Physics-based anomaly detection defined on manifold space

Current popular anomaly detection algorithms are capable of detecting global anomalies but often fail to distinguish local anomalies from normal instances. Inspired by contemporary physics theory (i.e., heat diffusion and quantum mechanics), we propose two unsupervised anomaly detection algorithms. Building on the embedding manifold derived from heat diffusion, we devise Local Anomaly Descriptor (LAD), which faithfully reveals the intrinsic neighborhood density. It uses a scale-dependent umbrella operator to bridge global and local properties, which makes LAD more informative within an adaptive scope of neighborhood. To offer more stability of local density measurement on scaling parameter tuning, we formulate Fermi Density Descriptor (FDD), which measures the probability of a fermion particle being at a specific location. By choosing the stable energy distribution function, FDD steadily distinguishes anomalies from normal instances with any scaling parameter setting. To further enhance the efficacy of our proposed algorithms, we explore the utility of anisotropic Gaussian kernel (AGK), which offers better manifold-aware affinity information. We also quantify and examine the effect of different Laplacian normalizations for anomaly detection. Comprehensive experiments on both synthetic and benchmark datasets verify that our proposed algorithms outperform the existing anomaly detection algorithms.