Varimax criterion

H.F. Kaiser, The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23 (1958) 187-200. 

The varimax criterion serves the purpose of an orthogonal rotation, where the variance of the squared loadings within a common factor is maximized. As a result, as many common factors should be retained that are described by as few features (variables) as possible. Large eigenvalues and loadings are increased, but small ones... 

Eigenvalues without (top) and with rotation after the varimax criterion bottom) for the hair data in Table 5.1. 

The columns of V are the abstract factors of X which should be rotated into real factors. The matrix V is rotated by means of an orthogonal rotation matrix R, so that the resulting matrix F = V R fulfils a given criterion. The criterion in Varimax rotation is that the rows of F obtain maximal simplicity, which is usually denoted as the requirement that F has a maximum row simplicity. The idea behind this criterion is that real factors should be easily interpretable which is the case when the loadings of the factor are grouped over only a few variables. For instance the vector f, =[000 0.5 0.8 0.33] may be easier to interpret than the vector = [0.1 0.3 0.1 0.4 0.4 0.75]. It is more likely that the simple vector is a pure factor than the less simple one. Returning to the air pollution example, the simple vector fi may represent the concentration profile of one of the pollution sources which mainly contains the three last constituents. 

A Varimax rotation (Vl ) is often used to achieve it. However, simple structure may not be the most useful criterion for environmental source resolution since an element may be present in an aerosol sample because of its emission by several sources. The variance should, therefore, be spread over several factors rather than concentrated in one. 

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