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3.5 Data Transformation and Data Discretization 113

data cleaning and was addressed in Section 3.2.2. Section 3.2.3 on the data cleaning
process also discussed ETL tools, where users specify transformations to correct data
inconsistencies. Attribute construction and aggregation were discussed in Section 3.4
on data reduction. In this section, we therefore concentrate on the latter three strategies.
Discretization techniques can be categorized based on how the discretization is per-
formed, such as whether it uses class information or which direction it proceeds (i.e.,
top-down vs. bottom-up). If the discretization process uses class information, then we
say it is supervised discretization. Otherwise, it is unsupervised. If the process starts by first
finding one or a few points (called split points or cut points) to split the entire attribute
range, and then repeats this recursively on the resulting intervals, it is called top-down
discretization or splitting. This contrasts with bottom-up discretization or merging, which
starts by considering all of the continuous values as potential split-points, removes some
by merging neighborhood values to form intervals, and then recursively applies this
process to the resulting intervals.
Data discretization and concept hierarchy generation are also forms of data reduc-
tion. The raw data are replaced by a smaller number of interval or concept labels. This
simplifies the original data and makes the mining more efficient. The resulting patterns
mined are typically easier to understand. Concept hierarchies are also useful for mining
at multiple abstraction levels.
The rest of this section is organized as follows. First, normalization techniques are
presented in Section 3.5.2. We then describe several techniques for data discretization,
each of which can be used to generate concept hierarchies for numeric attributes. The
techniques include binning (Section 3.5.3) and histogram analysis (Section 3.5.4), as
well as cluster analysis, decision tree analysis, and correlation analysis (Section 3.5.5).
Finally, Section 3.5.6 describes the automatic generation of concept hierarchies for
nominal data.

3.5.2 Data Transformation by Normalization

The measurement unit used can affect the data analysis. For example, changing mea-
surement units from meters to inches for height, or from kilograms to pounds for weight,
may lead to very different results. In general, expressing an attribute in smaller units will
lead to a larger range for that attribute, and thus tend to give such an attribute greater
effect or “weight.” To help avoid dependence on the choice of measurement units, the
data should be normalized or standardized. This involves transforming the data to fall
within a smaller or common range such as [−1,1] or [0.0, 1.0]. (The terms standardize
and normalize are used interchangeably in data preprocessing, although in statistics, the
latter term also has other connotations.)
Normalizing the data attempts to give all attributes an equal weight. Normaliza-
tion is particularly useful for classification algorithms involving neural networks or
distance measurements such as nearest-neighbor classification and clustering. If using
the neural network backpropagation algorithm for classification mining (Chapter 9),
normalizing the input values for each attribute measured in the training tuples will help
speed up the learning phase. For distance-based methods, normalization helps prevent