TY - JOUR
T1 - Computationally efficient algorithms for high-dimensional robust estimators
AU - Mount, David M.
AU - Netanyahu, Nathan S.
PY - 1994/7
Y1 - 1994/7
N2 - Given a set of n distinct points in d-dimensional space that are hypothesized to lie on a hyperplane, robust statistical estimators have been recently proposed for the parameters of the model that best fits these points. This paper presents efficient algorithms for computing median-based robust estimators (e.g., the Theil-Sen and repeated median (RM) estimators) in high-dimensional space. We briefly review basic computational geometry techniques that were used to achieve efficient algorithms in the 2-D case. Then generalization of these techniques to higher dimensions is introduced. Geometric observations are followed by a presentation of O(nd-1 log n) expected time algorithms for the d -dimensional Theil-Sen and RM estimators. Both algorithms are space optimal; i.e., they require O(n) storage, for fixed d. Finally, an extension of the methodology to nonlinear domain(s) is demonstrated.
AB - Given a set of n distinct points in d-dimensional space that are hypothesized to lie on a hyperplane, robust statistical estimators have been recently proposed for the parameters of the model that best fits these points. This paper presents efficient algorithms for computing median-based robust estimators (e.g., the Theil-Sen and repeated median (RM) estimators) in high-dimensional space. We briefly review basic computational geometry techniques that were used to achieve efficient algorithms in the 2-D case. Then generalization of these techniques to higher dimensions is introduced. Geometric observations are followed by a presentation of O(nd-1 log n) expected time algorithms for the d -dimensional Theil-Sen and RM estimators. Both algorithms are space optimal; i.e., they require O(n) storage, for fixed d. Finally, an extension of the methodology to nonlinear domain(s) is demonstrated.
UR - http://www.scopus.com/inward/record.url?scp=0028463578&partnerID=8YFLogxK
U2 - 10.1006/gmip.1994.1027
DO - 10.1006/gmip.1994.1027
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AN - SCOPUS:0028463578
SN - 1077-3169
VL - 56
SP - 289
EP - 303
JO - Graphical Models and Image Processing
JF - Graphical Models and Image Processing
IS - 4
ER -