3

Fundamentals of Machine Learning and Pattern Recognition

In this chapter a brief introduction to the main elements of machine learning and pattern recognition will be made that are related to the ALS such as normalisation, proximity measures, clustering, classification. They play an important role in automatic system structure identification, as will be detailed in Chapter 5, Part II.

3.1 Preprocessing

In machine learning the data is often represented as a multivariate set (in the offline case) or stream (in the online case). The number of objects/samples are characterised by more than one feature (sometimes also-called attribute in decision making, observation in data mining, measurable variable in control theory, or, simply, input). Let us denote the number of features by n:

(3.1) Numbered Display Equation

In the offline mode the following matrix of observations/inputs can be formed:

(3.2) Numbered Display Equation

where

N is the total number of observations/data samples recorded; in the online mode this will be replaced by k – the current data sample assuming that the first data sample has index 1; each row of the matrix refers to a data sample/observation characterised by the features/attributes in the columns; an element, xij denotes the jth feature of the ith sample.

3.1.1 Normalisation and Standardisation

If the data ...

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