Page 269 - Solid Waste Analysis and Minimization a Systems Approach

MULTIVARIATE CLUSTER ANALYSIS AND DISCUSSION 247

For this research, the objects were each SIC code group for which sufficient
data was collected (438 company records covering 65 SIC code groups). Details
on the attributes (waste material means and variances) for each object (SIC code
group) are listed in the following bullet points. As mentioned, if a material com-
prised less than 2 percent of total waste for all groups, the material was not
included in the analysis for simplification and noise reduction (four in total—
aerosol cans, rags, lamps, batteries). Material composition percentage means and
standard deviations of

■ Biohazard wastes
■ Construction and demolition debris (sand, stone, and concrete)
■ FABRIC and textiles
■ Food waste
■ Glass
■ Metal
■ Old corrugated containers (cardboard)
■ Chemicals, sludges, and used oil
■ Organic wastes (agricultural)
■ Paper (excluding cardboard)
■ Plastic
■ Rubber
■ Wood
■ Yard waste

15.4.2 STEP 2: STANDARDIZE THE DATA MATRIX
This is an optional step that standardizes the data matrix by converting the original
attributes into new unit-less attributes. This is important for two reasons (Romesburg,
1984):

1 The original units for measuring attributes can arbitrarily affect the similarities
among objects.
2 Attributes will contribute more equally to the similarities among objects.

To standardize the matrix, a standardizing function is selected and applied to nor-
malize the data matrix. The standardizing function (or standard normal form) that
is most commonly used in practice and applied for this research (Romesburg,
1984), was

X − X
Z = ij i
ij
S
i