Synthetic minority oversampling for function approximation problems

2019 ◽  
Vol 34 (11) ◽  
pp. 2741-2768 ◽  
Author(s):  
Lourdes Pelayo ◽  
Scott Dick
Keyword(s):  
Function Approximation ◽  
Approximation Problems

GENERATING BALANCED LEARNING AND TEST SETS FOR FUNCTION APPROXIMATION PROBLEMS

2011 ◽  
Vol 21 (03) ◽  
pp. 247-263 ◽  
Author(s):  
J. P. FLORIDO ◽  
H. POMARES ◽  
I. ROJAS
Keyword(s):  
Function Approximation ◽  
Nearest Neighbor ◽  
Learning Algorithm ◽  
Original Data ◽  
Input Output ◽  
Output Data ◽  
Data Set ◽  
Out Of Sample ◽  
Test Sets ◽  
Approximation Problems

In function approximation problems, one of the most common ways to evaluate a learning algorithm consists in partitioning the original data set (input/output data) into two sets: learning, used for building models, and test, applied for genuine out-of-sample evaluation. When the partition into learning and test sets does not take into account the variability and geometry of the original data, it might lead to non-balanced and unrepresentative learning and test sets and, thus, to wrong conclusions in the accuracy of the learning algorithm. How the partitioning is made is therefore a key issue and becomes more important when the data set is small due to the need of reducing the pessimistic effects caused by the removal of instances from the original data set. Thus, in this work, we propose a deterministic data mining approach for a distribution of a data set (input/output data) into two representative and balanced sets of roughly equal size taking the variability of the data set into consideration with the purpose of allowing both a fair evaluation of learning's accuracy and to make reproducible machine learning experiments usually based on random distributions. The sets are generated using a combination of a clustering procedure, especially suited for function approximation problems, and a distribution algorithm which distributes the data set into two sets within each cluster based on a nearest-neighbor approach. In the experiments section, the performance of the proposed methodology is reported in a variety of situations through an ANOVA-based statistical study of the results.

RBF CENTERS INITIALIZATION USING FUZZY CLUSTERING TECHNIQUE FOR FUNCTION APPROXIMATION PROBLEMS

2005 ◽  
Vol 10 (02) ◽  
Author(s):  
A. Guillén ◽  
I. Rojas ◽  
J. González ◽  
H. Pomares ◽  
L. J. Herrera
Keyword(s):  
Fuzzy Clustering ◽  
Function Approximation ◽  
Clustering Technique ◽  
Approximation Problems

Rational Function Functional Networks Based on Function Approximation

2012 ◽  
Vol 220-223 ◽  
pp. 2264-2268 ◽  
Author(s):  
Dong Dong Wang ◽  
You Jun Chen ◽  
Hai Jie Pang
Keyword(s):  
Rational Function ◽  
Lagrange Multiplier ◽  
Function Approximation ◽  
Learning Algorithm ◽  
Linear Equations ◽  
Mathematic Model ◽  
Auxiliary Function ◽  
Functional Networks ◽  
System Of Linear Equations ◽  
Approximation Problems

In order to solve function approximation, a mathematic model of Rational Function Functional Networks (RFFN) based on approximation was proposed and the learning algorithm for function approximation was presented. This algorithm used the lease square method thought and constructed auxiliary function by Lagrange multiplier method, and the parameters of the rational function functional networks were determined by solving a system of linear equations. Results illustrate the effectiveness of the rational function functional networks in solving approximation problems of the function with a pole.

Controlling Hidden Layer Capacity Through Lateral Connections

1997 ◽  
Vol 9 (6) ◽  
pp. 1381-1402 ◽  
Author(s):  
Kwabena Agyepong ◽  
Ravi Kothari
Keyword(s):  
Function Approximation ◽  
Learning Task ◽  
Feedforward Neural Network ◽  
Effective Number ◽  
Real World Data ◽  
Data Set ◽  
Approximation Problems ◽  
Free Parameters ◽  
Hidden Layer ◽  
Hidden Neurons

We investigate the effects of including selected lateral interconnections in a feedforward neural network. In a network with one hidden layer consisting of m hidden neurons labeled 1,2… m, hidden neuron j is connected fully to the inputs, the outputs, and hidden neuron j + 1. As a consequence of the lateral connections, each hidden neuron receives two error signals: one from the output layer and one through the lateral interconnection. We show that the use of these lateral interconnections among the hidden-layer neurons facilitates controlled assignment of role and specialization of the hidden-layer neurons. In particular, we show that as training progresses, hidden neurons become progressively specialized—starting from the fringes (i.e., lower and higher numbered hidden neurons, e.g., 1, 2, m — 1 m) and leaving the neurons in the center of the hidden layer (i.e., hidden-layer neurons numbered close to m/2) unspecialized or functionally identical. Consequently, the network behaves like network growing algorithms without the explicit need to add hidden units, and like soft weight sharing due to functionally identical neurons in the center of the hidden layer. Experimental results from one classification and one function approximation problems are presented to illustrate selective specialization of the hidden-layer neurons. In addition, the improved generalization that results from a decrease in the effective number of free parameters is illustrated through a simple function approximation example and with a real-world data set. Besides the reduction in the number of free parameters, the localization of weight sharing may also allow for a method that allows procedural determination for the number of hidden-layer neurons required for a given learning task.

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