| dc.description.sponsorship | Accurate classification by minimizing the error on test samples is the main
goal in pattern classification. Combinatorial optimization is a well-known
method for solving minimization problems, however, only a few examples of
classifiers axe described in the literature where combinatorial optimization is
used in pattern classification. Recently, there has been a growing interest
in combining classifiers and improving the consensus of results for a greater
accuracy. In the light of the "No Ree Lunch Theorems", we analyse the combination
of simulated annealing, a powerful combinatorial optimization method
that produces high quality results, with the classical perceptron algorithm.
This combination is called LSA machine. Our analysis aims at finding paradigms
for problem-dependent parameter settings that ensure high classifica,
tion results. Our computational experiments on a large number of benchmark
problems lead to results that either outperform or axe at least competitive to
results published in the literature. Apart from paxameter settings, our analysis
focuses on a difficult problem in computation theory, namely the network
complexity problem. The depth vs size problem of neural networks is one of
the hardest problems in theoretical computing, with very little progress over
the past decades. In order to investigate this problem, we introduce a new
recursive learning method for training hidden layers in constant depth circuits.
Our findings make contributions to a) the field of Machine Learning, as the
proposed method is applicable in training feedforward neural networks, and to
b) the field of circuit complexity by proposing an upper bound for the number
of hidden units sufficient to achieve a high classification rate. One of the major
findings of our research is that the size of the network can be bounded by
the input size of the problem and an approximate upper bound of 8 + √2n/n
threshold gates as being sufficient for a small error rate, where n := log/SL
and SL is the training set. | en_US |
