基于模糊组合熵的不完备多标签特征选择
Incomplete Multi-Label Feature Selection Based on Fuzzy Combination Entropy
摘要: 多标签数据通常具有高维特征空间与复杂的标签结构，这种高维性和复杂性易造成数据不同程度的不完备，从而影响多标签学习的性能。由此，本文提出基于模糊组合熵的不完备多标签特征选择方法。首先，在不完备多标签模糊信息系统中，通过引入特征值缺失率与调节参数定义模糊关系，进而定义模糊信息粒、模糊标签粒以及多标签模糊下上近似，建立不完备多标签模糊粗糙集。接着，在不完备多标签模糊粗糙集上引入组合熵的信息论思想，在此基础上定义模糊组合熵、模糊联合组合熵、模糊条件组合熵等信息度量，研究它们的性质和关系。最后，基于模糊组合熵分析特征的内外重要度，给出适用于不完备多标签数据的特征选择算法。实验结果表明，本文所提算法在5个多标签数据集上相较于对比方法取得了更优的分类性能：平均精度(AP)平均提升3.48%，汉明损失(HL)、排序损失(RL)、覆盖率(CV)、1-错误率(OE)分别平均降低3.02%、4.33%、2.83%和 4.64%。实验结果验证了本文所提算法的有效性。
Abstract: Multi-label data usually has high-dimensional feature Spaces and complex label structures. This high dimensionality and complexity can easily cause varying degrees of incompleteness in the data, thereby affecting the performance of multi-label learning. To address this issue, this paper proposes an incomplete multi-label feature selection method based on fuzzy combination entropy. Firstly, in the incomplete multi-label fuzzy information system, the fuzzy relationship is constructed by incorporating the feature-value missing rate together with a regulating parameter. Based on the defined fuzzy relationship, fuzzy information granule, fuzzy label granule, and multi-label fuzzy lower and upper approximation are defined to establish the incomplete multi-label fuzzy rough set. Then, the information-theoretic concept of combination entropy is introduced on the incomplete multi-label fuzzy rough set. On this basis, information metrics such as fuzzy combination entropy, fuzzy joint combination entropy, and fuzzy conditional combination entropy are defined, and their properties and relationships are studied. Finally, the intra- and extra-feature significances are analyzed based on fuzzy combination entropy, and a feature selection algorithm suitable for incomplete multi-label data is presented. The experimental results show that the algorithm proposed in this paper achieves better classification performance on five multi-label datasets compared with the comparison methods: The Average Precision (AP) is increased by an average of 3.48%, and the Hamming Loss (HL), Ranking Loss (RL), Coverage (CV), and One-Error (OE) are reduced by an average of 3.02%, 4.33%, 2.83% and 4.64% respectively. The experimental results verify the effectiveness of the algorithm proposed in this paper.
文章引用：杨心怡. 基于模糊组合熵的不完备多标签特征选择[J]. 应用数学进展, 2026, 15(1): 278-292. https://doi.org/10.12677/aam.2026.151028

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