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246 SOLID WASTE CHARACTERIZATION BY BUSINESS ACTIVITIES

15.4 Multivariate Cluster Analysis

and Discussion

This section discusses the final waste grouping process, multivariate cluster analysis,
utilized to reduce the 65 SIC code groups further. Cluster analysis is a group of mul-
tivariate techniques whose primary purpose is to objectively group objects based on
characteristics they possess. Cluster analysis was used to identify SIC code groups that
generate similar solid waste material composition percentages. Solid waste stream
composition percentage means and variances were calculated for all records gathered
from each SIC code group in the previous steps.
Based on previous research, a five-step cluster analysis procedure was applied for
this research (Romesburg, 1984):

1 Obtain data matrix
2 Standardize the data matrix (z scores)
3 Compute the resemblance matrix
4 Execute the cluster method
5 Report and evaluate the results (statistical testing)

Each step is discussed in the following sections.

15.4.1 STEP 1: OBTAIN THE DATA MATRIX

A data matrix is a table containing the objects and attributes of each object to be
grouped. The columns of the matrix represent each object (t total objects) and the rows
represent the attributes or properties of each object (n total attributes). For this
research, the objects are the 65 SIC code groups and the attributes are the means and
2
variances of each waste material generated by the respective waste group (μ and ).
Figure 15.5 displays the canonical form of the data matrix.

SIC Code Groups
Waste 1 j t
Material μ S 2 … j … t
1 X 11 X 12 … X 1j … X 1t
2 X 21 X 22 … X 2j … X 2t
… … … … …
i X i1 X i2 … X ij … X it
… … … … …
n X n1 X n2 … X nj … X nt

Figure 15.5 Format of cluster analysis data
matrix.