Abstract
This article provides a tool that can be used in the exact sciences to obtain good approximations to reality when noisy data is inevitable. Two heuristic optimization algorithms are implemented: Simulated Annealing and Particle Swarming for the determination of the extreme learning machine output weights. The first operates in a large search space and at each iteration it probabilistically decides between staying at its current state or moving to another. The swarm of particles, it optimizes a problem from a population of candidate solutions, moving them throughout the search space according to position and speed. The methodology consists of building data sets around a polynomial function, implementing the heuristic algorithms and comparing the errors with the traditional computation method using the Moore–Penrose inverse. The results show that the heuristic optimization algorithms implemented improve the estimation of the output weights when the input have highly noisy data.
Highlights
A basic problem in science is to create prediction models from observations that are subject to errors
The results show that the heuristic optimization algorithms implemented improve the estimation of the output weights when the input have highly noisy data
The objectives of this work are: first to show that the estimation error with the MoorePenrose inverse increases as the noise in the data increases and second that the hueristic optimization processes: simulated annealing and particle swarm improve the robustness of the extreme learning machine for highly noisy data
Summary
A basic problem in science is to create prediction models from observations that are subject to errors. One of the techniques for obtaining prediction models are artificial neural networks, which can find nonlinear relationships between data sets through learning algorithms, obtaining models of complex problems. The extreme learning machine consists of randomly initializing the weights of the hidden network layer and calculating the output weights using the Moore-Penrose inverse. In this sense, the objectives of this work are: first to show that the estimation error with the MoorePenrose inverse increases as the noise in the data increases and second that the hueristic optimization processes: simulated annealing and particle swarm improve the robustness of the extreme learning machine for highly noisy data. The training of a neural network can be seen as an optimization process whose objective is to find a set of weights that minimizes the error produced by the network on the training data set [1, 2]
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