Technical Notes Effects of Disparate Bases and Norms on Minimizing a Least-Squares Reconstruction Error

Nomenclature b = least-squares coefficient of gappy proper orthogonal decomposition c = generalized least-squares coefficient d = dimension of an observed variable diag = diagonals of matrix N = Gaussian probability distribution q = dimension of a latent variable, i.e., model selection R = n-dimensional real number space r = estimation error V = eigenvector matrix, i.e., a proper orthogonal decomposition basis Ve = guessed Vq obtained from ~ Y 0 W = factor loading matrix x = latent variable Y = collection of observed variables y = observed variable ML = maximum likelihood estimate = general norm = basis _ = mean-centered data h i = expectation k kL2 = L norm k kn = gappy norm ~ = estimation

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