We evaluate 179 classifiers arising from 17 families (discriminant analysis, Bayesian, neural networks, support vector machines, decision trees, rule-based classifiers, boosting, bagging, stacking, random forests and other ensembles, generalized linear models, nearest-neighbors, partial least squares and principal component regression, logistic and multinomial regression, multiple adaptive regression splines and other methods), implemented in Weka, R (with and without the caret package), C and Matlab, including all the relevant classifiers available today. We use 121 data sets, which represent the whole UCI data base (excluding the large-scale problems) and other own real problems, in order to achieve significant conclusions about the classifier behavior, not dependent on the data set collection. The classifiers most likely to be the bests are the random forest (RF) versions, the best of which (implemented in R and accessed via caret) achieves 94.1% of the maximum accuracy overcoming 90% in the 84.3% of the data sets. However, the difference is not statistically significant with the second best, the SVM with Gaussian kernel implemented in C using LibSVM, which achieves 92.3% of the maximum accuracy. A few models are clearly better than the remaining ones: random forest, SVM with Gaussian and polynomial kernels, extreme learning machine with Gaussian kernel, C5.0 and avNNet (a committee of multi-layer perceptrons implemented in R with the caret package). The random forest is clearly the best family of classifiers (3 out of 5 bests classifiers are RF), followed by SVM (4 classifiers in the top-10), neural networks and boosting ensembles (5 and 3 members in the top-20, respectively).

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Do we need hundreds of classifiers to solve real world classification problems

Trends in extreme learning machines

Extreme learning machine (ELM) is an emerging learning algorithm for the generalized single hidden layer feedforward neural networks, of which the hidden node parameters are randomly generated and the output weights are analytically computed. However, due to its shallow architecture, feature learning using ELM may not be effective for natural signals (e.g., images/videos), even with a large number of hidden nodes. To address this issue, in this paper, a new ELM-based hierarchical learning framework is proposed for multilayer perceptron. The proposed architecture is divided into two main components: 1) self-taught feature extraction followed by supervised feature classification and 2) they are bridged by random initialized hidden weights. The novelties of this paper are as follows: 1) unsupervised multilayer encoding is conducted for feature extraction, and an ELM-based sparse autoencoder is developed via $\ell _{1}$ constraint. By doing so, it achieves more compact and meaningful feature representations than the original ELM; 2) by exploiting the advantages of ELM random feature mapping, the hierarchically encoded outputs are randomly projected before final decision making, which leads to a better generalization with faster learning speed; and 3) unlike the greedy layerwise training of deep learning (DL), the hidden layers of the proposed framework are trained in a forward manner. Once the previous layer is established, the weights of the current layer are fixed without fine-tuning. Therefore, it has much better learning efficiency than the DL. Extensive experiments on various widely used classification data sets show that the proposed algorithm achieves better and faster convergence than the existing state-of-the-art hierarchical learning methods. Furthermore, multiple applications in computer vision further confirm the generality and capability of the proposed learning scheme.

Extreme Learning Machine for Multilayer Perceptron

Extreme learning machines (ELMs) basically give answers to two fundamental learning problems: (1) Can fundamentals of learning (i.e., feature learning, clus- tering, regression and classification) be made without tuning hidden neurons (including biological neurons) even when the output shapes and function modeling of these neurons are unknown? (2) Does there exist unified frame- work for feedforward neural networks and feature space methods? ELMs that have built some tangible links between machine learning techniques and biological learning mechanisms have recently attracted increasing attention of researchers in widespread research areas. This paper provides an insight into ELMs in three aspects, viz: random neurons, random features and kernels. This paper also shows that in theory ELMs (with the same kernels) tend to outperform support vector machine and its variants in both regression and classification applications with much easier implementation.

An Insight into Extreme Learning Machines: Random Neurons, Random Features and Kernels

This special issue includes eight original works that detail the further developments of ELMs in theories, applications, and hardware implementation. In "Representational Learning with ELMs for Big Data," Liyanaarachchi Lekamalage Chamara Kasun, Hongming Zhou, Guang-Bin Huang, and Chi Man Vong propose using the ELM as an auto-encoder for learning feature representations using singular values. In "A Secure and Practical Mechanism for Outsourcing ELMs in Cloud Computing," Jiarun Lin, Jianping Yin, Zhiping Cai, Qiang Liu, Kuan Li, and Victor C.M. Leung propose a method for handling large data applications by outsourcing to the cloud that would dramatically reduce ELM training time. In "ELM-Guided Memetic Computation for Vehicle Routing," Liang Feng, Yew-Soon Ong, and Meng-Hiot Lim consider the ELM as an engine for automating the encapsulation of knowledge memes from past problem-solving experiences. In "ELMVIS: A Nonlinear Visualization Technique Using Random Permutations and ELMs," Anton Akusok, Amaury Lendasse, Rui Nian, and Yoan Miche propose an ELM method for data visualization based on random permutations to map original data and their corresponding visualization points. In "Combining ELMs with Random Projections," Paolo Gastaldo, Rodolfo Zunino, Erik Cambria, and Sergio Decherchi analyze the relationships between ELM feature-mapping schemas and the paradigm of random projections. In "Reduced ELMs for Causal Relation Extraction from Unstructured Text," Xuefeng Yang and Kezhi Mao propose combining ELMs with neuron selection to optimize the neural network architecture and improve the ELM ensemble's computational efficiency. In "A System for Signature Verification Based on Horizontal and Vertical Components in Hand Gestures," Beom-Seok Oh, Jehyoung Jeon, Kar-Ann Toh, Andrew Beng Jin Teoh, and Jaihie Kim propose a novel paradigm for hand signature biometry for touchless applications without the need for handheld devices. Finally, in "An Adaptive and Iterative Online Sequential ELM-Based Multi-Degree-of-Freedom Gesture Recognition System," Hanchao Yu, Yiqiang Chen, Junfa Liu, and Guang-Bin Huang propose an online sequential ELM-based efficient gesture recognition algorithm for touchless human-machine interaction.

Extreme Learning Machine

Due to the simplicity of their implementations, least square support vector machine (LS-SVM) and proximal support vector machine (PSVM) have been widely used in binary classification applications. The conventional LS-SVM and PSVM cannot be used in regression and multiclass classification applications directly, although variants of LS-SVM and PSVM have been proposed to handle such cases. This paper shows that both LS-SVM and PSVM can be simplified further and a unified learning framework of LS-SVM, PSVM, and other regularization algorithms referred to extreme learning machine (ELM) can be built. ELM works for the “generalized” single-hidden-layer feedforward networks (SLFNs), but the hidden layer (or called feature mapping) in ELM need not be tuned. Such SLFNs include but are not limited to SVM, polynomial network, and the conventional feedforward neural networks. This paper shows the following: 1) ELM provides a unified learning platform with a widespread type of feature mappings and can be applied in regression and multiclass classification applications directly; 2) from the optimization method point of view, ELM has milder optimization constraints compared to LS-SVM and PSVM; 3) in theory, compared to ELM, LS-SVM and PSVM achieve suboptimal solutions and require higher computational complexity; and 4) in theory, ELM can approximate any target continuous function and classify any disjoint regions. As verified by the simulation results, ELM tends to have better scalability and achieve similar (for regression and binary class cases) or much better (for multiclass cases) generalization performance at much faster learning speed (up to thousands times) than traditional SVM and LS-SVM.

Extreme Learning Machine for Regression and Multiclass Classification

Extreme learning machines (ELMs) have been proposed for generalized single-hidden-layer feedforward networks which need not be neuron-like and perform well in both regression and classification applications. In this brief, we propose an ELM with adaptive growth of hidden nodes (AG-ELM), which provides a new approach for the automated design of networks. Different from other incremental ELMs (I-ELMs) whose existing hidden nodes are frozen when the new hidden nodes are added one by one, in AG-ELM the number of hidden nodes is determined in an adaptive way in the sense that the existing networks may be replaced by newly generated networks which have fewer hidden nodes and better generalization performance. We then prove that such an AG-ELM using Lebesgue p-integrable hidden activation functions can approximate any Lebesgue p-integrable function on a compact input set. Simulation results demonstrate and verify that this new approach can achieve a more compact network architecture than the I-ELM.

Universal Approximation of Extreme Learning Machine With Adaptive Growth of Hidden Nodes

Extreme learning machines (ELMs) have been proposed for generalized single-hidden-layer feedforward networks which need not be neuron alike and perform well in both regression and classification applications. The problem of determining the suitable network architectures is recognized to be crucial in the successful application of ELMs. This paper first proposes a dynamic ELM (D-ELM) where the hidden nodes can be recruited or deleted dynamically according to their significance to network performance, so that not only the parameters can be adjusted but also the architecture can be self-adapted simultaneously. Then, this paper proves in theory that such D-ELM using Lebesgue p-integrable hidden activation functions can approximate any Lebesgue p-integrable function on a compact input set. Simulation results obtained over various test problems demonstrate and verify that the proposed D-ELM does a good job reducing the network size while preserving good generalization performance.

Dynamic Extreme Learning Machine and Its Approximation Capability

The online backpropagation (BP) training procedure has been extensively explored in scientific research and engineering applications. One of the main factors affecting the performance of the online BP training is the learning rate. This paper proposes a new dynamic learning rate which is based on the estimate of the minimum error. The global convergence theory of the online BP training procedure with the proposed learning rate is further studied. It is proved that: 1) the error sequence converges to the global minimum error; and 2) the weight sequence converges to a fixed point at which the error function attains its global minimum. The obtained global convergence theory underlies the successful applications of the online BP training procedure. Illustrative examples are provided to support the theoretical analysis.

Global Convergence of Online BP Training With Dynamic Learning Rate

Credit risk evaluation has become an increasingly important field in financial risk management for financial institutions, especially for banks and credit card companies. Many data mining and statistical methods have been applied to this field. Extreme learning machine (ELM) classifier as a type of generalized single hidden layer feed-forward networks has been used in many applications and achieve good classification accuracy. Thus, we use ELM (kernel based) as a classification tool to perform the credit risk evaluation in this paper. The simulations are done on two credit risk evaluation datasets with three different kernel functions. Simulation results show that the kernel based ELM is more suitable for credit risk evaluation than the popular used Support Vector Machines (SVMs) with consideration of overall, good and bad accuracies.

Rui Zhang

Papers

Extreme Learning Machine for Regression and Multiclass Classification

Universal Approximation of Extreme Learning Machine With Adaptive Growth of Hidden Nodes

Dynamic Extreme Learning Machine and Its Approximation Capability

Global Convergence of Online BP Training With Dynamic Learning Rate

Credit risk evaluation with extreme learning machine