Topological Signal Processing With Unoriented Operators
Read the original on arXiv Machine Learning →Topological signal processing (TSP) traditionally uses oriented boundary operators to process signals on simplicial complexes, which is suitable for flow signals or when topological invariants are important. This paper introduces an unoriented TSP (UTSP) framework that replaces oriented boundaries with unoriented incidence matrices, demonstrating that these matrices retain graph-like spectral properties across simplicial levels. By removing orientation, the authors develop an interaction-order decomposition—an analogue to Hodge decomposition—to quantify how higher-order signals are explained by aggregating lower-order signals, and use this decomposition to create order-aware regularizers that outperform oriented baselines in real-world experiments, especially when signal energy is unevenly distributed across orders.
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