<p>Multi-dimensional classification (MDC) aims to simultaneously train a number of multi-class classifiers for multiple heterogeneous class spaces. However, as supervised learning methods, the existing MDC algorithms require that all the training data be precisely labeled in multi-dimensional class spaces, which can be impractical in many real applications sometimes. The lack of high-quality labeled data may negatively affect their learning performance. Additionally, the existing MDC algorithms only address scenarios of centralized processing, where all training data must be centrally stored at a single fusion center. Nowadays, however, the training data are typically distributed at multiple nodes within a network, making it challenging to transmit them to a fusion center for further processing. To address these issues, in this paper, we propose a novel algorithm called distributed semi-supervised partial multi-dimensional learning (dS<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40747_2025_1942_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">$^2$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>PMDL), which is designed to handle distributed classification of a small proportion of partially multi-dimensional (PMD) data and a large proportion of unlabeled data across a network. In our proposed algorithm, an in-network framework of subspace learning is formulated for label recovery. By tracking the representations of non-noisy label vectors in the learned subspace, the reliable labels of training data can be recovered. Subsequently, the multi-dimensional classifier modeled by the random feature map can be adaptively trained using a two-level label dependencies exploitation strategy. The convergence performance and communication complexity of the dS<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40747_2025_1942_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">$^2$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>PMDL algorithm are analyzed. Furthermore, experiments on multiple datasets are performed to validate the effectiveness of the proposed algorithm in semi-supervised partial multi-dimensional classification.</p>

Distributed semi-supervised partial multi-dimensional learning via subspace learning

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2025年6月4日

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Zhen Xu,
Weibin Chen

摘要

Multi-dimensional classification (MDC) aims to simultaneously train a number of multi-class classifiers for multiple heterogeneous class spaces. However, as supervised learning methods, the existing MDC algorithms require that all the training data be precisely labeled in multi-dimensional class spaces, which can be impractical in many real applications sometimes. The lack of high-quality labeled data may negatively affect their learning performance. Additionally, the existing MDC algorithms only address scenarios of centralized processing, where all training data must be centrally stored at a single fusion center. Nowadays, however, the training data are typically distributed at multiple nodes within a network, making it challenging to transmit them to a fusion center for further processing. To address these issues, in this paper, we propose a novel algorithm called distributed semi-supervised partial multi-dimensional learning (dS $^2$ $^{2}$ PMDL), which is designed to handle distributed classification of a small proportion of partially multi-dimensional (PMD) data and a large proportion of unlabeled data across a network. In our proposed algorithm, an in-network framework of subspace learning is formulated for label recovery. By tracking the representations of non-noisy label vectors in the learned subspace, the reliable labels of training data can be recovered. Subsequently, the multi-dimensional classifier modeled by the random feature map can be adaptively trained using a two-level label dependencies exploitation strategy. The convergence performance and communication complexity of the dS $^2$ $^{2}$ PMDL algorithm are analyzed. Furthermore, experiments on multiple datasets are performed to validate the effectiveness of the proposed algorithm in semi-supervised partial multi-dimensional classification.