Universal approximation of extreme learning machine with adaptive growth of hidden nodes

Robust Extreme Learning Machine Using New Activation and Loss Functions Based on M-Estimation for Regression and Classification

This paper provides an analysis of the combining effect of novel activation function and loss function based on M-estimation in application to extreme learning machine (ELM), a feed-forward neural network. Due to the computational efficiency and classification/prediction accuracy of ELM and its variants, they have been widely exploited in the development of new technologies and applications. However, in real applications, the performance of classical ELMs deteriorates in the presence of outliers, thus, negatively impacting the precision and accuracy of the system. To further enhance the performance of ELM and its variants, we proposed novel activation functions based on the psi function of M and redescend the M-estimation method along with the smooth $\mathcal{l}$ 2-norm weight-loss functions to reduce the negative impact of the outliers. The proposed psi functions of several M and redescending M-estimation methods are more flexible to make more distinct features space. For the first time, the idea of the psi function as an activation function in the neural network is introduced in the literature to ensure accurate prediction. In addition, new robust $\mathcal{l}$ 2 norm-loss functions based on M and redescending M-estimation are proposed to deal with outliers efficiently in ELM. To evaluate the performance of the proposed methodology against other state-of-the-art techniques, experiments have been performed in diverse environments, which show promising improvements in application to regression and classification problems.

Multi-Scale LBP Texture Feature Learning Network for Remote Sensing Interpretation of Land Desertification

Land desertification is a major challenge to global sustainable development. Therefore, the timely and accurate monitoring of the land desertification status can provide scientific decision support for desertification control. The existing automatic interpretation methods are affected by factors such as “same spectrum different matter”, “different spectrum same object”, staggered distribution of desertification areas, and wide ranges of ground objects. We propose an automatic interpretation method for the remote sensing of land desertification that incorporates multi-scale local binary pattern (MSLBP) and spectral features based on the above issues. First, a multi-scale convolutional LBP feature extraction network is designed to obtain the spatial texture features of remote sensing images and fuse them with spectral features to enhance the feature representation capability of the model. Then, considering the continuity of the distribution of the same kind of ground objects in local space, we designed an adaptive median filtering method to process the probability map of the extreme learning machine (ELM) classifier output to improve the classification accuracy. Four typical datasets were developed using GF-1 multispectral imagery with the Horqin Left Wing Rear Banner as the study area. Experimental results on four datasets show that the proposed method solves the problem of ill classification and omission in classifying the remote sensing images of desertification, effectively suppresses the effects of “homospectrum” and “heterospectrum”, and significantly improves the accuracy of the remote sensing interpretation of land desertification.

Prototype Regularized Manifold Regularization Technique for Semi-Supervised Online Extreme Learning Machine

Data streaming applications such as the Internet of Things (IoT) require processing or predicting from sequential data from various sensors. However, most of the data are unlabeled, making applying fully supervised learning algorithms impossible. The online manifold regularization approach allows sequential learning from partially labeled data, which is useful for sequential learning in environments with scarcely labeled data. Unfortunately, the manifold regularization technique does not work out of the box as it requires determining the radial basis function (RBF) kernel width parameter. The RBF kernel width parameter directly impacts the performance as it is used to inform the model to which class each piece of data most likely belongs. The width parameter is often determined off-line via hyperparameter search, where a vast amount of labeled data is required. Therefore, it limits its utility in applications where it is difficult to collect a great deal of labeled data, such as data stream mining. To address this issue, we proposed eliminating the RBF kernel from the manifold regularization technique altogether by combining the manifold regularization technique with a prototype learning method, which uses a finite set of prototypes to approximate the entire data set. Compared to other manifold regularization approaches, this approach instead queries the prototype-based learner to find the most similar samples for each sample instead of relying on the RBF kernel. Thus, it no longer necessitates the RBF kernel, which improves its practicality. The proposed approach can learn faster and achieve a higher classification performance than other manifold regularization techniques based on experiments on benchmark data sets. Results showed that the proposed approach can perform well even without using the RBF kernel, which improves the practicality of manifold regularization techniques for semi-supervised learning.

Mixture Correntropy-Based Kernel Extreme Learning Machines

Kernel-based extreme learning machine (KELM), as a natural extension of ELM to kernel learning, has achieved outstanding performance in addressing various regression and classification problems. Compared with the basic ELM, KELM has a better generalization ability owing to no needs of the number of hidden nodes given beforehand and random projection mechanism. Since KELM is derived under the minimum mean square error (MMSE) criterion for the Gaussian assumption of noise, its performance may deteriorate under the non-Gaussian cases, seriously. To improve the robustness of KELM, this article proposes a mixture correntropy-based KELM (MC-KELM), which adopts the recently proposed maximum mixture correntropy criterion as the optimization criterion, instead of using the MMSE criterion. In addition, an online sequential version of MC-KELM (MCOS-KELM) is developed to deal with the case that the data arrive sequentially (one-by-one or chunk-by-chunk). Experimental results on regression and classification data sets are reported to validate the performance superiorities of the new methods.

A hybrid deep kernel incremental extreme learning machine based on improved coyote and beetle swarm optimization methods

The iteration times and learning efficiency of kernel incremental extreme learning machines are always affected by the redundant nodes. A hybrid deep kernel incremental extreme learning machine (DKIELM) based on the improved coyote and beetle swarm optimization methods was proposed in this paper. A hybrid intelligent optimization algorithm based on the improved coyote optimization algorithm (ICOA) and improved beetle swarm optimization algorithm (IBSOA) was proposed to optimize the parameters and determine the number of effectively hidden layer neurons for the proposed DKIELM. A Gaussian global best-growing operator was adopted to replace the original growing operator in the intelligent optimization algorithm to improve COA searching efficiency and convergence. In the meantime, IBSOA was designed based on tent mapping inverse learning and dynamic mutation strategies to avoid falling into a local optimum. The experimental results demonstrated the feasibility and effectiveness of the proposed DKIELM with encouraging performances compared with other ELMs.

Exploiting heterogeneity in operational neural networks by synaptic plasticity

The recently proposed network model, Operational Neural Networks (ONNs), can generalize the conventional Convolutional Neural Networks (CNNs) that are homogenous only with a linear neuron model. As a heterogenous network model, ONNs are based on a generalized neuron model that can encapsulate any set of non-linear operators to boost diversity and to learn highly complex and multi-modal functions or spaces with minimal network complexity and training data. However, the default search method to find optimal operators in ONNs, the so-called Greedy Iterative Search (GIS) method, usually takes several training sessions to find a single operator set per layer. This is not only computationally demanding, also the network heterogeneity is limited since the same set of operators will then be used for all neurons in each layer. To address this deficiency and exploit a superior level of heterogeneity, in this study the focus is drawn on searching the best-possible operator set(s) for the hidden neurons of the network based on the “Synaptic Plasticity” paradigm that poses the essential learning theory in biological neurons. During training, each operator set in the library can be evaluated by their synaptic plasticity level, ranked from the worst to the best, and an “elite” ONN can then be configured using the top-ranked operator sets found at each hidden layer. Experimental results over highly challenging problems demonstrate that the elite ONNs even with few neurons and layers can achieve a superior learning performance than GIS-based ONNs and as a result, the performance gap over the CNNs further widens.

IncDet: In Defense of Elastic Weight Consolidation for Incremental Object Detection

Elastic weight consolidation (EWC) has been successfully applied for general incremental learning to overcome the catastrophic forgetting issue. It adaptively constrains each parameter of the new model not to deviate much from its counterpart in the old model during fine-tuning on new class data sets, according to its importance weight for old tasks. However, the previous study demonstrates that it still suffers from catastrophic forgetting when directly used in object detection. In this article, we show EWC is effective for incremental object detection if with critical adaptations. First, we conduct controlled experiments to identify two core issues why EWC fails if trivially applied to incremental detection: 1) the absence of old class annotations in new class images makes EWC misclassify objects of old classes in these images as background and 2) the quadratic regularization loss in EWC easily leads to gradient explosion when balancing old and new classes. Then, based on the abovementioned findings, we propose the corresponding solutions to tackle these issues: 1) utilize pseudobounding box annotations of old classes on new data sets to compensate for the absence of old class annotations and 2) adopt a novel Huber regularization instead of the original quadratic loss to prevent from unstable training. Finally, we propose a general EWC-based incremental object detection framework and implement it under both Fast R-CNN and Faster R-CNN, showing its flexibility and versatility. In terms of either the final performance or the performance drop with respect to the upper bound of joint training on all seen classes, evaluations on the PASCAL VOC and COCO data sets show that our method achieves a new state of the art.

Recomputation of the Dense Layers for Performance Improvement of DCNN

Gradient descent optimization of learning has become a paradigm for training deep convolutional neural networks (DCNN). However, utilizing other learning strategies in the training process of the DCNN has rarely been explored by the deep learning (DL) community. This serves as the motivation to introduce a non-iterative learning strategy to retrain neurons at the top dense or fully connected (FC) layers of DCNN, resulting in, higher performance. The proposed method exploits the Moore-Penrose Inverse to pull back the current residual error to each FC layer, generating well-generalized features. Further, the weights of each FC layers are recomputed according to the Moore-Penrose Inverse. We evaluate the proposed approach on six most widely accepted object recognition benchmark datasets: Scene-15, CIFAR-10, CIFAR-100, SUN-397, Places365, and ImageNet. The experimental results show that the proposed method obtains improvements over 30 state-of-the-art methods. Interestingly, it also indicates that any DCNN with the proposed method can provide better performance than the same network with its original Backpropagation (BP)-based training.

A Hybrid Method Based on Extreme Learning Machine and Self Organizing Map for Pattern Classification

Extreme learning machine is a fast learning algorithm for single hidden layer feedforward neural network. However, an improper number of hidden neurons and random parameters have a great effect on the performance of the extreme learning machine. In order to select a suitable number of hidden neurons, this paper proposes a novel hybrid learning based on a two-step process. First, the parameters of hidden layer are adjusted by a self-organized learning algorithm. Next, the weights matrix of the output layer is determined using the Moore–Penrose inverse method. Nine classification datasets are considered to demonstrate the efficiency of the proposed approach compared with original extreme learning machine, Tikhonov regularization optimally pruned extreme learning machine, and backpropagation algorithms. The results show that the proposed method is fast and produces better accuracy and generalization performances.

Operational neural networks

Feed-forward, fully connected artificial neural networks or the so-called multi-layer perceptrons are well-known universal approximators. However, their learning performance varies significantly depending on the function or the solution space that they attempt to approximate. This is mainly because of their homogenous configuration based solely on the linear neuron model. Therefore, while they learn very well those problems with a monotonous, relatively simple and linearly separable solution space, they may entirely fail to do so when the solution space is highly nonlinear and complex. Sharing the same linear neuron model with two additional constraints (local connections and weight sharing), this is also true for the conventional convolutional neural networks (CNNs) and it is, therefore, not surprising that in many challenging problems only the deep CNNs with a massive complexity and depth can achieve the required diversity and the learning performance. In order to address this drawback and also to accomplish a more generalized model over the convolutional neurons, this study proposes a novel network model, called operational neural networks (ONNs), which can be heterogeneous and encapsulate neurons with any set of operators to boost diversity and to learn highly complex and multi-modal functions or spaces with minimal network complexity and training data. Finally, the training method to back-propagate the error through the operational layers of ONNs is formulated. Experimental results over highly challenging problems demonstrate the superior learning capabilities of ONNs even with few neurons and hidden layers.

An automatic estimation of the ridge parameter for extreme learning machine

Extreme learning machine (ELM) is an emerging learning method with a single-hidden layer feed-forward neural network that involves obtaining a solution to the system of linear equations. Unlike traditional gradient-based back-propagating neural networks, ELM is computationally efficient with fast training speed and good generalization capability. However, most of the time when applied to real-time problems, the linear system becomes ill-posed in the structure and needs the inclusion of a ridge parameter to obtain a reliable solution, and hence, the selection of the ridge parameter (C) is a crucial task. The ridge parameter is chosen heuristically from a predefined set. The generalized cross-validation is a widely used technique for the automatic estimation of the same, which is computationally expensive as it involves inversion of large matrices. The focus of the proposed work is on pragmatic aspects of the time-efficient automatic estimation of ridge parameter that result in a better generalization performance. In this work, methods are proposed that use the L-curve and U-curve techniques to automatically estimate the ridge parameter, and these methods are effective in the estimation of the ridge parameter even for systems with larger data. Through extensive numerical results, it is shown that the proposed methods outperform the existing ones in terms of accuracy, precision, sensitivity, specificity, F₁-score, and computational time on various benchmark binary as well as multiclass classification data sets. Finally, the proposed methods are statistically analyzed using the nonparametric Friedman ranking test, which is also proving the effectiveness of the proposed method as it is providing a better rank for the same over existing methods.

Spectral-Spatial Hyperspectral Image Classification with Superpixel Pattern and Extreme Learning Machine

Spectral-spatial classification of hyperspectral images (HSIs) has recently attracted great attention in the research domain of remote sensing. It is well-known that, in remote sensing applications, spectral features are the fundamental information and spatial patterns provide the complementary information. With both spectral features and spatial patterns, hyperspectral image (HSI) applications can be fully explored and the classification performance can be greatly improved. In reality, spatial patterns can be extracted to represent a line, a clustering of points or image texture, which denote the local or global spatial characteristic of HSIs. In this paper, we propose a spectral-spatial HSI classification model based on superpixel pattern (SP) and kernel based extreme learning machine (KELM), called SP-KELM, to identify the land covers of pixels in HSIs. In the proposed SP-KELM model, superpixel pattern features are extracted by an advanced principal component analysis (PCA), which is based on superpixel segmentation in HSIs and used to denote spatial information. The KELM method is then employed to be a classifier in the proposed spectral-spatial model with both the original spectral features and the extracted spatial pattern features. Experimental results on three publicly available HSI datasets verify the effectiveness of the proposed SP-KELM model, with the performance improvement of 10% over the spectral approaches.

Individual-Specific Classification of Mental Workload Levels Via an Ensemble Heterogeneous Extreme Learning Machine for EEG Modeling

In a human–machine cooperation system, assessing the mental workload (MW) of the human operator is quite crucial to maintaining safe operation conditions. Among various MW indicators, electroencephalography (EEG) signals are particularly attractive because of their high temporal resolution and sensitivity to the occupation of working memory. However, the individual difference of the EEG feature distribution may impair the machine-learning based MW classifier. In this paper, we employed a fast-training neural network, extreme learning machine (ELM), as the basis to build an individual-specific classifier ensemble to recognize binary MW. To improve the diversity of the classification committee, heterogeneous member classifiers were adopted by fusing multiple ELMs and Bayesian models. Specifically, a deep network structure was applied in each weak model aiming at finding informative EEG feature representations. The structure of hyper-parameters of the proposed heterogeneous ensemble ELM (HE-ELM) was then identified and then its performance was compared against several competitive MW classifiers. We found that the HE-ELM model was superior for improving the individual-specific accuracy of MW assessments.

Stationary Wavelet-Fourier Entropy and Kernel Extreme Learning for Bearing Multi-Fault Diagnosis

Bearing fault diagnosis methods play an important role in rotating machine health monitoring. In recent years, various intelligent fault diagnosis methods have been proposed, which are mainly based on the features extraction method combined with either shallow or deep learning methods. During the last few years, Shannon entropy features have been widely used in machine health monitoring, improving the accuracy of the bearing fault diagnosis process. Therefore, in this paper, we consider the combination of multi-scale stationary wavelet packet analysis with the Fourier amplitude spectrum to obtain a new discriminative Shannon entropy feature that we call stationary wavelet packet Fourier entropy (SWPFE). Features extracted by our SWPFE method are then passed onto a shallow kernel extreme learning machine (KELM) classifier to diagnose bearing failure types with different severities. The proposed method was applied on two experimental vibration signal databases of a rolling element bearing and compared to two recently proposed methods called stationary wavelet packet permutation entropy (SWPPE) and stationary wavelet packet dispersion entropy (SWPPE). Based on our results, we can say that the proposed method is able to achieve better accuracy levels than both the SWPPE and SWPDE methods using fewer failure features. Further, as our method does not require any hyperparameter calibration step, it is less dependent on user experience/expertise.

Combining Multi-Scale Wavelet Entropy and Kernelized Classification for Bearing Multi-Fault Diagnosis

Discriminative feature extraction and rolling element bearing failure diagnostics are very important to ensure the reliability of rotating machines. Therefore, in this paper, we propose multi-scale wavelet Shannon entropy as a discriminative fault feature to improve the diagnosis accuracy of bearing fault under variable work conditions. To compute the multi-scale wavelet entropy, we consider integrating stationary wavelet packet transform with both dispersion (SWPDE) and permutation (SWPPE) entropies. The multi-scale entropy features extracted by our proposed methods are then passed on to the kernel extreme learning machine (KELM) classifier to diagnose bearing failure types with different severities. In the end, both the SWPDE–KELM and the SWPPE–KELM methods are evaluated on two bearing vibration signal databases. We compare these two feature extraction methods to a recently proposed method called stationary wavelet packet singular value entropy (SWPSVE). Based on our results, we can say that the diagnosis accuracy obtained by the SWPDE–KELM method is slightly better than the SWPPE–KELM method and they both significantly outperform the SWPSVE–KELM method.

An unsupervised parameter learning model for RVFL neural network

With the direct input-output connections, a random vector functional link (RVFL) network is a simple and effective learning algorithm for single-hidden layer feedforward neural networks (SLFNs). RVFL is a universal approximator for continuous functions on compact sets with fast learning property. Owing to its simplicity and effectiveness, RVFL has attracted significant interest in numerous real-world applications. In reality, the performance of RVFL is often challenged by randomly assigned network parameters. In this paper, we propose a novel unsupervised network parameter learning method for RVFL, named sparse pre-trained random vector functional link (SP-RVFL for short) network. The proposed SP-RVFL uses a sparse autoencoder with ℓ₁-norm regularization to adaptively learn superior network parameters for specific learning tasks. By doing so, the learned network parameters in SP-RVFL are embedded with the valuable information of input data, which alleviate the randomly generated parameter issue and improve the algorithmic performance. Experiments and comparisons on 16 diverse benchmarks from different domains confirm the effectiveness of the proposed SP-RVFL. The corresponding results also demonstrate that RVFL outperforms extreme learning machine (ELM).

Evolutionary Cost-Sensitive Extreme Learning Machine

Conventional extreme learning machines (ELMs) solve a Moore-Penrose generalized inverse of hidden layer activated matrix and analytically determine the output weights to achieve generalized performance, by assuming the same loss from different types of misclassification. The assumption may not hold in cost-sensitive recognition tasks, such as face recognition-based access control system, where misclassifying a stranger as a family member may result in more serious disaster than misclassifying a family member as a stranger. Though recent cost-sensitive learning can reduce the total loss with a given cost matrix that quantifies how severe one type of mistake against another, in many realistic cases, the cost matrix is unknown to users. Motivated by these concerns, this paper proposes an evolutionary cost-sensitive ELM, with the following merits: 1) to the best of our knowledge, it is the first proposal of ELM in evolutionary cost-sensitive classification scenario; 2) it well addresses the open issue of how to define the cost matrix in cost-sensitive learning tasks; and 3) an evolutionary backtracking search algorithm is induced for adaptive cost matrix optimization. Experiments in a variety of cost-sensitive tasks well demonstrate the effectiveness of the proposed approaches, with about 5%-10% improvements.

Highly Efficient Framework for Predicting Interactions Between Proteins

Protein-protein interactions (PPIs) play a central role in many biological processes. Although a large amount of human PPI data has been generated by high-throughput experimental techniques, they are very limited compared to the estimated 130 000 protein interactions in humans. Hence, automatic methods for human PPI-detection are highly desired. This work proposes a novel framework, i.e., Low-rank approximation-kernel Extreme Learning Machine (LELM), for detecting human PPI from a protein's primary sequences automatically. It has three main steps: 1) mapping each protein sequence into a matrix built on all kinds of adjacent amino acids; 2) applying the low-rank approximation model to the obtained matrix to solve its lowest rank representation, which reflects its true subspace structures; and 3) utilizing a powerful kernel extreme learning machine to predict the probability for PPI based on this lowest rank representation. Experimental results on a large-scale human PPI dataset demonstrate that the proposed LELM has significant advantages in accuracy and efficiency over the state-of-art approaches. Hence, this work establishes a new and effective way for the automatic detection of PPI.

An Incremental Type-2 Meta-Cognitive Extreme Learning Machine

Existing extreme learning algorithm have not taken into account four issues: 1) complexity; 2) uncertainty; 3) concept drift; and 4) high dimensionality. A novel incremental type-2 meta-cognitive extreme learning machine (ELM) called evolving type-2 ELM (eT2ELM) is proposed to cope with the four issues in this paper. The eT2ELM presents three main pillars of human meta-cognition: 1) what-to-learn; 2) how-to-learn; and 3) when-to-learn. The what-to-learn component selects important training samples for model updates by virtue of the online certainty-based active learning method, which renders eT2ELM as a semi-supervised classifier. The how-to-learn element develops a synergy between extreme learning theory and the evolving concept, whereby the hidden nodes can be generated and pruned automatically from data streams with no tuning of hidden nodes. The when-to-learn constituent makes use of the standard sample reserved strategy. A generalized interval type-2 fuzzy neural network is also put forward as a cognitive component, in which a hidden node is built upon the interval type-2 multivariate Gaussian function while exploiting a subset of Chebyshev series in the output node. The efficacy of the proposed eT2ELM is numerically validated in 12 data streams containing various concept drifts. The numerical results are confirmed by thorough statistical tests, where the eT2ELM demonstrates the most encouraging numerical results in delivering reliable prediction, while sustaining low complexity.

Extreme Learning Machine With Subnetwork Hidden Nodes for Regression and Classification

As demonstrated earlier, the learning effectiveness and learning speed of single-hidden-layer feedforward neural networks are in general far slower than required, which has been a major bottleneck for many applications. Huang et al. proposed extreme learning machine (ELM) which improves the training speed by hundreds of times as compared to its predecessor learning techniques. This paper offers an ELM-based learning method that can grow subnetwork hidden nodes by pulling back residual network error to the hidden layer. Furthermore, the proposed method provides a similar or better generalization performance with remarkably fewer hidden nodes as compared to other ELM methods employing huge number of hidden nodes. Thus, the learning speed of the proposed technique is hundred times faster compared to other ELMs as well as to back propagation and support vector machines. The experimental validations for all methods are carried out on 32 data sets.

An Improved Ensemble of Random Vector Functional Link Networks Based on Particle Swarm Optimization with Double Optimization Strategy

For ensemble learning, how to select and combine the candidate classifiers are two key issues which influence the performance of the ensemble system dramatically. Random vector functional link networks (RVFL) without direct input-to-output links is one of suitable base-classifiers for ensemble systems because of its fast learning speed, simple structure and good generalization performance. In this paper, to obtain a more compact ensemble system with improved convergence performance, an improved ensemble of RVFL based on attractive and repulsive particle swarm optimization (ARPSO) with double optimization strategy is proposed. In the proposed method, ARPSO is applied to select and combine the candidate RVFL. As for using ARPSO to select the optimal base RVFL, ARPSO considers both the convergence accuracy on the validation data and the diversity of the candidate ensemble system to build the RVFL ensembles. In the process of combining RVFL, the ensemble weights corresponding to the base RVFL are initialized by the minimum norm least-square method and then further optimized by ARPSO. Finally, a few redundant RVFL is pruned, and thus the more compact ensemble of RVFL is obtained. Moreover, in this paper, theoretical analysis and justification on how to prune the base classifiers on classification problem is presented, and a simple and practically feasible strategy for pruning redundant base classifiers on both classification and regression problems is proposed. Since the double optimization is performed on the basis of the single optimization, the ensemble of RVFL built by the proposed method outperforms that built by some single optimization methods. Experiment results on function approximation and classification problems verify that the proposed method could improve its convergence accuracy as well as reduce the complexity of the ensemble system.