Encoding Robust Topological Signatures for Hyperdimensional Computing

Hyperdimensional computing (HDC) enables lightweight prototype-based classification but pixel-based encoders are brittle under geometric and pixel-level corruption. We introduce a topology-guided HDC classifier that combines local HOG features, rotation/translation/scale-stable spatial-pyramid Zernike descriptors, and a robust hole-count compatibility score. Hole candidates are generated from multiscale bounded background components and validated using a spoke-wheel enclosure test. Their counts are converted into class-conditional topology scores learned from clean training data and fused with cosine similarities from HOG and Zernike HDC prototypes. On MNIST and EMNIST Letters, the method substantially improves robustness over naive HDC and often outperforms a compact CNN under Gaussian noise, salt-and-pepper noise, and severe scaling, without corruption-specific training. OnlineHD updates further improve clean and occlusion performance, although adaptation can reduce robustness under some noise settings. These results show that explicit, interpretable topology provides a practical complement to appearance-based HDC.