A Semi-supervised Affinity Propagation Clustering Method with Homogeneity Constraint
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摘要: 以近邻反射传播 (Affinity propagation, AP) 聚类算法为基础, 提出了一种基于同类约束的半监督近邻反射传播聚类方法 (Semi-supervised affinity propagation clustering method with homogeneity constraints, HCSAP).该方法在聚类目标函数中引入同类约束项, 以保证聚类结果与同类集先验信息一致.利用最大和信任传播 (Max-sum belief propagation) 优化过程对目标函数进行求解, 导出同类约束下的吸引度 (Responsibility) 和归属度 (Availability) 的迭代方程.人工数据集和真实数据集上的实验结果表明本文所提方法的有效性.Abstract: In this paper, a semi-supervised affinity propagation (AP) clustering algorithm with homogeneity constraint, called HCSAP (semi-supervised affinity propagation clustering method with homogeneity constraints), is proposed. To keep consistency between the clustering results and the priori information about homogeneity sets, the constraint terms are introduced to the objection function of algorithm AP. With the max-sum belief propagation procedure, the objection function can be resolved into the corresponding responsibility and availability update equations. Experiments on synthetic dataset and real-world datasets indicate the effectiveness of the proposed HCSAP.
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图 3 $\eta_{ij}$ 与其相关信息关系图
Fig. 3 Relationship among $\eta_{ij}$ and its correlative message
图 4 $\alpha_{ij}$ 与其相关信息关系图
Fig. 4 Relationship among $\alpha_{ij}$ and its correlative message
表 1 部分符号说明
Table 1 The explanation of some symbol
符号 意义 $N$ 聚类数据点个数 $M$ 同类集个数 $h_1,h_2$ 数据点 $h_1,h_2$ $c_{ij}$ 变量节点, 为0表示 $j$ 不是 $i$ 的类中心点; 为1表示 $j$ 是 $i$ 的类中心点 $E_{ij}(\cdot)$ $E_j(c_{1j},\cdots,c_{Nj})$ 数据点 $j$ 的同类约束与一致性约束函数 $\rho_{ij}$ 表示变量节点 $c_{ij}$ 向函数节点 $E_j$ 所发送的标量信息 $c_i$ 数据点 $i$ 的类中心点 $P$ 全体同类集所构成的集合 $p^i$ 数据点 $i$ 所在的同类约束集 $I_i(\cdot)$ $I_i(c_{i1},\cdots,c_{iN})$ 为数据点 $i$ 的唯一性约束函数 $\alpha_{ij}$ 表示函数节点 $E_j$ 向变量节点 $ c_{ij}$ 所发送的标量信息 $\beta_{ij}$ 表示变量节点 $c_{ij}$ 向函数节点 $I_i$ 所发送的标量信息 $p_v$ 第 $v$ 个同类集 ⊕ 异或 ${{\bar P}}$ 无同类约束的数据点集 $S_{ij}(\cdot)$ 定义在数据点 $i$ , $j$ 之间的相似度函数 $s(i,j)$ 数据点 $i$ , $j$ 之间的相似度 $\eta_{ij}$ 表示函数节点 $I_i$ 向变量节点 $c_{ij}$ 所发送的标量信息 
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表 2 人工数据上的聚类结果参数对比
Table 2 Performance comparison on man-made dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 72.12 72.12 72.12 70.31 69.3 56.50 56.50 56.50 53.43 55.0 0 std (0) (0) (0) (1.3) (3.6) (0) (0) (0) (1.1) (2.1) p-value - - - 4.2E-3 6.6E-3 - - - 1.8E-1 3.4E-1 Mean 87.24 82.74 80.22 85.27 81.66 80.47 72.41 70.50 77.39 75.4 10 std (6.6) (4.7) (0.8) (5.2) (9.2) (1.7) (1.1) (2.4) (2.1) (3.7) p-value - 3.1E-2 (+) 2.2E-5 (+) 9.7E-2 6.3E-3 (+) - 3.9E-2 (+) 4.1E-5 (+) 6.4E-2 6.8E-2 Mean 96.15 80.45 81.78 90.00 88.6 95.75 72.57 73.66 90.41 76.8 20 std (1.0) (1.6) (1.8) (4.1) (4.5) (4.0) (1.6) (2.7) (0.5) (1.4) p-value - 9.4E-4 (+) 7.8E-5 (+) 9.2E-3 (+) 9.2E-3 (+) - 1.7E-7 (+) 2.3E-6 (+) 1.4E-2 (+) 7.5E-6 (+) Mean 96.24 91.24 92.47 90.36 91.33 97.58 89.00 85.74 90.06 89.6 30 std (2.0) (4.1) (5.1) (0.8) (1.6) (0.2) (6.6) (4.1) (0.2) (2.8) p-value - 4.9E-2 (+) 5.1E-2 8.4E-3 (+) 7.4E-3 (+) - 3.4E-3 (+) 9.5E-8 (+) 1.6E-2 (+) 4.7E-4 (+) Mean 96.66 88.57 87.98 90.21 89.2 97.35 88.65 86.97 90.33 90.5 40 std (1.3) (3.0) (2.7) (0.2) (4.5) (2.0) (1.2) (0.9) (0.5) (7.7) p-value - 5.7E-3 (+) 1.1E-3 (+) 6.6E-3 (+) 3.9E-3 (+) - 1.1E-4 (+) 2.4E-7 (+) 1.8E-2 (+) 7.1E-3 (+) Mean 98.05 90.34 88.84 90.70 90.8 98.25 89.65 90.45 88.87 90.0 50 std (0.2) (7.1) (1.4) (0.6) (2.3) (0.2) (2.8) (9.6) (0.7) (3.4) p-value - 5.1E-2 7.2E-4 (+) 9.0E-5 (+) 1.4E-4 (+) - 42E-4 (+) 3.7E-7 (+) 8.4E-3 (+) 6.7E-3 (+) 注:表中p-value为5 %显著性水平下的 $t$ 检验值, "+"表示HCSAP在5 %显著性水平下优于对比聚类算法."-"表示在5 %显著性水平下HCSAP劣于对比聚类算法.粗体字表示对比较优者 (下同).
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表 3 实验数据集
Table 3 Dataset used in experiment
Item Number of instance Dimension Class Preference Optdigit 1 797 64 10 $1\times Mid$ Iris 150 4 3 $3\times Mid$ Ionosphere 351 34 2 $10\times Mid$ Letter recogni- 2 241 16 3 $1\times Mid$ tion {I, J, L} Pendigits 3 498 16 10 $1\times Mid$ glass 214 9 6 $5\times Mid$ wine 178 13 3 $5\times Mid$ wdbc 768 8 2 $50\times Mid$
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表 4 Optdigit数据集上的聚类结果对比
Table 4 Performance comparison on Optdigit dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 22.35 22.35 22.35 19.14 20.61 12.57 12.57 12.57 10.68 11.46 0 std (0) (0) (0) (1.25) (3.87) (0) (0) (0) (1.6) (0.9) p-value - - - 4.3E-3 4.9E-2 - - - 4.1E-2 (+) 4.8E-2 Mean 31.86 30.03 29.30 27.98 30.41 18.97 17.75 15.34 14.68 16.35 10 std (4.69) (1.30) (2.47) (1.50) (4.94) (5.02) (5.92) (6.1) (5.7) (2.2) p-value - 3.1E-1 3.3E-1 2.6E-1 5.1E-1 - 2.7E-1 6.1E-1 1.4E-1 9.9E-2 Mean 42.57 43.15 44.63 40.55 41.55 27.10 27.71 27.96 27.30 24.63 20 std (7.4) (8.01) (6.91) (7.65) (9.52) (9.00) (3.36) (4.86) (7.96) (8.14) p-value - 2.2E-1 6.6E-1 1.0E-1 2.9E-1 - 5.7E-1 6.7E-1 4.3E-1 7.4E-2) Mean 54.41 52.5 51.23 49.87 52.44 36.61 35.78 34.79 30.76 31.87 30 std (9.02) (2.01) (4.31) (2.44) (3.75) (2.67) (0.79) (6.6) (8.2) (7.8) p-value - 2.6E-1 1.7E-1 4.6E-2 (+) 5.7E-1 - 4.3E-1 8.7E-2 4.4E-2 (+) 2.5E-2 (+) Mean 62.67 61.35 61.22 59.57 61.24 45.85 44.46 45.20 41.85 40.27 40 std (2.39) (1.71) (1.6) (4.21) (8.34) (0.86) (3.12) (4.20) (7.14) (9.48) p-value - 4.0E-1 4.3E-1 2.9E-1 1.6E-1 - 1.7E-1 2.7E-1 7.7E-2 2.1E-2 (+) Mean 71.75 68.84 68.8 69.54 69.33 56.09 52.69 51.27 48.62 50.11 50 std (9.58) (6.32) (9.96) (8.47) (10.20) (2.45) (4.79) (2.70) (5.47) (5.50) p-value - 2.4E-1 2.4E-11 8.1E-2 9.8E-2 - 1.4E-2 (+) 1.1E-1 2.5E-3 (+) 5.8E-2
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表 5 Iris数据集的聚类结果对比
Table 5 Performance comparison on Iris dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 61.87 61.87 61.87 56.27 55.38 55.33 55.33 55.33 52.61 53.70 0 std (0) (0) (0) (3.1) (3.6) (0) (0) (0) (2.30) (4.81) p-value - - - 1.4E-2 2.2E-2 - - - 1.6E-1 4.8E-1 Mean 73.36 72.93 72.55 71.84 69.57 75.60 56.53 55.22 60.77 58.45 10 std (2.69) (0.93) (1.21) (6.40) (3.72) (5.3) (0.87) (4.11) (2.57) (12.72) p-value - 1.5E-4 (+) 1.3E-4 (+) 5.3E-4 (+) 2.2E-4 (+) - 1.3E-3 (+) 1.4E-3 (+) 5.6E-3 (+) 4.2E-2 (+) Mean 79.04 79.78 76.99 81.21 74.31 75.33 69.11 66.22 64.21 70.40 20 std (3.22) (8.02) (5.90) (8.3) (6.61) (7.33) (12.10) (18.9) (14.1) (11.23) p-value - 2.8E-1 1.4E-1 8.2E-1 5.4E-3 - 2.7E-1 2.3E-1 5.4E-1 9.1E-1 Mean 88.46 80.33 81.24 80.74 75.33 81.33 72.22 71.25 72.11 69.44 30 std (1.75) (9.15) (9.47) (4.4) (10.1) (2.91) (12.15) (11.41) (13.15) (10.9) p-value - 2.1E-1 3.4E-1 1.1E-2 1.2E-2 - 2.3E-1 2.0E-1 2.8E-1 1.1E-1 Mean 94.72 89.62 88.25 85.74 84.27 92.93 84.40 84.00 81.23 83.78 40 std (3.64) (3.79) (4.8) (5.9) (5.6) (5.77) (6.95) (8.3) (7.9) (9.1) p-value - 1.5E-1 4.6E-2 (+) 4.9E-1 5.9E-1 - 1.7E-1 1.1E-1 1.4E-1 2.4E-1 Mean 94.43 92.38 93.50 90.22 89.01 94.44 88.22 87.20 86.33 90.01 50 std (0.39) (1.39) (2.0) (7.1) (5.1) (0.03) (5.00) (6.89) (6.12) (10.88) p-value - 1.0E-1 1.7E-1 5.5E-1 6.4E-1 - 1.5E-1 1.2E-1 2.7E-1 1.4E-1
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表 6 Ionosphere数据集上的聚类结果对比
Table 6 Performance comparison on Ionosphere dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 51.96 51.96 51.96 45.89 46.31 40.35 40.35 40.35 43.48 41.25 0 std (0) (0) (0) (5.2) (3.4) (0) (0) (0) (2.50) (1.31) p-value - - - 7.3E-1 6.9E-1 - 4.4E-1 5.2E-1 1.3E-1 2.3E-1 Mean 55.24 56.74 57.30 58.21 54.21 58.21 59.38 57.66 55.24 58.00 10 std (2.45) (7.87) (1.2) (7.2) (3.6) (7.32) (2.78) (7.27) (6.17) (5.48) p-value - 3.5E-2 (-) 4.8E-2 (-) 5.4E-1 7.9E-1 - 8.2E-1 6.3E-1 5.2E-1 4.5E-1 Mean 56.45 61.13 60.34 54.29 55.12 63.41 64.12 64.30 62.34 61.25 20 std (1.97) (2.36) (1.90) (4.87) (3.57) (5.79) (3.18) (5.54) (7.53) (4.74) p-value - 5.40E-3 (-) 3.47E-2 (-) 4.4E-1 5.1E-1 - 2.8E-1 3.5E-1 6.4E-1 4.1E-1 Mean 66.61 61.16 65.14 57.02 59.54 63.74 67.20 61.42 61.28 60.11 30 std (3.25) (5.47) (3.32) (5.42) (4.14) (5.20) (1.44) (8.54) (3.15) (7.21) p-value - 2.8E-1 4.2E-1 3.3E-1 2.4E-1 - 1.9E-1 2.9E-1 1.6E-1 1.7E-1 Mean 67.61 71.68 68.50 64.71 69.87 62.66 64.04 57.99 60.34 61.23 40 std (4.23) (3.03) (1.20) (4.56) (1.57) (8.17) (7.24) (4.8) (1.36) (5.4) p-value - 2.4E-2 (-) 3.7E-2 (-) 1.7E-1 5.6E-1 - 2.5E-1 3.6E-1 2.2E-1 1.4E-1 Mean 84.16 83.17 80.26 80.66 84.78 72.53 71.33 72.55 70.21 69.88 50 std (6.12) (4.87) (2.80) (2.69) (4.31) (5.60) (7.53) (5.33) (2.42) (4.69) p-value - 3.6E-1 3.4E-1 4.7E-1 2.1E-1 - 1.9E-1 3.9E-1 2.2E-1 1.0E-1
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表 7 Letter-recognition {I, J, L}上的聚类结果对比
Table 7 Performance comparison on Letter-recognition dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 49.87 49.87 49.87 41.30 42.33 33.33 33.33 33.33 31.54 30.36 0 std (0) (0) (0) (1.9) (4.1) (0) (0) (0) (2.5) (3.1) p-value - - - 5.7E-2 6.9E-2 - - - 1.7E-1 1.0E-1 Mean 54.42 55.01 54.36 55.11 57.21 39.00 38.10 40.23 39.98 40.05 10 std (8.90) (2.63) (5.7) (6.4) (3.89) (8.08) (2.78) (1.4) (2.0) (3.7) p-value - 6.2E-1 2.1E-1 4.8E-1 1.2E-1 - 2.3E-1 5.6E-1 7.4E-1 6.1E-1 Mean 59.47 52.01 51.69 57.20 55.31 42.66 35.33 34.88 37.90 35.87 20 std (1.92) (5.73) (4.8) (6.8) (5.0) (9.57) (7.26) (5.8) (3.2) (2.8) p-value - 4.2E-2 (+) 3.2E-2 (+) 1.1E-1 3.1E-1 - 4.9E-2 2.3E-2 4.7E-2 2.6E-2 Mean 67.90 65.36 66.30 64.87 60.45 52.66 50.00 49.68 50.33 51.74 30 std (0.41) (6.44) (3.2) (5.6) (4.9) (1.84) (1.54) (1.74) (2.53) (3.40) p-value - 2.6E-1 3.0E-1 1.7E-1 2.6E-1 - 2.3E-1 1.2E-1 2.9E-1 5.4E-1 Mean 77.05 72.97 73.33 71.4 70.24 64.66 60.00 59.40 58.67 51.77 40 std (2.00) (4.43) (1.5) (2.6) (2.4) (8.17) (4.26) (7.26) (8.11) (14.25) p-value - 3.3E-1 4.2E-1 1.1E-1 1.5E-1 - 3.4E-1 2.9E-1 4.1E-1 5.3E-1 Mean 84.16 83.17 84.12 83.00 81.47 73.33 71.33 70.11 68.25 67.49 50 std (4.55) (7.41) (5.4) (4.9) (4.4) (2.62) (7.53) (5.1) (7.6) (5.3) p-value - 4.9E-1 5.0E-1 2.3E-1 2.3E-1 - 3.3E-1 2.8E-1 1.0E-1 4.4E-2 (+)
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表 8 Pendigits数据集的聚类结果对比
Table 8 Performance comparison on Pendigits dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 19.23 19.23 19.23 17.21 16.32 11.20 11.20 11.20 9.79 9.64 0 std (0) (0) (0) (1.42) (2.51) (0) (0) (0) (0.25) (0.36) p-value - - - 9.4E-3 (+) 2.8E-3 (+) - - - 3.9E-2 (+) 2.8E-2 (+) Mean 27.40 23.17 24.65 24.68 21.97 16.72 13.75 12.99 13.58 11.95 10 std (1.38) (8.62) (7.64) (9.17) (4.11) (5.03) (3.15) (2.87) (2.77) (1.44) p-value - 2.3E-1 5.6E-2 2.8E-1 5.8E-2 - 4.1E-1 9.6E-2 6.7E-1 6.1E-1 Mean 38.66 35.19 34.67 33.74 34.21 36.14 25.58 24.71 21.95 27.64 20 std (0.88) (3.67) (4.25) (5.50) (6.67) (3.13) (8.79) (3.34) (5.61) (4.13) p-value - 5.6E-1 2.4E-1 2.7E-1 3.1E-1 - 8.3E-3 2.3E-3 9.8E-4 1.9E-3 Mean 60.54 57.56 55.82 51.64 56.83 46.19 43.08 40.27 39.87 41.56 30 std (9.90) (0.26) (1.13) (4.21) (6.57) (0.54) (2.86) (3.41) (4.12) (3.49) p-value - 8.3E-1 5.3E-1 5.6E-2 6.6E-1 - 5.8E-1 4.1E-1 8.6E-2 2.9E-1 Mean 68.49 62.12 63.77 60.16 62.57 55.46 48.51 44.21 39.48 41.67 40 std (1.28) (5.29) (6.84) (3.46) (4.57) (6.09) (1.93) (1.53) (4.85) (3.34) p-value - 5.6E-1 6.8E-1 4.9E-1 1.4E-1 - 4.6E-2 (+) 5.3E-3 (+) 2.1E-4 (+) 9.4E-3 (+) Mean 75.75 66.30 67.38 67.22 64.14 65.23 53.60 54.69 55.21 53.96 50 std (4.58) (8.38) (7.52) (7.31) (5.63) (2.58) (6.82) (7.39) (4.61) (9.42) p-value - 6.1E-2 7.6E-1 4.9E-1 2.0E-1 - 3.8E-2 (+) 4.2E-2 (+) 1.6E-2 (+) 6.4E-3 (+)
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表 9 glass数据集的聚类结果对比
Table 9 Performance comparison on glass dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 31.02 31.02 31.02 28.66 27.14 31.66 31.66 31.66 28.51 30.69 0 std (0) (0) (0) (2.80) (3.74) (0) (0) (0) (1.90) (2.45) p-value - - - 2.63E-1 1.77E-1 - - - 2.1E-1 2.6E-1 Mean 37.24 35.85 35.62 31.89 33.57 38.00 38.00 37.15 35.46 34.76 10 std (8.90) (3.17) (4.66) (5.78) (9.51) (8.08) (2.78) (3.64) (5.21) (4.23) p-value - 6.0E-1 3.4E-1 1.9E-1 2.4E-1 - 8.4E-1 5.6E-1 3.6E-1 3.1E-1 Mean 40.98 37.80 35.70 36.44 37.15 42.66 35.33 34.36 31.93 32.19 20 std (0.06) (0.02) (0.08) (1.62) (3.48) (9.57) (7.26) (6.19) (8.42) (2.96) p-value - 1.1E-1 6.4E-2 8.3E-2 4.8E-1 - 5.4E-2 4.9E-2 (+) 2.5E-2 (+) 3.4E-2 (+) Mean 46.05 43.32 44.22 40.35 45.11 70.87 54.52 55.21 52.94 57.14 30 std (0.15) (3.21) (3.90) (5.44) (7.16) (1.50) (6.36) (4.83) (8.91) (7.88) p-value - 2.9E-1 5.2E-1 9.7E-2 4.5E-1 - 4.6E-2 (+) 2.0E-2 (+) 9.4E-3 (+) 5.6E-2 Mean 53.23 47.71 46.25 42.18 47.84 80.06 61.06 64.37 59.81 60.56 40 std (1.46) (5.89) (4.77) (4.65) (7.21) (5.00) (7.27) (8.36) (7.24) (4.98) p-value - 1.8E-1 1.3E-1 7.6E-2 5.5E-1 - 5.7E-2 1.7E-1 8.7E-3 (+) 7.68E-2 Mean 54.67 50.70 51.28 49.57 51.14 79.63 64.02 61.44 62.37 59.87 50 std (7.43) (4.98) (6.40) (7.15) (8.44) (8.83) (5.42) (6.48) (7.21) (9.18) p-value - 1.6E-1 3.6E-1 7.4E-2 6.1E-1 - 5.0E-2 (+) 4.4E-2 (+) 4.5E-2 (+) 6.9E-3 (+)
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表 10 wine数据集的聚类结果对比
Table 10 Performance comparison on wine dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 60.21 60.21 60.21 54.39 57.82 70.54 70.54 70.54 64.87 61.49 0 std (0) (0) (0) (5.67) (4.10) (0) (0) (0) (5.10) (6.54) p-value - - - 2.9E-1 4.6E-1 - - - 1.3E-1 9.3E-2 Mean 79.16 68.98 69.33 65.47 67.26 84.94 72.36 73.66 75.19 70.58 10 std (5.450) (3.82) (5.44) (8.21) (4.94) (8.35) (5.26) (5.87) (4.24) (6.29) p-value - 6.3E-3 (+) 9.2E-4 (+) 6.1E-3 (+) 8.1E-2 (+) - 4.7E-2 (+) 4.9E-2 (+) 6.7E-2 8.1E-3 (+) Mean 81.36 71.82 69.88 68.15 60.47 84.83 73.88 71.20 69.64 65.88 20 std (3.65) (5.49) (5.40) (8.14) (6.47) (8.22) (4.55) (6.88) (7.52) (10.37) p-value - 7.4E-2 4.8E-2 1.3E-1 9.1E-2 - 1.5E-1 8.3E-2 7.2E-2 4.3E-2 (+) Mean 84.78 83.27 80.31 81.55 82.41 92.06 89.40 85.94 90.31 88.49 30 std (2.93) (5.21) (6.40) (3.70) (7.52) (1.68) (6.34) (5.80) (1.23) (3.54) p-value - 1.8E-1 1.1E-1 3.4E-1 4.4E-1 - 1.7E-1 8.3E-2 4.6E-1 9.7E-2 Mean 90.22 84.24 80.64 81.47 72.63 95.06 89.66 88.33 90.27 87.92 40 std (2.81) (3.51) (4.36) (1.42) (0.99) (1.51) (5.82) (6.42) (8.66) (9.11) p-value - 4.0E-2 (+) 2.2E-3 (+) 3.6E-2 (+) 9.4E-3 (+) - 1.3E-1 8.4E-2 5.2E-2 4.3E-2 (+) Mean 89.76 86.68 85.85 80.74 81.69 88.82 85.74 85.63 84.22 80.75 50 std (1.99) (4.99) (6.41) (6.28) (7.11) (2.62) (7.53) (8.90) (7.24) (9.11) p-value - 2.7E-1 2.0E-1 5.7E-2 3.3E-1 - 2.7E-1 1.1E-1 3.4E-1 2.1E-1
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表 11 wdbc数据集的聚类结果对比
Table 11 Performance comparison on wdbc dataset
Sample rate Item F-measure (%) Pure (%) (%) HCSAP SAP SSAP MPCK-MEAN DSCA HCSAP SAP SSAP MPCK-MEAN DSCA Mean 52.31 52.31 52.31 48.42 47.49 55.74 55.74 55.74 51.78 52.69 0 std (0) (0) (0) (1.10) (1.67) (0) (0) (0) (0.62) (0.37) p-value - - - 4.5E-2 (+) 3.1E-2 (+) - - - 4.8E-2 (+) 5.7E-2 Mean 66.35 50.72 48.39 51.46 49.21 61.39 47.80 47.92 44.91 51.68 10 std (13.38) (1.42) (2.82) (2.6) (5.06) (11.73) (3.50) (6.41) (17.46) (14.25) p-value - 1.5E-1 9.2E-2 3.4E-1 1.1E-1 - 1.2E-1 2.4E-1 4.2E-1 2.9E-1 Mean 74.27 66.58 67.24 64.21 60.37 72.16 61.16 60.58 57.26 59.34 20 std (13.78) (14.87) (11.35) (15.87) (9.58) (14.45) (17.51) (15.68) (11.34) (8.48) p-value - 5.0E-1 6.2E-1 9.8E-2 4.1E-1 - 4.1E-1 5.4E-1 1.2E-1 2.6E-1 Mean 85.90 59.10 58.22 57.31 56.74 84.23 52.42 50.72 48.64 51.77 30 std (0. 86) (17.4) (20.55) (8.27) (4.90) (1.26) (4.28) (5.60) (4.89) (2.77) p-value - 9.0E-03 (+) 2.5E-2 (+) 5.1E-3 (+) 6.4E-3 (+) - 7.4E-04 (+) 5.6E-5 (+) 4.9E-6 (+) 1.8E-7 (+) Mean 88.09 71.83 71.27 69.58 64.96 87.39 70.61 71.33 64.99 68.41 40 std (1.35) (8.86) (7.89) (10.54) (9.73) (3.0) (8.14) (6.64) (10.37) (12.85) p-value - 4.70E-2 (+) 2.8E-2 (+) 4.2E-3 (+) 7.7E-3 (+) - 5.3E-2 5.1E-2 4.8E-3 (+) 2.5E-2 (+) Mean 87.53 84.82 84.32 81.62 82.44 88.32 84.74 80.16 75.32 72.19 50 std (7.18) (9.02) (10.33) (8.27) (9.11) (7.80) (9.83) (8.12) (10.77) (11.65) p-value - 4.8E-2 (+) 3.4E-2 (+) 8.9E-3 (+) 7.7E-3 (+) - 4.1E-2 (+) 2.2E-2 (+) 3.6E-2 (+) 1.8E-2 (+)
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