caa a22 4500 605478406 CHVBK 20210128100405.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10994-015-5524-x doi (NATIONALLICENCE)springer-10.1007/s10994-015-5524-x Half-space mass: a maximally robust and efficient data depth method [Elektronische Daten] [Bo Chen, Kai Ting, Takashi Washio, Gholamreza Haffari] 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 $$L_2$$ 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. The Author(s), 2015 Half-space mass nationallicence Mass estimation nationallicence Data depth nationallicence Robustness nationallicence Chen Bo Faculty of Information Technology, Monash University, 3168, Clayton, VIC, Australia aut Ting Kai School of Engineering and Information Technology, Federation University Australia, 3842, Churchill, VIC, Australia aut Washio Takashi The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, 5670047, Ibarakishi, Osaka, Japan aut Haffari Gholamreza Faculty of Information Technology, Monash University, 3168, Clayton, VIC, Australia aut Machine Learning Springer US; http://www.springer-ny.com 100/2-3(2015-09-01), 677-699 0885-6125 100:2-3<677 2015 100 10994 https://doi.org/10.1007/s10994-015-5524-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-015-5524-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Bo Faculty of Information Technology, Monash University, 3168, Clayton, VIC, Australia aut NATIONALLICENCE 700 1- Ting Kai School of Engineering and Information Technology, Federation University Australia, 3842, Churchill, VIC, Australia aut NATIONALLICENCE 700 1- Washio Takashi The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, 5670047, Ibarakishi, Osaka, Japan aut NATIONALLICENCE 700 1- Haffari Gholamreza Faculty of Information Technology, Monash University, 3168, Clayton, VIC, Australia aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 100/2-3(2015-09-01), 677-699 0885-6125 100:2-3<677 2015 100 10994