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<p>Extreme learning machine (ELM) exemplifies a single-hidden layer feedforward neural network, offering many advantages, especially fast training speed, and has been successfully applied to classification and regression problems. However, it also has some shortcomings. When faced with data containing outliers, it is shown that ELM will be affected by the outliers, which results in poor robustness, and that the output weights of most ELM models do not exhibit sparse performance. In recent years, regularization techniques have been used to improve the robustness and sparsity of ELM. In this study, a correntropy function is utilized as a loss function and regularization term to improve robustness and sparsity. Under the condition that large outliers are present, the correntropy loss function can suppress the influence of these outliers on the objective function. For the correntropy function, if the parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7620_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> is sufficiently small, it serves as a regularizer that approximates the zero-norm, resulting in good sparsity. Moreover, since the objective function is a non-convex function, it is difficult to solve it using the optimization method designed for convex functions. An effective approach is to solve the non-convex optimization problem of the objective function using the DC algorithm, which has been shown to be efficient in handling such problems. Experiments with benchmark datasets show that the proposed approach offers improved robustness and sparsity, particularly in cases where the dataset contains high outliers level.</p>

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Enhancing robustness and sparsity of extreme learning machine in regression problems using correntropy function

  • 期刊论文

  • 发表日期：

    2025年9月4日

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  • Yuzhu Jiang,
  • Kuaini Wang,
  • Jinge Li

摘要

Extreme learning machine (ELM) exemplifies a single-hidden layer feedforward neural network, offering many advantages, especially fast training speed, and has been successfully applied to classification and regression problems. However, it also has some shortcomings. When faced with data containing outliers, it is shown that ELM will be affected by the outliers, which results in poor robustness, and that the output weights of most ELM models do not exhibit sparse performance. In recent years, regularization techniques have been used to improve the robustness and sparsity of ELM. In this study, a correntropy function is utilized as a loss function and regularization term to improve robustness and sparsity. Under the condition that large outliers are present, the correntropy loss function can suppress the influence of these outliers on the objective function. For the correntropy function, if the parameter \(\sigma\) σ is sufficiently small, it serves as a regularizer that approximates the zero-norm, resulting in good sparsity. Moreover, since the objective function is a non-convex function, it is difficult to solve it using the optimization method designed for convex functions. An effective approach is to solve the non-convex optimization problem of the objective function using the DC algorithm, which has been shown to be efficient in handling such problems. Experiments with benchmark datasets show that the proposed approach offers improved robustness and sparsity, particularly in cases where the dataset contains high outliers level.