Extreme Learning for Evolving Hybrid Neural Networks
Fernando Bordignon and Fernando Gomide
School of Electrical and Computer Engineering
University of Campinas
Campinas, SP, Brazil
E-mail: {bordi,gomide}@dca.fee.unicamp.br
Abstract—This paper addresses a structure and introduces
an evolving learning approach to train uninorm-based hybrid
neural networks using extreme learning concepts. Evolving
systems are high level adaptive systems able to simultaneously
modify their structures and parameters from a stream of
data, online. Learning from data streams is a contemporary
and challenging issue due to the increasing rate of the size
and temporal availability of data, turning traditional learn-
ing methods impracticable. Uninorm-based neurons, rooted
in triangular norms and conorms, generalize fuzzy neurons.
Uninorms bring flexibility and generality to fuzzy neuron
models as they can behave like triangular norms, triangular
conorms, or in between by adjusting identity elements. This
feature adds a form of plasticity in neural network modeling.
An online clustering method is used to granulate the input
space, and a scheme based on extreme learning is developed
to train the neural network. Computational results show that
the learning approach is competitive when compared with
alternative evolving modeling methods.
Keywords-hybrid neural networks; unineurons; evolving sys-
tems; online learning; extreme learning.
I. I NTRODUCTION
Machine learning methods are being reevaluated over
the last years as the need of online capabilities is made
evident by the massive growth in numbers and accessibility
of computing devices [1] [2]. Computers are connected in
a unprecedented level making available a massive amount
of data, generating interest to understand and forecast key
economic, technical, and social variables.
With this context in mind new methods have been con-
ceived during recent years. A new class of machine learning
approach with adaptive abilities to simultaneously learn a
system structure and its parameters emerged, namely, the
evolving system approach. The term evolving means online,
gradual systems development and adaptation. Evolving sys-
tems are an alternative and innovative way of adapt, learn
and represent knowledge about changing environments [1].
Fuzzy set theory provides solid methods and efficient
mechanisms to develop evolving systems as reported in early
works on fuzzy rule-based modeling [3] and neural fuzzy
inference DENFIS models [4]. More recently, more gen-
eral evolving connectionist systems (ECOS) framework [5],
flexible fuzzy inference systems (FLEXFIS) [6], evolving
Takagi-Sugeno (eTS) modeling [7] and its improved versions
[8] [9] have been developed. Current research focuses on
granular computing and modeling extensions such as interval
and fuzzy set-based evolving modeling (FBeM) systems [2]
From the neural networks perspective, extensions of clas-
sic neuron model using triangular norms and co-norms (t-
norms and t-conorms) have been extensively studied in
the literature lately e.g. [10], [11], [12], [13] and [14].
In particular, the notion of uninorm has been explored to
generalize further both, the basic fuzzy neuron model, and
neural architectures through hybridizations. Uninorms are
interesting not only because they add flexibility in neuron
and neural network design, but also because they naturally
provide a way to add neuronal plasticity through a single
parameter called the identity element. This is also very
useful for evolving systems and neural structures.
In this paper we address a hybrid neural fuzzy network
whose structure has two main parts: a fuzzy neural system
and a neural network. The multilayer structure of the net-
work has membership functions in the input layer neurons,
uninorm-based neurons in the second layer, and classic
neurons in the third layer. Uninorms provide flexibility at the
cost of an extra parameter (identity element) to learn for each
unineuron. Interesting, however, the identity element can be
either chosen by the designer if he has prior knowledge or
needs a particular structure, or leave it to be learnt using
data. Due to its inherent highly nonlinear nature, learning
complexity can be reduced using extreme learning [15].
Basically, extreme learning consists in randomly assigning
weights for the hidden layer of feed-forward neural networks
and analytically determine the output weights. Extreme
learning has shown to provide fast training, accurate results
and good generalization performance [16].
The input layer of the hybrid neural fuzzy network ad-
dressed in this paper uses Gaussian membership functions
to granulate the input space. Centers of the membership
functions are determined online via recursive clustering
methods. The hidden layer unineurons are compositions of
uninorms at local synaptic processing, with t-conorm
at global aggregation level. A typical neural network layer
with sigmoid activation function forms the output layer.
After this brief introduction, the paper proceeds as fol-
lows. Section II gives detailed description of the learning
steps including the evolving fuzzy neural network system
approach. Next, computational results of the tests conducted
2012 Brazilian Symposium on Neural Networks
1522-4899/12 $26.00 © 2012 IEEE
DOI 10.1109/SBRN.2012.14
196