In this work a technique that combines clustering and dimension reduction for functional data is proposed. The optimal subspace and partition are identified by optimizing a unique loss function. To prevent the identification of subspaces with very low deviance, a penalty equal to the negative total deviance in the reduced space is added to the objective function. It can be shown that by varying the value of the penalty, the proposed loss function could recover several existing methods such as the Functional Reduced K-means and the Functional Factorial K-means. Finally, to consider the functional nature of the data, regularization is also incorporated in the estimation.

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Simultaneous Clustering and Dimension Reduction of Functional Data

  • Roberto Rocci,
  • S. Antonio Gattone

摘要

In this work a technique that combines clustering and dimension reduction for functional data is proposed. The optimal subspace and partition are identified by optimizing a unique loss function. To prevent the identification of subspaces with very low deviance, a penalty equal to the negative total deviance in the reduced space is added to the objective function. It can be shown that by varying the value of the penalty, the proposed loss function could recover several existing methods such as the Functional Reduced K-means and the Functional Factorial K-means. Finally, to consider the functional nature of the data, regularization is also incorporated in the estimation.