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Physics-Based Anomaly Detection Defined on Manifold Space

Physics-Based Anomaly Detection Defined on Manifold Space Physics-Based Anomaly Detection Defined on Manifold Space HAO HUANG and HONG QIN, Computer Science Department, Stony Brook University SHINJAE YOO and DANTONG YU, Computational Science Center, Brookhaven National Laboratory 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Knowledge Discovery from Data (TKDD) Association for Computing Machinery

Physics-Based Anomaly Detection Defined on Manifold Space

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References (56)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
1556-4681
DOI
10.1145/2641574
Publisher site
See Article on Publisher Site

Abstract

Physics-Based Anomaly Detection Defined on Manifold Space HAO HUANG and HONG QIN, Computer Science Department, Stony Brook University SHINJAE YOO and DANTONG YU, Computational Science Center, Brookhaven National Laboratory 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

Journal

ACM Transactions on Knowledge Discovery from Data (TKDD)Association for Computing Machinery

Published: Sep 23, 2014

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