Degrees of freedom estimation in Principal Component Analysis and Consensus Principal Component Analysis

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Hassani, Sahar | Martens, Harald | Qannari, El Mostafa | Kohler, Achim

Edité par CCSD ; Elsevier -

International audience. The concept of degree of freedom (DF) is an important issue in statistical model assessment and parameter estimation. In this paper, we investigate this concept within the context of data modeling by Principal Component Analysis (PCA) and its multi-block extension, the Consensus Principal Component Analysis (CPCA). We run simulation studies and assess the degrees of freedom by comparing cross-validated error estimates with error estimates from uncorrected model fits. These simulation studies reveal that the OF consumption in PCA and CPCA depends on the eigenvalue structure of the data at hand. We also show that the obtained DF estimates can be used to obtain realistic error estimations without performing cross-validation. Furthermore, it is shown how different strategies of cross-validation and the use of an independent test set affect the estimate of the degrees of freedom and the estimate of the model error. (C) 2012 Elsevier B.V. All rights reserved.

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