An efficient algorithm for weighted PCA

The method for analyzing three-way data where one of the three components matrices in TUCKALS3 is chosen to have one column is called Replicated PCA. The corresponding algorithm is relatively inefficient. This is shown by offering an alternative algorithm called Weighted PCA. Specifically it is proven that the algorithms Replicated PCA and Weighted PCA produce identical convergent sequences of loss-function values, and that Weighted PCA attains these values using: fewer floating point operations.