8. 2 Configuration Analysis

The final configuration issued by Mdscal is an n p matrix. Each row of the configuration matrix provides the coordinates of one point. Thus, the number of rows equals the number of variables (or objects) and the number of columns equals the number of dimensions.

Let A (n, p) be a rectangular matrix of n rows and p columns. Thus, each point has p coordinates.

ais = elements of the matrix A in the ith row and the sth column

i, j = subscripts for variables (rows)

n = number of variables

p = number of dimensions

Centered Configuration

The variables are centered within each dimension by subtracting the mean of each element in the column

Centered

After centering, the mean of the coordinates of the n variables is zero for each dimension.

Normalized Configuration

The sum of squares of all the elements of the matrix A divided by the number of variables:

is the mean of the second moments of the variables. Normalized configuration is obtained by dividing each element by the square root of the above expression.

Normalized

The sum of squares of all normalized ais is equal to n.