State of the Art and Development Trend - Computational Intelligence in Time Series Forecasting - page 341

of pairs of inhibitory neurons and excitatory neurons , so that they are structured
as multi-input, multi-output neurons.

Interpretation and
Decision Level

Abstraction
Level

Recognition
Level

Sensory
Level

Figure 10.7. Hierarchically organized modular neural network

NNN

NNN

NNN

Figure 10.8. Simplified structure of a non-monotone neural network

It should finally be mentioned that although the discovery of fractally based
neural networks was introduced in the late 1980s, the subsequent work on their
implementation and application was rather dilatory.

10.5 Fuzzy Clustering

In Chapter 4 we have already described various fuzzy clustering algorithms, such
as the fuzzy c-means algorithm that relies on fixed distance norm and the
Gustafsson-Kessel algorithm that takes into account the adaptive version of
distance norms for various geometrical shapes of clusters. Here, two other fuzzy
clustering algorithms will be described, one that relies on the neural self-organizing
network of Kohonen and the other is an entropy-based method.
Once the data clustering algorithm is applied in the product space of X and y ,
where a regression matrix X

T

[ xx , ,..., x ] and the corresponding output vector

12 N

are constructed from a given set of time series data, the
identification of a nonlinear time series model is simply a two-step procedure.

y

T

[, , ] y y y

12 N