mlpca_d: Maximum likelihood principal component analysis for mode D...
In RMLPCA: Maximum Likelihood Principal Component Analysis

Description Usage Arguments Details Value References Examples

Performs maximum likelihood principal components analysis for mode D error conditions (commom row covariance matrices). Employs rotation and scaling of the original data.

1	mlpca_d(X, Cov, p)

`X`	IxJ matrix of measurements
`Cov`	JxJ matrix of measurement error covariance, which is commom to all rows
`p`	Rank of the model's subspace

The returned parameters, U, S and V, are analogs to the truncated SVD solution, but have somewhat different properties since they represent the MLPCA solution. In particular, the solutions for different values of p are not necessarily nested (the rank 1 solution may not be in the space of the rank 2 solution) and the eigenvectors do not necessarily account for decreasing amounts of variance, since MLPCA is a subspace modeling technique and not a variance modeling technique.

The parameters returned are the results of SVD on the estimated subspace. The quantity Ssq represents the sum of squares of weighted residuals.

Wentzell, P. D. "Other topics in soft-modeling: maximum likelihood-based soft-modeling methods." (2009): 507-558.

  library(RMLPCA)
  data(data_clean)
  data(data_error_d)
  # covariance matrix
  data(cov_d)
  data(data_cleaned_mlpca_d)
  # data that you will usually have on hands
  data_noisy <- data_clean + data_error_d

  # run mlpca_c with rank p = 5
  results <- RMLPCA::mlpca_d(
    X = data_noisy,
    Cov = cov_d,
    p = 2
  )

  # estimated clean dataset
  data_cleaned_mlpca <- results$U %*% results$S %*% t(results$V)