Abstract
We propose a new approach to the construction of \(k \)-means clustering algorithms in which the Mahalanobis distance is used instead of the Euclidean distance. The approach is based on minimizing differentiable estimates of the mean insensitive to outliers. Illustrative examples convincingly show that the proposed algorithm is highly likely to be robust with respect to a large amount of outliers in the data.
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Notes
\(d(\mathbf {x},\mathbf {c},\mathbf {S}) =-\ln \bigl (|\mathbf {S}|^{-1/2} \exp \bigl \{-\frac {1}{2}(\mathbf {x} -\mathbf {c})^{\prime }\mathbf {S}^{-1}(\mathbf {x}-\mathbf {c}) \bigr \}\bigr )\).
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Funding
This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00050.
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Translated by V. Potapchouck
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Shibzukhov, Z.M. On a Robust Approach to Search for Cluster Centers. Autom Remote Control 82, 1742–1751 (2021). https://doi.org/10.1134/S0005117921100118
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DOI: https://doi.org/10.1134/S0005117921100118