Multi-label data with high dimensionality often occurs,which will produce large time and energy overheads when directly used in classification tasks.To solve this problem,a novel algorithm called multi-label dimension...Multi-label data with high dimensionality often occurs,which will produce large time and energy overheads when directly used in classification tasks.To solve this problem,a novel algorithm called multi-label dimensionality reduction via semi-supervised discriminant analysis(MSDA) was proposed.It was expected to derive an objective discriminant function as smooth as possible on the data manifold by multi-label learning and semi-supervised learning.By virtue of the latent imformation,which was provided by the graph weighted matrix of sample attributes and the similarity correlation matrix of partial sample labels,MSDA readily made the separability between different classes achieve maximization and estimated the intrinsic geometric structure in the lower manifold space by employing unlabeled data.Extensive experimental results on several real multi-label datasets show that after dimensionality reduction using MSDA,the average classification accuracy is about 9.71% higher than that of other algorithms,and several evaluation metrices like Hamming-loss are also superior to those of other dimensionality reduction methods.展开更多
等度量映射(ISOMAP)算法是一种被广泛应用的非线性无监督降维算法,通过保持各个观测样本间的测地距离进行等距嵌入,从而实现高维空间向低维空间的坐标转换。但在实际应用中,观测数据无可避免地会存在噪声,由于测地距离的计算对噪声比较...等度量映射(ISOMAP)算法是一种被广泛应用的非线性无监督降维算法,通过保持各个观测样本间的测地距离进行等距嵌入,从而实现高维空间向低维空间的坐标转换。但在实际应用中,观测数据无可避免地会存在噪声,由于测地距离的计算对噪声比较敏感,并且也没有考虑数据集的密度分布,导致ISOMAP算法降维后低维坐标表示存在几何变形。针对这一缺点,根据局部密度的思想,提出一种基于密度缩放因子的ISOMAP(Density Scaling Factor Based ISOMAP,D-ISOMAP)算法。在传统的ISOMAP算法框架下,首先,针对每个观测样本计算一个局部密度缩放因子;然后,在测地距离的计算过程中,将直接相邻的两个样本之间的测地距离除以这两个样本密度缩放因子的乘积;最后,通过最短路径算法求得改进后的距离矩阵,并对其进行降维处理。改进的测地距离在密度较大的区域被缩小,而在密度较小的区域被放大,这样可以减小噪声对降维效果的影响,提升可视化和聚类效果。人工数据集和UCI数据集上的实验结果表明,在数据集的可视化和聚类效果方面,D-ISOMAP算法较经典的无监督降维算法具有一定的优势。展开更多
基金Project(60425310) supported by the National Science Fund for Distinguished Young ScholarsProject(10JJ6094) supported by the Hunan Provincial Natural Foundation of China
文摘Multi-label data with high dimensionality often occurs,which will produce large time and energy overheads when directly used in classification tasks.To solve this problem,a novel algorithm called multi-label dimensionality reduction via semi-supervised discriminant analysis(MSDA) was proposed.It was expected to derive an objective discriminant function as smooth as possible on the data manifold by multi-label learning and semi-supervised learning.By virtue of the latent imformation,which was provided by the graph weighted matrix of sample attributes and the similarity correlation matrix of partial sample labels,MSDA readily made the separability between different classes achieve maximization and estimated the intrinsic geometric structure in the lower manifold space by employing unlabeled data.Extensive experimental results on several real multi-label datasets show that after dimensionality reduction using MSDA,the average classification accuracy is about 9.71% higher than that of other algorithms,and several evaluation metrices like Hamming-loss are also superior to those of other dimensionality reduction methods.
文摘等度量映射(ISOMAP)算法是一种被广泛应用的非线性无监督降维算法,通过保持各个观测样本间的测地距离进行等距嵌入,从而实现高维空间向低维空间的坐标转换。但在实际应用中,观测数据无可避免地会存在噪声,由于测地距离的计算对噪声比较敏感,并且也没有考虑数据集的密度分布,导致ISOMAP算法降维后低维坐标表示存在几何变形。针对这一缺点,根据局部密度的思想,提出一种基于密度缩放因子的ISOMAP(Density Scaling Factor Based ISOMAP,D-ISOMAP)算法。在传统的ISOMAP算法框架下,首先,针对每个观测样本计算一个局部密度缩放因子;然后,在测地距离的计算过程中,将直接相邻的两个样本之间的测地距离除以这两个样本密度缩放因子的乘积;最后,通过最短路径算法求得改进后的距离矩阵,并对其进行降维处理。改进的测地距离在密度较大的区域被缩小,而在密度较小的区域被放大,这样可以减小噪声对降维效果的影响,提升可视化和聚类效果。人工数据集和UCI数据集上的实验结果表明,在数据集的可视化和聚类效果方面,D-ISOMAP算法较经典的无监督降维算法具有一定的优势。
