A robust method for cluster analysis

By M. Gallegos, G. Ritter. 2005

135 citations recorded by the source corpus.

Let there be given a contaminated list of n R d -valued observations coming from g different, normally distributed populations with a common covariance matrix. We compute the ML-estimator with respect to a certain statistical model with n - r outliers for the parameters of the g populations; it detects outliers and simultaneously partitions their complement into g clusters. It turns out that the estimator unites both the minimum-covariance-determinant rejection method and the well-known pooled determinant criterion of cluster analysis. We also propose an efficient algorithm for approximating this estimator and study its breakdown points for mean values and pooled SSP matrix.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4aa4bf4723fe2fd59946ce0fe4d2a8061ec24fda

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Robust statistics for outlier detection (2011, methodology): “47 For nonspherical clusters, constrained maximum likelihood approaches 48 , 49 were developed.”
Anomaly detection by robust statistics (2017, methodology): “For non-spherical clusters, constrained maximum likelihood approaches 61,62 were developed.”
Robust estimation in the normal mixture model based on robust clustering (2008, methodology): “In this case we have used as initial region for our procedure the solution provided by Gallegos and Ritter [7] (covering the 50% of the data by a union of two identical ellipses suitably located).”