5. Experiment 4: ${\rm IVGA_{VQ}}$(A) + ${\rm IVGA_{VQ}}$(B) + ${\rm IVGA_{VQ}}$(C)

Next, we simulated a situation where the three main groups of variables (A, B and C) are known based on prior information. Now the ${\rm IVGA_{VQ}}$ algorithm was used to find the best possible sub-groupings for A, B and C separately. The results are shown in Table 2. Note also that the variable groupings obtained are almost, but not exactly, identical in Experiments 3 and 4. The slight improvement in total cost compared to Experiment 3 is as expected, since computational resources needed not be allocated for separating the groups A, B and C.

The results of the four experiments are summarized in Table 3.

   

Table: Results when ${\rm IVGA_{VQ}}$ was run separately for each set A, B and C.

Variable	Group	Variables	Cost	Codebook	Parameters
set				vectors
A	1	1,6	-4773.4	9	18
A	2	2-5, 7-8, 11	-33432.8	12	84
A	3	9-10,13,16,18,20,25	-32122.6	13	91
A	4	12,14-15,17,19,21-24,26-27	-46778.0	14	154
B	1	28-34	-3868.6	17	119
C	1	35-38	-6646.1	8	32
C	2	39-42,45-46	-9934.4	26	156
C	3	43-44	-3190.7	7	14
C	4	47-50	-7187.7	11	44
Total			-147934.3	117	712

   

Table 3: Summary of results of all experiments.

Experiment	Total cost	#VQs	Parameters
1. VQ(A+B+C)	-138115.5	1	2200
2. VQ(A) + VQ(B) + VQ(C)	-145796.2	3	1045
3. ${\rm IVGA_{VQ}}$(A+B+C)	-147206.8	12	618
4. ${\rm IVGA_{VQ}}$(A) + ${\rm IVGA_{VQ}}$(B) + ${\rm IVGA_{VQ}}$(C)	-147934.3	9	712