mlpca_d {RMLPCA}

Maximum likelihood principal component analysis for mode D error conditions

Description

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

Usage

mlpca_d(X, Cov, p)

Arguments

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

Details

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.

Value

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

References

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

Examples

  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)