Page 273 - Solid Waste Analysis and Minimization a Systems Approach

MULTIVARIATE CLUSTER ANALYSIS AND DISCUSSION 251

TABLE 15.3 ANOVA TABLE USED TO DETERMINE OPTIMAL NUMBER OF
CLUSTERS (CONTINUED)

NUMBER OF WASTE SSA SSE AVERAGE
GROUPS (CLUSTERS) (BETWEEN) (WITHIN) (SSE/K)

8 1084 657 82.13

9 1130 611 67.89
10 1260 481 48.10

11 1321 420 38.18
12 1402 339 28.25

13 1432 309 23.77
14 1488 253 18.07

15 1570 171 11.40
16 1590 151 9.44

17 1617 124 7.29
18 1644 97 5.39

19 1658 83 4.37
20 1676 65 3.25

21 1690 51 2.43
22* 1700 41 1.86

23 1703 38 1.65

24 1707 34 1.42
... ... ... ...
35 1726 15 0.43

* Using the Thorndike method, 22 waste groups (k = 22) is the optimal cluster number. This may
be observed from the relatively little gain in average variance within groups from increases in k.
The Thorndike method involves plotting average within cluster variation (noise) against the number
of groups. Thorndike suggested that a marked flattening of the curve at any point indicates the
optimal for k (please see the next page for graphs of the curve, with the optimal point identified).

As shown from the statistical analysis in Table 15.4 and multivariate clus-
ter analysis, 22 waste groups is the optimal number of clusters to balance vari-
ation between groups and the number of groups. A sum of squares between
groups (variation between groups) of 1700.21 and a sum of squares within
groups (noise) of 40.96 was achieved using the clustering techniques. The
sum of square calculations may be found in Sec. 16.3. The next section dis-
cusses the results of the cluster analysis and details of the 22 waste groups.