Robust linear clustering around affine subspaces

• Autores: Ricardo A. San Martín, Luis Angel García Escudero, Alfonso Gordaliza Ramos, Stefan Van Aelst, Ruben H. Zamar
• Localización: XXX Congreso Nacional de Estadística e Investigación Operativa y de las IV Jornadas de Estadística Pública: actas, 2007, ISBN 978-84-690-7249-3
• Idioma: español
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• Resumen

  • Non-hierarchical clustering methods are frequently based on the idea of forming groups around �objects�. The main exponent of this class of methods is the k-means method, where these objects are points. However, clusters in a data set may often be due to the existence of certain relationships among the measured variables. For instance, we can find linear structures such as straight lines, planes and so on, around which the observations are grouped in a natural way.

    These structures are not well represented by points.

    We present a method that searches for linear groups in the presence of outliers. The method is based on the idea of impartial trimming. We search for the �best�subsample containing a proportion 1 - of the data and the best k affine subspaces fitting to those non-discarded observations by measuring discrepancies through orthogonal distances.

    The population version of the sample problem will also be considered. We prove the existence of solutions for the sample and population problems together with their consistency. A feasible algorithm for solving the sample problem is described as well. Examples showing how the proposed method works in simulated data sets and in a Computer Vision problem are provided.