A High-Dimensional Extension of TCLUST

L. Trapote Reglero, L. Á. García-Escudero, A. Mayo Íscar

Outliers distort traditional clustering, leading to unreliable partitions. Robust methods like TCLUST address this by extending trimming to multi-cluster settings. While effective in low dimensions, TCLUST struggles in high-dimensional spaces due to parameter estimation complexity. Robust Linear Grouping (RLG) offers an alternative by assuming clusters lie near lower-dimensional subspaces, yet it fails when subspaces intersect or errors are non-isotropic.

We propose a robust method extending TCLUST by integrating the High Dimensional Data Clustering (HDDC) framework, incorporating trimming and eigenvalue constraints. This approach bridges TCLUST and RLG through a careful adaptation of implementation steps. We present its theoretical properties, a feasible algorithm, and a strategy for selecting input parameters. The methodology's performance is demonstrated via a simulation study and a real-data example, proving its effectiveness in complex, high-dimensional scenarios.

Keywords: Robust clustering, Trimming, High-dimensional data, TCLUST, Eigenvalue constraints

Multivariate Analysis
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