Problematic Projection to the In-Sample Subspace for a Kernelized Anomaly Detector

We examine the properties and performance of kernelized anomaly detectors, with an emphasis on the Mahalanobis-distance-based kernel RX (KRX) algorithm. Although the detector generally performs well for high-bandwidth Gaussian kernels, it exhibits problematic (in some cases, catastrophic) performanc...

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Bibliographic Details
Published in:IEEE geoscience and remote sensing letters 2016-04, Vol.13 (4), p.485-489
Main Authors: Theiler, James, Grosklos, Guen
Format: Article
Language:English
Subjects:
Adaptive signal detection
Algorithms
Anomalies
Anomaly detection
Bandwidth
Covariance matrices
data models
Detectors
Gaussian
Gaussian distribution
GEOSCIENCES
Hyperspectral imaging
kernel density estimation
kernel-RX
Kernels
mahalanobis distance
MATHEMATICS AND COMPUTING
multidimensional signal processing
pattern recognition
Projection
Remote sensing
singular value decomposition
spectral analysis
Unsupervised learning
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Description
Summary:We examine the properties and performance of kernelized anomaly detectors, with an emphasis on the Mahalanobis-distance-based kernel RX (KRX) algorithm. Although the detector generally performs well for high-bandwidth Gaussian kernels, it exhibits problematic (in some cases, catastrophic) performance for distances that are large compared to the bandwidth. By comparing KRX to two other anomaly detectors, we can trace the problem to a projection in feature space, which arises when a pseudoinverse is used on the covariance matrix in that feature space. We show that a regularized variant of KRX overcomes this difficulty and achieves superior performance over a wide range of bandwidths.
ISSN:1545-598X
1558-0571
DOI:10.1109/LGRS.2016.2516985