Robust regression and outlier detection
Robust regression and outlier detection
Algorithms for clustering data
Algorithms for clustering data
Robust Clustering with Applications in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Determinant Maximization with Linear Matrix Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
An empirical comparison of four initialization methods for the K-Means algorithm
Pattern Recognition Letters
Robust space transformations for distance-based operations
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Computation of Minimum-Volume Covering Ellipsoids
Operations Research
An algorithm for separating patterns by ellipsoids
IBM Journal of Research and Development
Robust clustering methods: a unified view
IEEE Transactions on Fuzzy Systems
An outlier-aware data clustering algorithm in mixture models
ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
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This paper develops theory and algorithms concerning a new metric for clustering data. The metric minimizes the total volume of clusters, where the volume of a cluster is defined as the volume of the minimum volume ellipsoid (MVE) enclosing all data points in the cluster. This metric is scale-invariant, that is, the optimal clusters are invariant under an affine transformation of the data space. We introduce the concept of outliers in the new metric and show that the proposed method of treating outliers asymptotically recovers the data distribution when the data comes from a single multivariate Gaussian distribution. Two heuristic algorithms are presented that attempt to optimize the new metric. On a series of empirical studies with Gaussian distributed simulated data, we show that volume-based clustering outperforms well-known clustering methods such as k-means, Ward's method, SOM, and model-based clustering.