# Fpga implementation of random feature mapping in elm algorithm for binary classification

29 Jan 2020-Vol. 659, pp 504-510

TL;DR: In this article, a low-cost hardware implementation of 16-bit H-matrix generation on FPGA is discussed, which is carried out on Nexys-4 board using MATLAB and hardware description language (HDL).

Abstract: Extreme learning machine (ELM) is a single layer feedforward neural network algorithm used for classification problems due to its accuracy and speed. It provides a robust learning algorithm, free of local minima, suitable for high-speed computation along with fast learning speed. In this paper, ELM algorithm implementation on hardware and software is discussed. A low-cost hardware implementation of 16-bit H-matrix generation on FPGA is discussed in the paper. Hardware implementation is carried out on Nexys-4 board using MATLAB and hardware description language (HDL). Generation of H-matrix is carried out using two activation functions, piecewise log-sigmoid and piecewise tan-sigmoid. This paper aims at optimizing the hardware implementation of ELM algorithm by minimizing the utilized resources of the FPGA. Finally, the ELM algorithm accuracy and hardware utilization for both activation functions are compared.

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Bell Labs

^{1}TL;DR: High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated and the performance of the support- vector network is compared to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.

Abstract: The support-vector network is a new learning machine for two-group classification problems. The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space. In this feature space a linear decision surface is constructed. Special properties of the decision surface ensures high generalization ability of the learning machine. The idea behind the support-vector network was previously implemented for the restricted case where the training data can be separated without errors. We here extend this result to non-separable training data.
High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated. We also compare the performance of the support-vector network to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.

35,157 citations

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TL;DR: A new learning algorithm called ELM is proposed for feedforward neural networks (SLFNs) which randomly chooses hidden nodes and analytically determines the output weights of SLFNs which tends to provide good generalization performance at extremely fast learning speed.

Abstract: It is clear that the learning speed of feedforward neural networks is in general far slower than required and it has been a major bottleneck in their applications for past decades. Two key reasons behind may be: (1) the slow gradient-based learning algorithms are extensively used to train neural networks, and (2) all the parameters of the networks are tuned iteratively by using such learning algorithms. Unlike these conventional implementations, this paper proposes a new learning algorithm called e xtreme l earning m achine (ELM) for s ingle-hidden l ayer f eedforward neural n etworks (SLFNs) which randomly chooses hidden nodes and analytically determines the output weights of SLFNs. In theory, this algorithm tends to provide good generalization performance at extremely fast learning speed. The experimental results based on a few artificial and real benchmark function approximation and classification problems including very large complex applications show that the new algorithm can produce good generalization performance in most cases and can learn thousands of times faster than conventional popular learning algorithms for feedforward neural networks. 1

8,861 citations

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TL;DR: ELM provides a unified learning platform with a widespread type of feature mappings and can be applied in regression and multiclass classification applications directly and in theory, ELM can approximate any target continuous function and classify any disjoint regions.

Abstract: 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.

4,130 citations

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TL;DR: This paper shows that while retaining the same simplicity, the convergence rate of I-ELM can be further improved by recalculating the output weights of the existing nodes based on a convex optimization method when a new hidden node is randomly added.

Abstract: Unlike the conventional neural network theories and implementations, Huang et al. [Universal approximation using incremental constructive feedforward networks with random hidden nodes, IEEE Transactions on Neural Networks 17(4) (2006) 879-892] have recently proposed a new theory to show that single-hidden-layer feedforward networks (SLFNs) with randomly generated additive or radial basis function (RBF) hidden nodes (according to any continuous sampling distribution) can work as universal approximators and the resulting incremental extreme learning machine (I-ELM) outperforms many popular learning algorithms. I-ELM randomly generates the hidden nodes and analytically calculates the output weights of SLFNs, however, I-ELM does not recalculate the output weights of all the existing nodes when a new node is added. This paper shows that while retaining the same simplicity, the convergence rate of I-ELM can be further improved by recalculating the output weights of the existing nodes based on a convex optimization method when a new hidden node is randomly added. Furthermore, we show that given a type of piecewise continuous computational hidden nodes (possibly not neural alike nodes), if SLFNs f"n(x)=@?i=1n@b"iG(x,a"i,b"i) can work as universal approximators with adjustable hidden node parameters, from a function approximation point of view the hidden node parameters of such ''generalized'' SLFNs (including sigmoid networks, RBF networks, trigonometric networks, threshold networks, fuzzy inference systems, fully complex neural networks, high-order networks, ridge polynomial networks, wavelet networks, etc.) can actually be randomly generated according to any continuous sampling distribution. In theory, the parameters of these SLFNs can be analytically determined by ELM instead of being tuned.

1,010 citations

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TL;DR: The proposed enhanced I-ELM works for the widespread type of piecewise continuous hidden nodes and is proposed as a universal approximator for constructive feedforward networks.

Abstract: Recently an incremental algorithm referred to as incremental extreme learning machine (I-ELM) was proposed by Huang et al. [G.-B. Huang, L. Chen, C.-K. Siew, Universal approximation using incremental constructive feedforward networks with random hidden nodes, IEEE Trans. Neural Networks 17(4) (2006) 879-892], which randomly generates hidden nodes and then analytically determines the output weights. Huang et al. [G.-B. Huang, L. Chen, C.-K. Siew, Universal approximation using incremental constructive feedforward networks with random hidden nodes, IEEE Trans. Neural Networks 17(4) (2006) 879-892] have proved in theory that although additive or RBF hidden nodes are generated randomly the network constructed by I-ELM can work as a universal approximator. During our recent study, it is found that some of the hidden nodes in such networks may play a very minor role in the network output and thus may eventually increase the network complexity. In order to avoid this issue and to obtain a more compact network architecture, this paper proposes an enhanced method for I-ELM (referred to as EI-ELM). At each learning step, several hidden nodes are randomly generated and among them the hidden node leading to the largest residual error decreasing will be added to the existing network and the output weight of the network will be calculated in a same simple way as in the original I-ELM. Generally speaking, the proposed enhanced I-ELM works for the widespread type of piecewise continuous hidden nodes.

818 citations

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