8.2.1 Rotation of configuration

Rotation with principal axes

The configuration is rotated so that successive dimensions account for the maximum possible variance. The symmetric matrix A^TA of dimensions (p ´ p) is computed and eigenvectors P of A^TA are determined, using Jacobi’s diagonalization method.

The matrix A is transformed into a matrix B of b_is elements, such that B = AP_p, B having n rows and p columns like the matrix A.

Rotated Configuration

The rotation can be performed only on two dimensions at a time. It is up to the researcher to select the dimensions and the angle f of rotation.

a_il =

The calculations are performed for each value of i (variable) and as many times as there are variables.

Varimax rotation

The elements a_is of A are normalized by the square roots of the communalities corresponding to each variable. Define

Having constructed B =, find the best projection axes for the variables, after equalization of their inertia. Define the function

The maximization of the function V_e is performed through successive rotations of two dimensions at a time, until convergence is reached.

The resulting matrix B of b_is elements has the same number of rows and columns as the initial matrix A.

The module Config also computes the matrices of Scalar products and Inter-point distances. These metrics are computed by the following formulae:

Matrix of Inter-point distances:

This is a square and symmetric matrices of Euclidean distances between variables.

Matrix of scalar products

The matrix SP is a square and symmetric matrix of scalar products of variables. If each variable is centered and normalized (mean = 0, standard deviation = 1), then the matrix SP becomes a correlation matrix.