### 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.

a_{is}_{
}= elements of the matrix *A* in the *i*^{th} row
and the *s*^{th} 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 *a*_{is}_{
}is equal to *n*.