Comparing error minimized extreme learning machines and support vector sequential feed-forward neural networks

Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. These approaches are referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the sequential approximation with optimal coefficients and interacting frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the computation of the optimal output-layer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems. © 2011 Elsevier Ltd.This work was supported in part by the Ministerio de Ciencia e Innovación (MICINN), under project TIN2009-13895-C02-01.Peer Reviewe

Comparing error minimized extreme learning machines and support vector sequential feed-forward neural networks

Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. By analogy with the concept of support vectors original of support vector machines (SVMs), these approaches can be referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the Sequential Approximation with Optimal Coefficients and Interacting Frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the calculation of the optimal output-layer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems.Postprint (published version

Aviation Safety Evaluation by Wavelet Kernel-Based Support Vector Machine

In order to obtain the excellent evaluation effects, the wavelet kernel function is used as the kernel function of support vector machine,and the model is defined as wavelet kernel-based support vector machine.Thus, wavelet kernel-based support vector machine is applied to aviation safety evaluation. The two dimensional input vector of the training samples is employed to construct the training samples.The traditional radial basis function kernel-based support vector machine is used to compare with the wavelet kernel-based support vector machine.The testing results show that the evaluation error of the wavelet kernel-based support vector machine belongs to the range from 0.015 to 0.04,and the evaluation error of the traditional radial basis function kernel-based support vector machine belongs to the range from 0.02 to 0.07.Then,we can conclude that aviation accidents evaluation accuracy of wavelet kernel-based support vector machine is higher than those of traditional radial basis function kernel-based support vector machine

Bearing fault diagnosis based on EMD-KPCA and ELM

In recent years, many studies have been conducted in bearing fault diagnosis, which has attracted increasing attention due to its nonlinear and non-stationary characteristics. To solve this problem, this paper proposes, a fault diagnosis method based on Empirical Mode Decomposition (EMD), Kernel Principal Component Analysis (KPCA), and Extreme Learning Machines (ELM) neural network, which combines the existing self-adaptive time-frequency signal processing with the advantages of non-linear multivariate dimensionality reduction KPCA approach and ELM neural network. First, EMD is applied to decompose the vibration signals into a finite number of intrinsic mode functions, in which the corresponding energy values are selected as the initial feature vector. Second, KPCA is used to further reduce the dimensionality for a simplified low-dimension feature vector. Finally, ELM is introduced to classify the extracted fault feature vectors for lessening the human intervention and reducing the fault diagnosis time. Experimental results demonstrate that the proposed diagnostic can effectively identify and classify typical bearing faults

Comparing error minimized extreme learning machines and support vector sequential feed-forward neural networks

Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. These approaches are referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the sequential approximation with optimal coefficients and interacting frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the computation of the optimal outputlayer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems.Peer Reviewe

Comparing error minimized extreme learning machines and support vector sequential feed-forward neural networks

Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. These approaches are referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the sequential approximation with optimal coefficients and interacting frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the computation of the optimal outputlayer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems.Peer ReviewedPostprint (published version

Comparing error minimized extreme learning machines and support vector sequential feed-forward neural networks

Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. These approaches are referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the sequential approximation with optimal coefficients and interacting frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the computation of the optimal outputlayer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems.Peer Reviewe

Comparing error minimized extreme learning machines and support vector sequential feed-forward neural networks

Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. By analogy with the concept of support vectors original of support vector machines (SVMs), these approaches can be referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the Sequential Approximation with Optimal Coefficients and Interacting Frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the calculation of the optimal output-layer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems

Benchmarking the selection of the hidden-layer weights in extreme learning machines

Recent years have seen a growing interest in neural networks whose hidden-layer weights are randomly selected, such as Extreme Learning Machines (ELMs). These models are motivated by their ease of development, high computational learning speed and relatively good results. Alternatively, constructive models that select the hidden-layer weights as a subset of the data have shown superior performance than random-based ones in some cases. In this work, we present a comparison between original ELMs (i.e., ELMs where the hidden-layer weights are selected randomly, that we will call ELM-Random) and a modified version of ELMs where the hidden-layer weights are a subset of the input data (that we will call ELM-Input). We will focus our comparison on the behavior of both strategies for different sizes of the training set and different network sizes. The results on several benchmark data sets for classification problems show that ELM-Input has superior performance than ELM-Random in some cases and similar in the rest. In some cases, this general trend is observed for all sizes of the training set and all network sizes. In other cases, it is mostly observed when the size of the training set is small. Therefore, the strategy of selecting the hidden-layer weights among the data can be considered as a good alternative or complement to the standard random selection for ELMs.Peer ReviewedPostprint (author's final draft

Parametric and Nonparametric Statistical Methods for Genomic Selection of Traits with Additive and Epistatic Genetic Architectures

Parametric and nonparametric methods have been developed for purposes of predicting phenotypes. These methods are based on retrospective analyses of empirical data consisting of genotypic and phenotypic scores. Recent reports have indicated that parametric methods are unable to predict phenotypes of traits with known epistatic genetic architectures. Herein, we review parametric methods including least squares regression, ridge regression, Bayesian ridge regression, least absolute shrinkage and selection operator (LASSO), Bayesian LASSO, best linear unbiased prediction (BLUP), Bayes A, Bayes B, Bayes C, and Bayes Cπ. We also review nonparametric methods including Nadaraya-Watson estimator, reproducing kernel Hilbert space, support vector machine regression, and neural networks. We assess the relative merits of these 14 methods in terms of accuracy and mean squared error (MSE) using simulated genetic architectures consisting of completely additive or two-way epistatic interactions in an F2 population derived from crosses of inbred lines. Each simulated genetic architecture explained either 30% or 70% of the phenotypic variability. The greatest impact on estimates of accuracy and MSE was due to genetic architecture. Parametric methods were unable to predict phenotypic values when the underlying genetic architecture was based entirely on epistasis. Parametric methods were slightly better than nonparametric methods for additive genetic architectures. Distinctions among parametric methods for additive genetic architectures were incremental. Heritability, i.e., proportion of phenotypic variability, had the second greatest impact on estimates of accuracy and MSE