Page 44 - Rapid Learning in Robotics

30 Artificial Neural Networks

Most methods prefer orderable, variables as input variables type (neu-
ral nets), some others prefer categorical variables (artificial intelligence
and machine learning approaches). Depending on the type of output vari-
ables different frameworks offer methods called regression, approxima-
tion, classification, system identification, system estimation, pattern recog-
nition, or learning. Tab. 3.1 compares names for learning task, common in
different domains of research.

Output Type Continuous Values Symbolic Values
vs. Framework Orderable Variables Categorical Variables
Neural Networks Learning Learning
Machine Learning Sub-symbolic & Fuzzy Learning Learning
Mathematics Approximation Quantization
Statistics Regression Classification
Engineering System Identification & Estimation Pattern Recognition

Table 3.1: Creating and refining a model in order to solve a learning task
has various common names in different disciplines.

In the following we mainly focus on the variable type continuous and
orderable. It can be considered as the most general case, since periodic
variables (2) can transformed by the trick of mapping the phase infor-
mation into a pair of sine and cosine values (of course the topology is
unchanged). Categorical output values (3) are often prepared by a com-
petitive component which selects the dominating component in a multi-
dimensional output (“winner takes all”). It is interesting to notice, that
Fuzzy Systems work the opposite way. Continuous valued inputs are ex-
amined on their probability to belong to a particular class (fuzzy mem-
bership). All combinations are propagated through a symbolic rule set
(if-then-else type) and the output “de-fuzzificated” into a continuous out-
put. The attractive point is the simplicity how to insert categorical “expert
knowledge” into the system.
We consider a system that generates data and is presumed to be de-
scribed by the multivariate function f x (possible perturbed by noise).
With continuous valued variables, the learning task is to model the system
by the function F w x that can serve as a reasonable approximation of f
over the domain D of interest. The regression is based on a set of given