Page 128 - Artificial Intelligence in the Age of Neural Networks and Brain Computing

2. Evolving Connectionist Systems (ECOS) 117

While a chromosome in the EC represents one individual, a quantum chromo-
some in a quantum inspired EC method represents the entire space of possible states
of the chromosome in a probabilistic way so that any state in this space is repre-
sented with a probability to be the best state at the current moment of the evolution.
Quantum inspired optimization methods use the principle of superposition of
states to represent and optimize features (input variables) and parameters. Features
and parameters are represented as qubits, which are in a superposition of 1 (selected)
with a probability a, and 0 (not selected) with a probability b. When the model has to
be calculated, the quantum bits “collapse” into a value of 1 or 0.
Several successful methods have been proposed for quantum inspired EC;
among them are quantum-inspired evolutionary algorithm (QiEA) [31] and
quantum-inspired particle swarm optimization method (QiPSO) [32].

2. EVOLVING CONNECTIONIST SYSTEMS (ECOS)
2.1 PRINCIPLES OF ECOS
In the evolving connectionist systems (ECOS) instead of training a fixed ANN
through changing its connection weights, the connectionist structure and its func-
tionality are evolving from incoming data, often in an online, one-pass learning
mode [33e36].
ECOS are modular connectionist-based systems that evolve their structure
and functionality in a continuous, self-organized, online, adaptive, interactive way
from incoming information [33]. They can process both data and knowledge in a
supervised and/or unsupervised way. ECOS learn local models from data through
clustering of the data and associating a local output function for each cluster repre-
sented in a connectionist structure. They can learn incrementally single data items
or chunks of data and also incrementally change their input features [35,37]. Ele-
ments of ECOS have been proposed as part of the classical neural network models,
such as self-organizing maps, radial basis functions, fuzzy ARTMap, growing neural
gas, neuro-fuzzy systems, and resource allocation network (for a review, see
Ref. [22]). Other ECOS models, along with their applications, have been reported
in Refs. [38] and [39].
The principle of ECOS is based on local learningdneurons are allocated as
centers of data clusters and the system creates local models in these clusters.
Methods of fuzzy clustering, as a means to create local knowledge-based systems,
were developed by Bezdek, Yager, Filev, and others [40,41].
To summarize, the following are the main principles of ECOS as stated in
Ref. [33]:

1. Fast learning from large amount of data, for example, using “one-pass” training,
starting with little prior knowledge;
2. Adaptation in real-time and in an online mode where new data is accommodated
as it comes based on local learning;