NDLI: Half-space mass: a maximally robust and efficient data depth method

Content Provider	Springer Nature Link
Author	Chen, Bo Ting, Kai Ming Washio, Takashi Haffari, Gholamreza
Copyright Year	2015
Abstract	Data depth is a statistical method which models data distribution in terms of center-outward ranking rather than density or linear ranking. While there are a lot of academic interests, its applications are hampered by the lack of a method which is both robust and efficient. This paper introduces Half-Space Mass which is a significantly improved version of half-space data depth. Half-Space Mass is the only data depth method which is both robust and efficient, as far as we know. We also reveal four theoretical properties of Half-Space Mass: (i) its resultant mass distribution is concave regardless of the underlying density distribution, (ii) its maximum point is unique which can be considered as median, (iii) the median is maximally robust, and (iv) its estimation extends to a higher dimensional space in which the convex hull of the dataset occupies zero volume. We demonstrate the power of Half-Space Mass through its applications in two tasks. In anomaly detection, being a maximally robust location estimator leads directly to a robust anomaly detector that yields a better detection accuracy than half-space depth; and it runs orders of magnitude faster than $$L_2$$ depth, an existing maximally robust location estimator. In clustering, the Half-Space Mass version of K-means overcomes three weaknesses of K-means.
Starting Page	677
Ending Page	699
Page Count	23
File Format	PDF
ISSN	08856125
Journal	Machine Learning
Volume Number	100
Issue Number	2-3
e-ISSN	15730565
Language	English
Publisher	Springer US
Publisher Date	2015-08-05
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Half-space mass Mass estimation Data depth Robustness Artificial Intelligence (incl. Robotics) Control, Robotics, Mechatronics Computing Methodologies Simulation and Modeling Language Translation and Linguistics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Software

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