<p>Matrix decomposition is widely employed in data mining and machine learning. It serves to transform high-dimensional image data into lower-dimensional representations, thereby facilitating dimensionality reduction. By means of dimensionality reduction, the intricacy of the data is lessened, enabling the extraction of its most salient features. This, in turn, aids clustering algorithms in gaining a deeper understanding of the data. However, matrix decomposition also comes with certain limitations. Firstly, matrix decomposition is sensitive to noise and outliers in the data, which can adversely affect the decomposition results and consequently impact the accuracy of clustering outcomes. Secondly, if too many potential features are selected, it may lead to overfitting and reduce the generalization ability of the model. To address these issues, we propose a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha {-}\beta \)</EquationSource> </InlineEquation>-divergences reconstruction (AB) and non-convex sparse regularization (NCSR) based fast and robust matrix decomposition (ABN-FRMD). In ABN-FRMD, we introduce <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha {-}\beta \)</EquationSource> </InlineEquation>-divergences. <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation> divergence promotes weight sparsity, reducing the number of features and simplifying image clustering. The <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\beta \)</EquationSource> </InlineEquation> divergence helps maintain the stability and smoothness of parameters. By combining different regularization terms, the robustness of image clustering to noise and outliers can be enhanced. We introduce the Minimax Concave Penalty (MCP) function as a non-convex sparse regularization term in ABN-FRMD. By more effectively controlling the complexity of the model and reducing overfitting, the non-convex sparse regularization term can enhance the generalization ability of the model on unseen data. Moreover, using a non-convex continuous function to approximate the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\ell _0\)</EquationSource> </InlineEquation>-norm can more effectively promote sparsity. Finally, our experimental studies on five datasets demonstrate that compared with other clustering algorithm, ABN-FRMD algorithm achieves superior performance in terms of image clustering performance.</p>

Joint \(\alpha {-}\beta \)-divergences reconstruction and non-convex sparse regularization for image clustering

期刊论文
发表日期：

2026年2月3日

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Xiaoran Li,
Jinglei Liu

摘要

Matrix decomposition is widely employed in data mining and machine learning. It serves to transform high-dimensional image data into lower-dimensional representations, thereby facilitating dimensionality reduction. By means of dimensionality reduction, the intricacy of the data is lessened, enabling the extraction of its most salient features. This, in turn, aids clustering algorithms in gaining a deeper understanding of the data. However, matrix decomposition also comes with certain limitations. Firstly, matrix decomposition is sensitive to noise and outliers in the data, which can adversely affect the decomposition results and consequently impact the accuracy of clustering outcomes. Secondly, if too many potential features are selected, it may lead to overfitting and reduce the generalization ability of the model. To address these issues, we propose a \(\alpha {-}\beta \) -divergences reconstruction (AB) and non-convex sparse regularization (NCSR) based fast and robust matrix decomposition (ABN-FRMD). In ABN-FRMD, we introduce \(\alpha {-}\beta \) -divergences. \(\alpha \) divergence promotes weight sparsity, reducing the number of features and simplifying image clustering. The \(\beta \) divergence helps maintain the stability and smoothness of parameters. By combining different regularization terms, the robustness of image clustering to noise and outliers can be enhanced. We introduce the Minimax Concave Penalty (MCP) function as a non-convex sparse regularization term in ABN-FRMD. By more effectively controlling the complexity of the model and reducing overfitting, the non-convex sparse regularization term can enhance the generalization ability of the model on unseen data. Moreover, using a non-convex continuous function to approximate the \(\ell _0\) -norm can more effectively promote sparsity. Finally, our experimental studies on five datasets demonstrate that compared with other clustering algorithm, ABN-FRMD algorithm achieves superior performance in terms of image clustering performance.