7.1 Introducing Feature Space

Advanced data mining requires data to be expressed in a form that facilitates representation and analysis. Since advanced data mining applications are mathematically intensive, many data mining techniques work exclusively with data in numeric form. Several methods for encoding nominal data in numeric form, along with their implications, are discussed. Once nominal data has been encoded, it can support the mathematics required by data mining. Even more difficult than nominal-to-numeric encoding, is the process of feature extraction: the collection and synthesis of salient, independent features from a broad set of data, as discussed later in this chapter.

Fortunately, mathematicians have provided an ideal framework within which to conduct data mining. It is called "Euclidean space," and the mathematical theory describing it is known as "linear algebra." Euclidean space is named for the Greek mathematician Euclid, who derived many of its properties in his magnum opus, "The Elements." There are infinitely many Euclidean spaces, which is quite beneficial because there are infinitely many data mining problems, and each...