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摘要: 在实际应用场景中越来越多的数据具有多标签的特性，且特征维度较高，包含大量冗余信息.为提高多标签数据挖掘的效率，多标签特征提取已经成为当前研究的热点.本文采用去噪自编码器获取多标签数据特征空间的鲁棒表达，在此基础上结合超图学习理论，融合多个标签对样本间几何关系的影响以提升特征提取的性能，构建多标签数据样本间几何关系所对应超图的Laplacian矩阵，并通过Laplacian矩阵的特征值分解得到低维投影空间.实验结果证明了本文所提出的算法在分类性能上是有效可行的.Abstract: In practical application scenarios, more and more data tend to be assigned with multiple labels and contain much redundant information in the high dimensional feature space. To improve the efficiency and effectiveness of multi-label data mining, multi-label data feature selection has become a hotspot. This paper utilizes denoising autoencoders to obtain a more robust version of multi-label data feature representation. Furthermore, based on hypergraph learning theory, a hypergraph Laplacian matrix corresponding to multi-label data is constructed by fusing the effects of all labels on geometrical relationship among all the samples, and then a projection space with lower dimension is obtained by conducting eigenvalue decomposition of the Laplacian matrix. Experimental results demonstrate the effectiveness and feasibility of the proposed algorithm according to its multi-label data classification performance.
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Key words:
- Deep learning /
- autoencoders /
- multi-label /
- hypergraph /
- feature selection
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图 1 参数ks对AverageP recision的影响(kd=3)
Fig. 1 The influences of ks to AverageP recision (kd=3)
图 2 参数kd对AveragePrecision的影响(ks=8)
Fig. 2 The influences of kd to AveragePrecision (ks=8)
表 1 重要的标记定义
Table 1 Definitions of important notations
标记 标记语义 n 训练集中训练样本的个数 u, V 顶点 f ∈ Rn 所有样本的得分向量 f(u)或者fu 样本u的得分函数 e, E 超边，超边集合 δ(e) 超边e的度 d(u) 顶点u的度 Dv 顶点集的度矩阵 De 超边集的度矩阵 W(e) 超边e的权重 H 超图对应的邻接矩阵 Ω Ω(i, i)是第i条超边的权重，其他取0 r 约简后的特征维度 I 超图学习前的原特征空间 S 超图学习后的语义特征空间 Pi 基于样本xi的局部批 Pi 基于样本xi的局部批特征投影矩阵 
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表 2 算法空间复杂度
Table 2 Space consumption
矩阵 空间复杂度 Dv |V|×|V| De |E|×|E| H |E|×|V| Ω |E|×|E| Lg |E|×|V|
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表 3 数据集信息
Table 3 Information of data sets
编号 名称 样本数 特征数 标签数 1 Emotions 593 72 6 2 Yeast 2417 103 14 3 Scene 2 407 294 6 4 Birds 645 260 19 5 Computer 5 000 681 33
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表 4 数据集Emotions测试结果(params=(8, 3, 15))
Table 4 Results on Emotions (params=(8, 3, 15))
指标 a0 a1 a2 a3 MLFS-AH OE↓ 0.290 0.277 0.489 0.265 0.256 Cov↓ 1.893 1.842 2.791 1.733 1.756 RL↓ 0.173 0.181 0.349 0.168 0.152 AP↑ 0.770 0.784 0.658 0.811 0.825
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表 5 数据集Yeast测试结果(params=(7, 3, 30))
Table 5 Results on Yeast (params=(7, 3, 30))
指标 a0 al a2 a3 MLFS-AH OE↓ 0.283 0.274 0.289 0.268 0.243 Cov↓ 6.452 6.331 6.538 6.245 6.121 RL↓ 0.174 0.168 0.203 0.156 0.160 AP↑ 0.760 0.758 0.717 0.782 0.811
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表 6 数据集Scene测试结果(params=(8, 3, 20))
Table 6 Results on Scene (params=(8, 3, 20))
指标 a0 a1 a2 a3 MLFS-AH OE↓ 0.275 0.261 0.318 0.260 0.248 Cov↓ 0.573 0.536 0.619 0.425 0.429 RL↓ 0.163 0.165 0.230 0.166 0.157 AP↑ 0.776 0.795 0.723 0.792 0.815
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表 7 数据集Birds测试结果(params=(8, 2, 45))
Table 7 Results on Birds (params=(8, 2, 45))
指标 a0 a1 a2 a3 MLFS-AH OE↓ 0.379 0.371 0.369 0.352 0.344 Cov↓ 3, 411 3.426 3.724 3.385 3.389 RL↓ 0.129 0.125 0.138 0.124 0.121 AP↓ 0.712 0.718 0.705 0.727 0.742
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表 8 数据集Computer测试结果(params=(7, 2, 60))
Table 8 Results on Computer (params=(7, 2, 60))
指标 a0 a1 a2 a3 MLFS-AH OE↓ 0.434 0.438 0.439 0.432 0.425 Cov↓ 4.435 4.439 4.532 4.378 4.339 RL↓ 0.108 0.104 0.106 0.089 0.091 AP↑ 0.641 0.643 0.647 0.649 0.675
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