7.2.2 Building of an initial typology

        Case profiles of t cases, selected randomly (using random numbers), constitute the starting configuration; in order to obtain the initial configuration, the remaining cases are distributed into t-groups.

        Case profiles of t cases, selected in a stepwise manner, constitute the starting configuration; in order to obtain the initial configuration.

When the construction starts from t case profiles, the program considers this set of t vectors as a set of t ‘starting cases’ and distributes the remaining cases according to their distance to each of the starting case.

Denote the set of t starting cases by

and the distance between groups and/or cases i and j by D(Pii,Pj).

Note that D(Pi, Pj) can be any distance - City block distance, Euclidean distance or Chi-square distance.

For each case the program calculates

There are two possibilities:

  1. b g : case i is assigned to the closest group, Pkj and the profile is recalculated

  1. b > g : case i forms a new group which is added to the set Pstarting, and the two closest profiles Pkj and Pkj are aggregated forming one group with the new profile

At the end of this procedure, the initial configuration is a set of t profiles

where Pj is a mean profile of all the cases belonging to the group j.

At this stage the program does not take into account weighting of cases, if any.

Here, again there are two possibilities:

  1. when case and

then this case remains in the group Pj;

  1. when case but

then the case i is moved from the group Pj to the group Pj, and the profiles of those two groups are recalculated as follows:

After this operation, the group Pj contains Nj-1 cases and the group Pj contains Nj+1 cases.

The procedure is repeated until the groups are stabilized or when the number of iterations fixed by the researcher is reached. Stability of groups is measured by the percentage of cases that do not change groups between two subsequent iterations.