Motivated by the arising realistic issues in big data , the problem of Minimum Enclosing Ball (MEB) with outliers has attracted a great deal of attention in recent years. Though several methods have been proposed in both theory and practice, most of them still suffer from the issues such as high time  complexities or unstable performances for different datasets. For example, Kumar et al. proposed the open problem `Are there practical methods for computing an MEB with outliers?' To answer this question, we extend the idea of core-set and present a randomized algorithm for MEB with outliers in high dimension . In particular, we provide a more `robust' analysis for the core-set construction of MEB, and propose a couple of novel improvements to further reduce the time complexity. The ideas behind are interesting in their own right and we expect to apply them to solve more high-dimensional problems. To show the efficiency and practicality, we test our algorithm on random datasets and also apply it to handle outlier recognition on benchmark datasets. To our best knowledge, this is the first algorithm yielding both solid theoretical quality guarantee and promising practical performance for the problem of MEB with outliers .
Outlier recognition is a fundamental problem in data analysis and has attracted a great deal of attention in the past decades. However, most existing methods still suffer from several issues such as high time and space complexities or unstable performances for different datasets. In this paper, we provide a novel algorithm for outlier recognition in high dimension based on the elegant geometric technique `` core-set ". The algorithm needs only linear time and space complexities and achieves a solid theoretical quality guarantee. Another advantage over the existing methods is that our algorithm can be naturally extended to handle multi-class inliers. Our experimental results show that our algorithm outperforms existing algorithms on both random and benchmark datasets .
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Motivated by the arising realistic issues in big data , the problem of Minimum Enclosing Ball (MEB) with outliers
Outlier recognition is a fundamental problem in data analysis and
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recent years. Though several methods have been proposed in both theory and practice, most of them
the past decades. However, most existing methods
R
the
several
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and space
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For example, Kumar et al. proposed the open problem `Are there practical methods for computing an MEB with outliers?' To answer this question, we extend the idea of core-set and present a randomized algorithm for MEB with outliers
In this paper, we provide a novel algorithm for outlier recognition
R
. In particular, we provide a more `robust' analysis for the
based on the elegant geometric technique ``
R
construction of MEB, and propose a couple of novel improvements to further reduce the time complexity. The ideas behind are interesting in their own right and we expect to apply them to solve more high-dimensional problems. To show the efficiency and practicality, we test our algorithm on random datasets and also apply it to handle outlier recognition on benchmark datasets. To our best knowledge, this is the first algorithm yielding both solid theoretical quality guarantee and promising practical performance for the problem of MEB with outliers
". The algorithm needs only linear time and space complexities and achieves a solid theoretical quality guarantee. Another advantage over the existing methods is that our algorithm can be naturally extended to handle multi-class inliers. Our experimental results show that our algorithm outperforms existing algorithms on both random and benchmark datasets