on images and time series data that our approach is superior to well established techniques and is able to separate signals with complex interactions.