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摘要: 现有子空间聚类方法通常以数据全局线性为前提，将每个样本点表示为其他样本点的线性组合，因而导致常见子空间聚类方法不能很好地应用于非线性数据.为克服全局线性表示的局限，借鉴流形学习思想，用k近邻局部线性表示代替全局线性表示，与稀疏子空间聚类和最小二乘子空间聚类方法相结合，提出局部稀疏子空间聚类和局部最小二乘子空间聚类方法，统称局部子空间聚类方法.在双月形数据、6个图像数据集和4个基因表达数据集上进行实验，实验结果表明该方法是有效的.Abstract: Existing subspace clustering methods usually rest on a global linear data set, which expresses each data point as a linear combination of all other data points, and thus common methods are not well suited for the nonlinear data. To overcome this limitation, the local sparse subspace clustering and local least squares regression subspace clustering are proposed. The idea of the two new methods comes from manifold learning which expresses each data point as a linear combination of its k nearest neighbors, and is combined with sparse subspace clustering and least squares subspace clustering respectively. Experimental results show that our method is effective on two-moon synthetic data, six image data sets and four gene expression data sets.
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Key words:
- Local linear /
- k nearest neighbors /
- subspace clustering /
- image data /
- gene expression data
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图 3 LSC在双月形数据学习得到的邻接图
Fig. 3 Learned adjacency graph by LSC on the two-moon synthetic data
图 5 在双月形数据上LSC的参数学习
Fig. 5 Study on the LSC's parameters on the two-moon synthetic data
表 1 双月形数据上聚类准确率(%)和运行时间(s)的对比
Table 1 Clustering accuracy (%) and running time (s)comparison on the two-moon synthetic data
HC K-means LRR SSC LSR BD-LRR RLLRR SMR LSSC LLSR ACC 100.00 72.00 53.50 53.50 50.00 50.00 52.00 51.50 100.00 100.00 (0.001) (0.005) (0.0001) (0.08) (0.1) (0.001) (0.0001,5) (0.0001,5) Time 0.0010 0.0026 1.89 4.80 0.0008 19.15 0.33 0.045 0.94 0.10 
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表 2 数据集描述
Table 2 Summary of the data sets
数据集 样本 长 宽 类别 ORL10P 100 112 92 10 PIX10P 100 100 100 10 PIE10P 210 55 44 10 Umist 575 28 23 20 USPS 1 000 16 16 10 COIL20 1 440 32 32 20
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表 3 聚类准确率
Table 3 Clustering accuracy (%)
HC K-means LRR SSC LSR BD-LRR RLLRR SMR LSSC LLSR ORL10P 41.00 73.40 79.00 71.00 83.00 70.30 74.70 78.00 86.00 87.00 PIX10P 77.00 79.90 87.00 86.00 85.00 76.80 56.10 88.00 96.00 97.00 PIE10P 70.95 32.95 100.00 90.00 90.00 80.00 79.43 100.00 98.57 100.00 Umist 45.57 47.58 52.17 61.57 52.35 48.35 50.96 69.91 76.87 74.09 USPS 10.90 73.14 78.60 60.80 71.30 63.90 65.50 77.10 81.20 91.20 COIL20 53.47 60.10 65.69 72.01 63.40 67.72 68.80 67.15 78.26 79.58
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表 4 运行时间的对比(s)
Table 4 Running time (s) comparison
HC K-means LRR SSC LSR BD-LRR RLLRR SMR LSSC LLSR ORL10P 0.0011 0.0071 0.54 0.21 0.00078 7.29 1.69 0.014 0.14 0.034 PIX10P 0.00095 0.0062 1.04 0.33 0.00073 7.60 1.72 0.012 1.25 0.035 PIE10P 0.0023 0.011 4.51 2.53 0.0015 22.23 2.14 0.057 0.32 0.13 Umist 0.011 0.037 25.14 62.27 0.015 240.70 13.48 0.71 1.52 0.92 USPS 0.034 0.091 130.61 124.57 0.044 884.42 120.33 4.53 3.57 2.75 COIL20 0.072 0.071 423.54 2.51 1446.67 926.78 134.86 18.92 18.97 5.69
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表 5 数据集描述
Table 5 Summary of the data sets
数据集 样本 基因 类别 Leukemia1 72 5 327 3 SRBCT 83 2 308 4 Lung_Cancer 203 12 600 5 Prostate_Tumor 102 10 509 2
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表 6 聚类准确率(%)
Table 6 Clustering accuracy (%)
HC K-means LRR SSC LSR BD-LRR RLLRR SMR LSSC LLSR Leukemia1 54.17 69.31 86.11 58.33 77.78 79.17 54.17 77.78 90.28 90.28 SRBCT 36.14 53.73 68.43 40.12 54.22 60.24 46.99 63.68 74.70 74.46 Lung_Cancer 78.33 83.50 87.39 83.74 92.61 85.22 84.24 90.64 91.63 92.61 Prostate_Tumor 51.96 63.73 62.75 56.86 62.75 60.78 60.78 59.80 66.67 69.61
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