Unsupervised feature selection based extreme learning machine for clustering

Chen, Jichao; Zeng, Yijie; Li, Yue; Huang, Guang-Bin

doi:10.1016/j.neucom.2019.12.065

Cited by 60 publications

(18 citation statements)

References 26 publications

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“…where V T is an (L − 1)-dimensional row vector, W T is an (L − 1) × (L − 1) square matrix, and v is a scalar. Substituting formula (14) to (13), A L−1 can be solved as…”

Section: E Solutions Of P-melm By Cholesky Factorization and Givens Rotation Transformation Previous Research Hasmentioning

confidence: 99%

“…In the ELM algorithm, the input weights and hidden biases are randomly generated from any continuous probability distribution, and then, the output weights can be solved using the generalized Moore-Penrose inverse. Compared with the BP neural network, this algorithm has a good performance network in regression [4][5][6], classification [7][8][9], feature learning [10][11][12], and cluster tasks [13][14][15]. Different from conventional gradient-based neural network learning algorithms, which are sensitive to the combination of parameters and easy to trap in local optimum, ELM not only has a faster training speed but also has a smaller training error.…”

Section: Introductionmentioning

confidence: 99%

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Pruning Multilayered ELM Using Cholesky Factorization and Givens Rotation Transformation

Liu

et al. 2021

Mathematical Problems in Engineering

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Extreme learning machine is originally proposed for the learning of the single hidden layer feedforward neural network to overcome the challenges faced by the backpropagation (BP) learning algorithm and its variants. Recent studies show that ELM can be extended to the multilayered feedforward neural network in which the hidden node could be a subnetwork of nodes or a combination of other hidden nodes. Although the ELM algorithm with multiple hidden layers shows stronger nonlinear expression ability and stability in both theoretical and experimental results than the ELM algorithm with the single hidden layer, with the deepening of the network structure, the problem of parameter optimization is also highlighted, which usually requires more time for model selection and increases the computational complexity. This paper uses Cholesky factorization strategy and Givens rotation transformation to choose the hidden nodes of MELM and obtains the number of nodes more suitable for the network. First, the initial network has a large number of hidden nodes and then uses the idea of ridge regression to prune the nodes. Finally, a complete neural network can be obtained. Therefore, the ELM algorithm eliminates the need to manually set nodes and achieves complete automation. By using information from the previous generation’s connection weight matrix, it can be evitable to re-calculate the weight matrix in the network simplification process. As in the matrix factorization methods, the Cholesky factorization factor is calculated by Givens rotation transform to achieve the fast decreasing update of the current connection weight matrix, thus ensuring the numerical stability and high efficiency of the pruning process. Empirical studies on several commonly used classification benchmark problems and the real datasets collected from coal industry show that compared with the traditional ELM algorithm, the pruning multilayered ELM algorithm proposed in this paper can find the optimal number of hidden nodes automatically and has better generalization performance.

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“…where V T is an (L − 1)-dimensional row vector, W T is an (L − 1) × (L − 1) square matrix, and v is a scalar. Substituting formula (14) to (13), A L−1 can be solved as…”

Section: E Solutions Of P-melm By Cholesky Factorization and Givens Rotation Transformation Previous Research Hasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pruning Multilayered ELM Using Cholesky Factorization and Givens Rotation Transformation

Liu

et al. 2021

Mathematical Problems in Engineering

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“…Extensions to this basic scheme include multilayer ELMs [14,30,59] and deep ELMs [60]. As with conventional neural networks, convolutional networks and deep learning, ELMs have been mainly used for classification purposes [4,11,12,32,59,61]. On the other hand, the use of ELMs for "traditional" numerical analysis tasks and in particular for the numerical solution of PDEs is still widely unexplored.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines

et al. 2021

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We address a new numerical method based on a class of machine learning methods, the so-called Extreme Learning Machines (ELM) with both sigmoidal and radial-basis functions, for the computation of steady-state solutions and the construction of (one-dimensional) bifurcation diagrams of nonlinear partial differential equations (PDEs). For our illustrations, we considered two benchmark problems, namely (a) the one-dimensional viscous Burgers with both homogeneous (Dirichlet) and non-homogeneous boundary conditions, and, (b) the one- and two-dimensional Liouville–Bratu–Gelfand PDEs with homogeneous Dirichlet boundary conditions. For the one-dimensional Burgers and Bratu PDEs, exact analytical solutions are available and used for comparison purposes against the numerical derived solutions. Furthermore, the numerical efficiency (in terms of numerical accuracy, size of the grid and execution times) of the proposed numerical machine-learning method is compared against central finite differences (FD) and Galerkin weighted-residuals finite-element (FEM) methods. We show that the proposed numerical machine learning method outperforms in terms of numerical accuracy both FD and FEM methods for medium to large sized grids, while provides equivalent results with the FEM for low to medium sized grids; both methods (ELM and FEM) outperform the FD scheme. Furthermore, the computational times required with the proposed machine learning scheme were comparable and in particular slightly smaller than the ones required with FEM.

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“…In addition to being used for traditional classification and regression tasks, ELM has recently been extended for clustering, feature selection, and representation learning [ 16 ]. For more research on ELM, please refer to related literatures [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Method Based on Extreme Learning Machine and Wavelet Transform Denoising for Stock Prediction

Wang

2021

Entropy

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The trend prediction of the stock is a main challenge. Accidental factors often lead to short-term sharp fluctuations in stock markets, deviating from the original normal trend. The short-term fluctuation of stock price has high noise, which is not conducive to the prediction of stock trends. Therefore, we used discrete wavelet transform (DWT)-based denoising to denoise stock data. Denoising the stock data assisted us to eliminate the influences of short-term random events on the continuous trend of the stock. The denoised data showed more stable trend characteristics and smoothness. Extreme learning machine (ELM) is one of the effective training algorithms for fully connected single-hidden-layer feedforward neural networks (SLFNs), which possesses the advantages of fast convergence, unique results, and it does not converge to a local minimum. Therefore, this paper proposed a combination of ELM- and DWT-based denoising to predict the trend of stocks. The proposed method was used to predict the trend of 400 stocks in China. The prediction results of the proposed method are a good proof of the efficacy of DWT-based denoising for stock trends, and showed an excellent performance compared to 12 machine learning algorithms (e.g., recurrent neural network (RNN) and long short-term memory (LSTM)).

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Unsupervised feature selection based extreme learning machine for clustering

Cited by 60 publications

References 26 publications

Pruning Multilayered ELM Using Cholesky Factorization and Givens Rotation Transformation

Pruning Multilayered ELM Using Cholesky Factorization and Givens Rotation Transformation

Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines

A Hybrid Method Based on Extreme Learning Machine and Wavelet Transform Denoising for Stock Prediction

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