Abstract: Latin hypercube designs (LHDs) have been applied in
many computer experiments among the space-filling designs found in
the literature. A LHD can be randomly generated but a randomly
chosen LHD may have bad properties and thus act poorly in
estimation and prediction. There is a connection between Latin
squares and orthogonal arrays (OAs). A Latin square of order s
involves an arrangement of s symbols in s rows and s columns, such
that every symbol occurs once in each row and once in each column
and this exists for every non-negative integer s. In this paper, a
computer program was written to construct orthogonal array-based
Latin hypercube designs (OA-LHDs). Orthogonal arrays (OAs) were
constructed from Latin square of order s and the OAs constructed
were afterward used to construct the desired Latin hypercube designs
for three input variables for use in computer experiments. The LHDs
constructed have better space-filling properties and they can be used
in computer experiments that involve only three input factors.
MATLAB 2012a computer package (www.mathworks.com/) was
used for the development of the program that constructs the designs.
Abstract: This paper proposes an efficient learning method for the layered neural networks based on the selection of training data and input characteristics of an output layer unit. Comparing to recent neural networks; pulse neural networks, quantum neuro computation, etc, the multilayer network is widely used due to its simple structure. When learning objects are complicated, the problems, such as unsuccessful learning or a significant time required in learning, remain unsolved. Focusing on the input data during the learning stage, we undertook an experiment to identify the data that makes large errors and interferes with the learning process. Our method devides the learning process into several stages. In general, input characteristics to an output layer unit show oscillation during learning process for complicated problems. The multi-stage learning method proposes by the authors for the function approximation problems of classifying learning data in a phased manner, focusing on their learnabilities prior to learning in the multi layered neural network, and demonstrates validity of the multi-stage learning method. Specifically, this paper verifies by computer experiments that both of learning accuracy and learning time are improved of the BP method as a learning rule of the multi-stage learning method. In learning, oscillatory phenomena of a learning curve serve an important role in learning performance. The authors also discuss the occurrence mechanisms of oscillatory phenomena in learning. Furthermore, the authors discuss the reasons that errors of some data remain large value even after learning, observing behaviors during learning.
Abstract: We study the spatial design of experiment and we want to select a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations and possibly at different times. In spatial design, when the design region and the set of interest are discrete then the covariance matrix completely describe any objective function and our goal is to choose a feasible design that minimizes the resulting uncertainty. The problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. This problem is NP-hard. For using these designs in computer experiments, in many cases, the design space is very large and it's not possible to calculate the exact optimal solution. Heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective and exact solution not possible. We developed a GA algorithm to take advantage of the exploratory power of this algorithm. The successful application of this method is demonstrated in large design space. We consider a real case of design of experiment. In our problem, design space is very large and for solving the problem, we used proposed GA algorithm.