Optimal outlier removal in high-dimensional spaces

Optimal outlier removal in high-dimensional spaces

We study the problem of finding an outlier-free subset of a set of points (or a probability distribution) in n-dimensional Euclidean space. As in [BFKV 99], a point x is defined to be a β-outlier if there exists some direction w in which its squared distance from the mean along w is greater than β times the average squared distance from the mean along w. Our main theorem is that for any ǫ > 0, ...

Optimal Outlier Removal in High-Dimensional Spa es

Algorithms for optimal outlier removal

We consider the problem of removing c points from a set S of n points so that the remaining point set is optimal in some sense. Definitions of optimality we consider include having minimum diameter, having minimum area (perimeter) bounding box, having minimum area (perimeter) convex hull. For constant values of c, all our algorithms run in O(n log n) time.

Feature Extraction for Outlier Detection in High-Dimensional Spaces

This work addresses the problem of feature extraction for boosting the performance of outlier detectors in high-dimensional spaces. Recent years have observed the prominence of multidimensional data on which traditional detection techniques usually fail to work as expected due to the curse of dimensionality. This paper introduces an efficient feature extraction method which brings nontrivial im...

Outlier rejection in high-dimensional deformable models

Deformable model tracking is a powerful methodology that allows us to track the evolution of high-dimensional parameter vectors from uncalibrated monocular video sequences. The core of the approach consists of using low-level vision algorithms, such as edge trackers or optical flow, to collect a large number of 2D displacements, or motion measurements, at selected model points and mapping them ...