Robust regression and outlier detection
Robust regression and outlier detection
On the complexity of approximating the maximal inscribed ellipsoid for a polytope
Mathematical Programming: Series A and B
Rounding of polytopes in the real number model of computation
Mathematics of Operations Research
Computational Optimization and Applications
Optimal outlier removal in high-dimensional
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On Numerical Solution of the Maximum Volume Ellipsoid Problem
SIAM Journal on Optimization
Computation of Minimum-Volume Covering Ellipsoids
Operations Research
Conditional minimum volume ellipsoid with application to multiclass discrimination
Computational Optimization and Applications
Estimating training data boundaries in surrogate-based modeling
Structural and Multidisciplinary Optimization
One class classification for anomaly detection: support vector data description revisited
ICDM'11 Proceedings of the 11th international conference on Advances in data mining: applications and theoretical aspects
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We propose minimum volume ellipsoids (MVE) clustering as an alternative clustering technique to k-means for data clusters with ellipsoidal shapes and explore its value and practicality. MVE clustering allocates data points into clusters in a way that minimizes the geometric mean of the volumes of each cluster's covering ellipsoids. Motivations for this approach include its scale-invariance, its ability to handle asymmetric and unequal clusters, and our ability to formulate it as a mixed-integer semidefinite programming problem that can be solved to global optimality. We present some preliminary empirical results that illustrate MVE clustering as an appropriate method for clustering data from mixtures of "ellipsoidal" distributions and compare its performance with the k-means clustering algorithm as well as the MCLUST algorithm (which is based on a maximum likelihood EM algorithm) available in the statistical package R.