Abstract:
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 moderate- to 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. In addition, we briefly discuss an extension to mixtures of $t$-distributions to handle data from heavy-tailed distributions. The methodology's performance is demonstrated via a simulation study, proving its effectiveness in complex, moderate-dimensional scenarios. Joint work with Luis Ángel García Escudero and Agustín Mayo Íscar. [1] L. A. García‑Escudero, A. Gordaliza, R. San Martín, S. Van Aelst y R. Zamar (2009), Robust linear clustering, Journal of the Royal Statistical Society. Series B: Statistical Methodology, 71(1), 301–318. DOI:10.1111/J.1467‑9868.2008.00682. [2] C. Bouveyron, S. Girard y C. Schmid (2007), High‑dimensional data clustering, Computational Statistics & Data Analysis, 52(1), 502–519. DOI:10.1016/j.csda.2007.02.009. [3] L. A. García‑Escudero, A. Gordaliza, C. Matrán y A. Mayo‑Iscar (2008), A general trimming approach to robust cluster analysis, Annals of Statistics, 36(3), 1324–1345. DOI:10.1214/07‑AOS515.