Maximum likelihood principal components

Andrews DT, Wentzell PD, Applications of maximum likelihood principal component analysis incomplete data sets and calibration transfer, Analytica Chimica Acta, 1997, 350, 341-352. 

Wentzell PD, Andrews DT, Hamilton DC, Faber NM, Kowalski BR, Maximum likelihood principal component analysis, Journal ofChemometrics, 1997, 11, 339-366. 

Wentzell PD, Lohnes MT, Maximum likelihood principal component analysis with correlated measurement errors theoretical and practical considerations, Chemometrics and Intelligent Laboratory Systems, 1999, 45, 65-85. 

Friedman and Frank [75] have shown that SIMCA is similar in form to quadratic discriminant analysis. The maximum-likelihood estimate of the inverse of the covariance matrix, which conveys information about the size, shape, and orientation of the data cloud for each class, is replaced by a principal component estimate. Because of the success of SIMCA, statisticians have recently investigated methods other than maximum likelihood to estimate the inverse of the covariance matrix, e.g., regularized discriminant analysis [76], For this reason, SIMCA is often viewed as the first successful attempt by scientists to develop robust procedures for carrying out statistical discriminant analysis on data sets where maximum-likelihood estimates fail because there are more features than samples in the data set. 

Figure 7.2 Authentication of monovarietal virgin olive oils results of applying factor analysis to the volatile compounds, (a) Maximum likelihood and Varimax rotation, (b) Principal components and Varimax rotation. Note A, cv. Arbequina C, cv. Coratina K, cv. Koroneiki P, cv. Picual (source SEXIA Group-Instituto de la Grasa, Seville, Spain).

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