- Title
- Half-space mass : a maximally robust and efficient data depth method
- Creator
- Chen, Bo; Ting, Kaiming; Washio, Takashi; Haffari, Gholamreza
- Date
- 2015
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/97185
- Identifier
- vital:10159
- Identifier
-
https://doi.org/10.1007/s10994-015-5524-x
- Identifier
- ISSN:0885-6125
- 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 L2 depth, an existing maximally robust location estimator. In clustering, the Half-Space Mass version of K-means overcomes three weaknesses of K-means.
- Publisher
- Kluwer Academic Publishers
- Relation
- Machine Learning Vol. 100, no. 2-3 (2015), p. 677-699
- Rights
- Copyright © 2015, The Author(s)
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0801 Artificial Intelligence and Image Processing; 1702 Cognitive Science; Half-space mass; Robustness; Artificial intelligence; Robustness (control systems); Software engineering; Anomaly detection; Data depth; Density distributions; Detection accuracy; Half spaces; Higher-dimensional; Mass estimation; Orders of magnitude; Geometry
- Reviewed
- Hits: 3454
- Visitors: 3267
- Downloads: 1
| Thumbnail | File | Description | Size | Format |
|---|