Single value decomposition SVD

Evaluate the feasibility of inpuf output combinations by single value decomposition (SVD) analysis. Estimate feasible pairing by relative gain array (RGA) and Niederllnski index. 

Through the application of single value decomposition (SVD) of the symmetric matrix, the dth power and hence the square root of the UIC spectrum is defined via the GIC matrix. Spectral artefacts due to covariance processing can be distinguished from native signals on account of their dependence on A. Further details on the GIC matrix calculation are given below, cf. Eq. (5.27). 

First formulated by Pearson in 1901, PCA was outlined by Fisher and MacKenzie in 1923 and by H. Wold in 1966, who discovered the NIPALS algorithm (see Wold and references therein). PCA is also called factorial analysis (FA), single-value decomposition (SVD, which is the full PCA), or Karhunen-Loewe expansion (KLE). Data reduction by PCA is of key importance in CoMFA because it allows large amounts of data to be approximated by a small mathematical structure. In PCA, the X matrix of a given training set (e.g., a CoMFA field) is assumed to include a model and noise (the part of the data that cannot be explained by the model). The X matrix is thus a combination of the principal component model matrix M and the noise matrix E ... 

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