NDLI: Outlier Detection with the Kernelized Spatial Depth Function

Content Provider	IEEE Xplore Digital Library
Author	Yixin Chen Xin Dang Hanxiang Peng Bart, H.L. Bart, H.L.
Copyright Year	1979
Abstract	Statistical depth functions provide from the deepest point a center-outward ordering of multidimensional data. In this sense, depth functions can measure the extremeness or outlyingness of a data point with respect to a given data set. Hence, they can detect outliers observations that appear extreme relative to the rest of the observations. Of the various statistical depths, the spatial depth is especially appealing because of its computational efficiency and mathematical tractability. In this article, we propose a novel statistical depth, the kernelized spatial depth (KSD), which generalizes the spatial depth via positive definite kernels. By choosing a proper kernel, the KSD can capture the local structure of a data set while the spatial depth fails. We demonstrate this by the half-moon data and the ring-shaped data. Based on the KSD, we propose a novel outlier detection algorithm, by which an observation with a depth value less than a threshold is declared as an outlier. The proposed algorithm is simple in structure: the threshold is the only one parameter for a given kernel. It applies to a one-class learning setting, in which normal observations are given as the training data, as well as to a missing label scenario, where the training set consists of a mixture of normal observations and outliers with unknown labels. We give upper bounds on the false alarm probability of a depth-based detector. These upper bounds can be used to determine the threshold. We perform extensive experiments on synthetic data and data sets from real applications. The proposed outlier detector is compared with existing methods. The KSD outlier detector demonstrates a competitive performance.
Sponsorship	IEEE Computer Society
Page Count	18
File Size	4701718
Starting Page	288
Ending Page	305
File Format	PDF
ISSN	01628828
Volume Number	31
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-02-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Kernel Detectors Fault detection Training data Detection algorithms Upper bound Object detection Multidimensional systems Computational efficiency Unsupervised learning unsupervised learning. Outlier detection novelty detection anomaly detection statistical depth function spatial depth kernel method Statistical Statistical computing Machine learning
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Computational Theory and Mathematics Computer Vision and Pattern Recognition Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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