Determining the number of principal components for best reconstruction

A well-de®ned variance of reconstruction error (VRE) is proposed to determine the number of principal components in a PCA model for best reconstruction. Unlike most other methods in the literature, this proposed VRE method has a guaranteed minimum over the number of PCʹs corresponding to the best reconstruction. Therefore, it avoids the arbitrariness of other methods with monotonic indices. The VRE can also be used to remove variables that are little correlated with others and cannot be reliably reconstructed from the correlation-based PCA model. The e€ectiveness of this method is demonstrated with a simulated process.