基于核最小二乘回归子空间分割的高维小样本数据聚类
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摘要
针对基于线性表示理论的子空间分割方法没有考虑高维小样本数据的非线性性质,借鉴核理论,提出核最小二乘回归子空间分割方法,使子空间分割方法适合高维小样本数据的非线性性质.经6个基因表达数据集和4个图像数据集上的实验,表明该方法是有效的.
The classical subspace segmentation methods based on linear representation theory do not consider the nonlinear properties of high dimension small sample data. In sight of the kernel theory,the kernel least square regression subspace segmentation method is proposed to make the subspace segmentation method suitable for the nonlinear properties of high dimension small sample data. Experiments on six gene expression datasets and four image datasets show that the method is effective.
The classical subspace segmentation methods based on linear representation theory do not consider the nonlinear properties of high dimension small sample data. In sight of the kernel theory,the kernel least square regression subspace segmentation method is proposed to make the subspace segmentation method suitable for the nonlinear properties of high dimension small sample data. Experiments on six gene expression datasets and four image datasets show that the method is effective.
引文
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[2]BISHOP C M.Pattern recognition and machine learning(information science and statistics)[M].New York:Springer-Verlag Inc,2006.
[3]WRIGHT J,YANG A Y,GANESH A,et al.Robust face recognition via sparse representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(2):210-227.
[4]ZHU X,HUANG Z,YANG Y,et al.Self-taught dimensionality reduction on the high-dimensional small-sized data[J].Pattern Recognition,2012,46(1):215-229.
[5]何进荣,丁立新,崔梦天,等.基于矩阵指数变换的边界Fisher分析[J].计算机学报,2014,37(10):2196-2205.
[6]王文俊.基于稀疏类别保留投影的基因表达数据降维方法[J].电子学报,2016,44(4):873-877.
[7]ELHAMIFAR E,VIDAL R.Sparse subspace clustering[C]//Proceedings of the 23rd IEEE Conference on Computer Vision and Pattern Recognition.Miami:[s.n.],2009:2790-2797.
[8]LIU G,LIN Z,YU Y.Robust subspace segmentation by low-rank representation[C]//Proceedings of the 27th International Conference on Machine Learning.Haifa:[s.n.],2010:663-670.
[9]LU C Y,MIN H,ZHAO Z Q,et al.Robust and efficient subspace segmentation via least squares regression[C]//Proceedings of the 12th Computer Vision.Florence:Springer,2012:347-360.
[10]简彩仁,陈晓云.基于投影最小二乘回归子空间分割的基因表达数据聚类[J].模式识别与人工智能,2015,28(8):728-734.
[11]SHI J,MALIK J.Normalized cuts and image segmentation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2000,22(8):888-905.
[12]张贤达.矩阵分析与应用[M].2版.北京:清华大学出版社,2013.
[13]SCHLKOPF B,SUNG K K,BURGES C J C,et al.Comparing support vector machines with Gaussian kernels to radial basis function classifiers[J].IEEE Transactions on Signal Processing,1996,45(11):2758-2765.
[14]CAI D,HE X,WU X,et al.Non-negative matrix factorization on manifold[C]//Proceedings of the 8th IEEE International Conference on Data Mining.Pisa:IEEE,2008:63-72.