Topology-Aware Optimal Transport for Sparse Representation Classification

Sparse representation classification (SRC) typically assigns a test sample to the class with the smallest Euclidean reconstruction residual. However, this comparison can be inappropriate when the feature representation has a known non-Euclidean topology. We propose topology-aware optimal-transport sparse representation classification (TAOT-SRC), which constructs class-specific reconstructions using the transport cost induced by an entropically regularized OT coupling whose ground cost reflects the intrinsic geometry of the feature support. For unsigned histograms of oriented gradients, the proposed formulation models orientation using circular geodesic distance rather than an unwrapped angular metric. Experiments with validation-seed-based hyperparameter selection show consistent improvements over canonical signed $\ell _{1}$-SRC. On Digits, TAOT-SRC achieves 76.00% clean accuracy and 55.73%/48.47% under $\pm 10^\circ /\pm 20^\circ$ rotations, compared with 67.53%/44.60%/40.47% for SRC. On LFW face/non-face classification, clean accuracy improves from 84.22% to 89.89%. Ablation studies further show that the improvement arises from matching the reconstruction geometry to the topology of the feature space rather than from transport scoring alone.