Target rotation factor analysis

Factor rotation by target transformation factor analysis (TTFA)... 

Varimax rotation is a commonly used and widely available factor rotation technique, but other methods have been proposed for interpreting factors from analytical chemistry data. We could rotate the axes in order that they align directly with factors from expected components. These axes, referred to as test vectors, would be physically significant in terms of interpretation and the rotation procedure is referred to as target transformation. Target transformation factor analysis has proved to be a valuable technique in chemo-metrics. The number of components in mixture spectra can be identified and the rotated factor loadings in terms of test data relating to standard, known spectra, can be interpreted. 

To transform the abstract factors determined in the first step into interpretable factors, rotation methods are applied. If definite target vectors can be assumed to be contained in the data, for example, a spectrum under a spectrochromatogram, the rotation of data is performed by using a target. This technique is known as target-transform factor analysis TTFA, c Example 5.6). 

The first study on curve resolution, carried out by Kaiser [1] in 1958, proposed the varimax method, wherein factor rotation was used in factor analysis. Studies by Lawton and Sylvestre of Kodak clearly picked up on curve resolution technology as a means of reaction analysis in chemistry (1971, 1974) [2]. The idea of employing rotating matrices was first used in iterative target transformation factor analysis... 

Roscoe, B. A. Hopke, P. K. Comparison of Weighted and Unweighted Target Transformation Rotations in Factor Analysis, Computers and Chemistry, in press,... 

The abstract spectra in matrix X represent a mathematical solution to Equation 3.44 but their interpretation and identification are not clear. True spectra can be obtained by rotating the abstract spectra to best match suspected (target) real spectra. This is the process of target transformation and is a powerful technique in factor analysis since it allows real factors to be identified individually. 

Factor analysis allows the extraction of the rank in a set of data and reduction of the amount of data produced in reaction spectra. This principle was applied to kinetics for the first time [80,191]. During the examinations of eigenvectors and eigenvalues, numerical problems are found using reaction spectra. Addition of a Fourier analysis of the rotated eigenvectors [80] solved the problem. Using a model normalised target transformation... 

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