A Learning Classifier Systems Model - Design and Analysis of Learning Classifier Systems - page 39

Before providing more details on how to find a good model structure, let us
first assume a fixed model structure with K classifiers and investigate in more
detail the components of such a model.

3.2.3 Classifiers as Localised Models

In LCS, the combination of condition and action of a classifier determines the
inputs that a classifier matches. Hence, given the training set, one classifier
matches only a subset of the observations in that set. It can be said that a
classifier is localised in the input space, where its location is determined by the
inputs that it matches.

Matching

Let be the subset of the input space that classifier k matches. The

classifier is trained by all observations that it matches, and hence its aim is to
provide a local model f k ( x ; θ k )thatmaps

X k ⊆X

,where θ k is the set of
parameters of the model of classifier k . More flexibly, matching can be defined
by a matching function m k :

X k into Y

X→ [0 , 1] specific to classifier k , and given by the

indicator function for the set X k ,

⎧
⎨

∈X k ,
0 rwi .

1if x

m k ( x )= (3.9)

⎩

The advantage of using a matching function m k rather than a set

X k is that the
former allows for degrees of matching in-between 0 and 1 - a feature that we will
be made use of in later chapters. Also note, that representing matching by

X k or
the matching function m k makes it independent of the choice of representation
of the condition/action of a classifier. This is an important point, as it makes all
future developments valid for all choices of representation.

Local Classifier Model

The local model of a classifier is usually a regression model with no particular
restrictions. As discussed in Section 2.3.1, initially only simple averaging predic-
tions were used, but more recently, classifiers have been extended to use linear
regression models, neural networks, and SVM regression. While averagers are
just a special case of linear models, neural networks might suffer from the pro-
blem of multiple local optima [104], and SVM regression has no clean approach
to incremental implementations [157]. Hence, we will restrict ourselves to the
well-studied class of linear models as a good trade-off between expressive power
and complexity of training, and equally easily trainable classification models.
Both are discussed in more depth in Chaps. 4 and 5.

Input to Matching and Local Models

Note that in LCS the input given to the matching function and that given to
the classifier's model usually differ in that the input to the model is often formed