多标签符号型属性值划分的聚类方法

doi:10.6040/j.issn.1671-9352.1.2019.154

摘要/Abstract

摘要：

提出了一种多标签符号型属性值划分的聚类方法(clustering method for multi-label symbolic value partition, CMSVP)。首先，利用标签排序和K-means算法，对原始标签信息进行聚类。然后，为每一个属性构建一个无向加权图。图中的每一个节点代表一个属性值，边的权重则表示节点之间的相似度。最后，对所有的无向加权图进行随机游走，得到属性值的聚类方案。实验在6个多标签数据集上进行。结果表明，CMSVP算法在对数据有效地进行压缩的同时，也能在一定程度上提高数据的分类性能。

关键词: 属性值划分, 聚类, 随机游走, 无向加权图, 多标签

Abstract:

A clustering method for multi-label symbolic value partition (CMSVP) is proposed. First, the label ranking and K-means algorithms are employed to cluster the original label information. Then, an undirected weighted graph is constructed for each attribute. Each node represents an attribute value, and the weight of each edge represents the similarity between the nodes. Finally, random walks are performed on all undirected weighted graphs to obtain a clustering scheme of attribute values. The experiment is conducted on six multi-label data sets. The results show that the CMSVP algorithm can improve the classification performance of data while effectively compressing the data.

Key words: symbolic value partition, clustering, random walk, undirected weighted graph, multi-label

中图分类号:

TP391

温柳英,袁伟. 多标签符号型属性值划分的聚类方法[J]. 《山东大学学报(理学版)》, 2020, 55(3): 58-69.

Liu-ying WEN,Wei YUAN. Clustering method for multi-label symbolic value partition[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 58-69.

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表10

RAkEL分类器下的性能比较"

Hamming Loss(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.051 7±0.007 0	0.036 4±0.009 6	0.050 3±0.005 6	0.052 6±0.006 1	0.050 8±0.006 2	0.049 5±0.005 9
Cal500	0.140 2±0.002 8	0.099 1±0.002 7	0.139 0±0.002 5	0.138 4±0.002 4	0.139 2±0.002 9	0.138 5±0.002 1
Emotions	0.238 4±0.015 3	0.172 1±0.026 6	0.271 8±0.031 8	0.260 0±0.034 0	0.248 5±0.034 7	0.239 3±0.036 7
Flags	0.271 9±0.032 5	0.217 6±0.053 7	0.257 9±0.024 4	0.260 8±0.022 8	0.265 2±0.027 7	0.265 2±0.027 7
Scene	0.137 3±0.009 5	0.146 5±0.011 5	0.158 8±0.007 4	0.158 1±0.007 1	0.159 5±0.009 3	0.159 2±0.008 3
Yeast	0.244 7±0.011 4	0.172 2±0.009 3	0.224 8±0.010 9	0.223 4±0.011 6	0.225 1±0.012 0	0.225 2±0.011 8

Ranking Loss(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.231 1±0.027 8	0.112 5±0.030 8	0.215 7±0.020 1	0.244 3±0.026 6	0.239 5±0.025 4	0.212 1±0.019 7
Cal500	0.422 8±0.010 1	0.434 1±0.007 0	0.413 2±0.009 6	0.417 4±0.008 9	0.395 5±0.007 4	0.413 9±0.009 6
Emotions	0.227 2±0.026 5	0.100 8±0.027 5	0.288 3±0.043 6	0.284 0±0.049 3	0.262 4±0.038 9	0.261 9±0.043 0
Flags	0.240 4±0.055 1	0.233 7±0.075 8	0.273 3±0.048 4	0.271 4±0.050 1	0.276 9±0.049 8	0.276 9±0.049 8
Scene	0.172 2±0.014 9	0.155 7±0.026 8	0.229 3±0.025 0	0.233 0±0.019 2	0.232 1±0.014 6	0.232 2±0.016 0
Yeast	0.241 7±0.015 7	0.185 4±0.015 1	0.271 8±0.014 0	0.278 8±0.015 2	0.262 3±0.017 6	0.262 3±0.019 5

One Error(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.820 3±0.044 8	0.877 5±0.052 5	0.773 6±0.043 6	0.835 5±0.045 3	0.818 4±0.045 0	0.765 8±0.061 7
Cal500	0.266 7±0.059 7	0.591 2±0.086 4	0.205 0±0.067 8	0.207 1±0.072 7	0.258 8±0.056 9	0.219 1±0.077 8
Emotions	0.377 8±0.060 7	0.495 9±0.049 3	0.438 6±0.063 2	0.438 4±0.063 6	0.396 4±0.063 2	0.386 3±0.072 4
Flags	0.257 1±0.098 5	0.412 6±0.058 1	0.292 9±0.095 2	0.277 6±0.104 8	0.283 2±0.083 8	0.283 2±0.083 8
Scene	0.395 9±0.033 1	0.719 2±0.032 7	0.491 9±0.036 0	0.491 5±0.026 7	0.489 8±0.026 3	0.489 4±0.025 9
Yeast	0.295 0±0.043 1	0.304 5±0.027 2	0.260 2±0.032 4	0.256 9±0.027 7	0.260 2±0.026 8	0.257 3±0.027 1

Coverage(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	5.421 4±0.502 9	1.618 1±0.387 7	5.313 2±0.408 9	5.684 0±0.443 3	5.670 4±0.467 4	5.286 0±0.419 6
Cal500	168.929 2±0.555 4	108.805 6±1.413 3	168.893 1±0.535 3	168.872 0±0.741 1	168.843 5±0.676 0	168.798 3±0.743 8
Emotions	2.104 6±0.120 0	0.460 8±0.117 1	2.401 5±0.219 7	2.401 7±0.277 3	2.299 9±0.208 2	2.299 9±0.221 7
Flags	3.921 3±0.497 1	1.744 2±0.423 8	4.093 2±0.423 8	4.103 4±0.427 9	4.112 4±0.433 1	4.112 4±0.433 1
Scene	0.953 4±0.064 2	0.492 7±0.090 2	1.235 9±0.118 0	1.257 5±0.094 0	1.253 8±0.077 0	1.255 0±0.079 3
Yeast	7.989 9±0.300 9	3.022 1±0.173 1	8.561 3±0.263 2	8.670 0±0.310 3	8.398 4±0.349 9	8.349 6±0.403 4

Average Precision(↑)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.356 7±0.050 8	0.464 7±0.112 8	0.409 9±0.041 3	0.324 9±0.048 9	0.344 4±0.044 6	0.414 6±0.057 1
Cal500	0.363 8±0.011 2	0.193 8±0.011 3	0.376 8±0.011 6	0.374 0±0.011 3	0.385 2±0.011 4	0.375 1±0.011 3
Emotions	0.740 2±0.027 6	0.838 4±0.042 0	0.690 0±0.038 8	0.693 4±0.041 3	0.718 3±0.040 4	0.722 4±0.042 7
Flags	0.803 2±0.041 2	0.759 6±0.059 7	0.786 3±0.038 7	0.788 4±0.042 3	0.783 5±0.038 8	0.783 5±0.038 8
Scene	0.748 2±0.018 0	0.707 0±0.037 4	0.684 0±0.025 8	0.681 1±0.019 6	0.682 2±0.016 9	0.682 5±0.017 0
Yeast	0.691 5±0.022 0	0.728 1±0.016 7	0.693 1±0.019 2	0.689 8±0.018 8	0.698 3±0.016 9	0.697 7±0.018 8

表10

表11

MLkNN分类器下的性能比较"

Hamming Loss(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.053 8±0.005 5	0.033 9±0.006 6	0.050 9±0.006 8	0.051 2±0.006 0	0.049 4±0.005 8	0.050 2±0.006 9
Cal500	0.138 4±0.003 1	0.097 9±0.002 9	0.138 3±0.002 8	0.138 6±0.002 6	0.138 8±0.002 8	0.138 4±0.003 0
Emotions	0.199 0±0.016 0	0.131 6±0.016 5	0.233 5±0.025 8	0.240 6±0.023 5	0.245 4±0.020 8	0.239 0±0.018 8
Flags	0.284 5±0.039 4	0.203 4±0.049 9	0.269 2±0.041 5	0.286 2±0.030 1	0.274 9±0.029 2	0.274 9±0.029 2
Scene	0.101 4±0.004 4	0.113 9±0.010 2	0.150 3±0.005 7	0.147 3±0.005 6	0.148 3±0.004 5	0.146 8±0.005 8
Yeast	0.207 9±0.013 6	0.151 1±0.010 5	0.217 6±0.012 1	0.221 8±0.008 3	0.216 3±0.011 8	0.213 5±0.011 5

Ranking Loss(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.117 6±0.023 7	0.060 7±0.017 2	0.082 3±0.019 8	0.083 3±0.020 0	0.084 7±0.022 5	0.084 1±0.021 4
Cal500	0.184 8±0.007 7	0.205 4±0.009 6	0.184 0±0.006 6	0.184 9±0.007 2	0.183 9±0.006 8	0.185 1±0.007 3
Emotions	0.165 3±0.024 4	0.056 3±0.017 4	0.213 5±0.026 0	0.224 5±0.031 2	0.224 3±0.017 4	0.225 0±0.021 5
Flags	0.214 5±0.044 5	0.228 9±0.078 9	0.198 5±0.036 9	0.206 3±0.028 7	0.196 6±0.041 1	0.196 6±0.041 1
Scene	0.100 8±0.012 4	0.084 0±0.010 6	0.190 0±0.012 4	0.180 9±0.014 9	0.172 0±0.014 5	0.172 7±0.017 4
Yeast	0.185 1±0.016 0	0.135 3±0.010 9	0.193 2±0.013 0	0.200 3±0.014 3	0.189 5±0.016 9	0.187 1±0.015 2

One Error(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.779 9±0.043 0	0.831 0±0.050 9	0.713 3±0.056 5	0.717 9±0.057 2	0.728 8±0.050 6	0.728 8±0.052 5
Cal500	0.119 3±0.065 0	0.651 4±0.040 8	0.119 3±0.061 7	0.119 3±0.065 5	0.119 2±0.069 9	0.117 3±0.069 8
Emotions	0.296 8±0.049 8	0.430 1±0.050 6	0.349 0±0.036 0	0.393 0±0.067 3	0.382 9±0.033 2	0.357 7±0.057 2
Flags	0.272 6±0.070 7	0.608 4±0.098 6	0.258 4±0.054 0	0.201 1±0.048 9	0.196 3±0.099 3	0.196 3±0.099 3
Scene	0.277 1±0.022 2	0.630 7±0.030 9	0.472 4±0.032 6	0.454 9±0.043 4	0.448 7±0.039 4	0.441 6±0.042 0
Yeast	0.248 7±0.027 0	0.254 0±0.029 8	0.254 9±0.030 1	0.250 3±0.030 5	0.244 9±0.024 4	0.247 0±0.031 0

Coverage(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	3.154 9±0.521 9	0.941 3±0.246 1	2.388 0±0.395 9	2.414 7±0.403 7	2.421 8±0.415 3	2.417 4±0.389 3
Cal500	129.451 6±2.226 7	74.915 2±2.068 7	129.751 7±1.949 0	129.841 6±1.706 7	129.482 6±1.941 1	129.806 3±1.883 3
Emotions	1.796 6±0.152 1	0.327 6±0.092 4	2.035 3±0.154 2	2.062 7±0.147 4	2.081 0±0.126 9	2.084 5±0.123 3
Flags	3.793 7±0.502 8	0.993 7±0.284 4	3.662 9±0.457 4	3.757 4±0.324 5	3.667 9±0.359 9	3.667 9±0.359 9
Scene	0.592 0±0.055 2	0.275 1±0.034 8	1.035 3±0.051 7	0.988 3±0.064 4	0.945 6±0.062 8	0.945 1±0.080 4
Yeast	6.523 3±0.256 9	2.441 4±0.155 4	6.644 0±0.224 0	6.727 3±0.195 2	6.632 5±0.279 3	6.582 5±0.251 8

Average Precision(↑)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.512 7±0.063 7	0.594 9±0.081 7	0.605 3±0.065 3	0.597 9±0.067 6	0.591 7±0.056 7	0.590 8±0.067 6
Cal500	0.487 5±0.012 5	0.328 3±0.010 4	0.490 4±0.012 1	0.488 6±0.013 0	0.487 9±0.010 6	0.489 0±0.013 9
Emotions	0.790 1±0.022 6	0.897 8±0.027 4	0.748 6±0.028 5	0.728 9±0.035 0	0.735 7±0.023 0	0.741 5±0.026 3
Flags	0.805 1±0.032 3	0.713 3±0.067 3	0.818 4±0.025 3	0.820 8±0.023 8	0.826 3±0.045 8	0.826 3±0.045 8
Scene	0.831 6±0.014 8	0.814 1±0.025 6	0.706 8±0.018 7	0.718 6±0.025 7	0.724 7±0.022 9	0.728 4±0.025 9
Yeast	0.739 3±0.021 7	0.772 7±0.017 8	0.727 0±0.020 9	0.719 8±0.021 8	0.733 9±0.021 3	0.735 6±0.022 7

表11

表12

BRkNN分类器下的性能比较"

Hamming Loss(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.053 2±0.006 1	0.035 9±0.008 3	0.049 4±0.005 8	0.050 1±0.005 7	0.049 8±0.005 8	0.049 4±0.006 6
Cal500	0.140 1±0.002 7	0.100 4±0.002 5	0.140 2±0.002 4	0.142 2±0.003 4	0.141 5±0.001 8	0.142 0±0.003 3
Emotions	0.198 2±0.016 8	0.130 0±0.021 0	0.223 1±0.022 6	0.227 7±0.021 5	0.238 0±0.014 6	0.231 6±0.016 6
Flags	0.273 1±0.027 2	0.208 5±0.048 3	0.260 6±0.030 4	0.267 0±0.024 2	0.254 8±0.027 0	0.254 8±0.027 0
Scene	0.109 5±0.005 1	0.123 5±0.007 6	0.155 7±0.007 5	0.149 1±0.008 4	0.151 3±0.006 8	0.150 2±0.009 2
Yeast	0.210 7±0.011 7	0.151 2±0.009 7	0.218 4±0.010 1	0.219 9±0.009 7	0.217 9±0.011 2	0.215 9±0.009 6

Ranking Loss(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.151 7±0.023 5	0.070 8±0.016 1	0.099 7±0.022 8	0.099 3±0.018 8	0.100 8±0.020 2	0.099 9±0.022 0
Cal500	0.201 1±0.007 9	0.237 3±0.013 1	0.212 5±0.007 7	0.215 7±0.008 9	0.220 2±0.008 6	0.214 9±0.008 6
Emotions	0.172 1±0.033 1	0.057 7±0.017 6	0.202 5±0.024 8	0.219 6±0.023 7	0.225 2±0.024 2	0.225 0±0.022 5
Flags	0.210 4±0.032 9	0.228 0±0.073 3	0.190 2±0.037 7	0.191 0±0.032 0	0.184 3±0.024 8	0.184 3±0.024 8
Scene	0.113 7±0.012 1	0.092 6±0.017 9	0.191 3±0.013 1	0.186 7±0.012 6	0.183 9±0.011 4	0.181 4±0.017 1
Yeast	0.197 8±0.016 4	0.145 6±0.012 1	0.201 1±0.014 2	0.214 1±0.013 1	0.199 0±0.015 2	0.194 1±0.011 3

One Error(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.815 5±0.034 9	0.823 2±0.054 0	0.707 0±0.048 9	0.696 3±0.052 2	0.717 9±0.045 6	0.702 3±0.047 1
Cal500	0.139 3±0.066 2	0.684 9±0.061 1	0.157 1±0.079 3	0.159 3±0.067 2	0.173 2±0.073 3	0.157 1±0.067 8
Emotions	0.293 6±0.055 1	0.441 9±0.051 4	0.335 6±0.047 9	0.362 4±0.048 6	0.377 7±0.041 7	0.364 4±0.056 6
Flags	0.237 6±0.054 3	0.628 9±0.103 3	0.200 8±0.061 7	0.180 5±0.047 9	0.180 3±0.057 0	0.180 3±0.057 0
Scene	0.300 8±0.026 2	0.644 8±0.026 8	0.477 3±0.044 1	0.457 8±0.036 1	0.454 5±0.036 7	0.450 3±0.040 2
Yeast	0.256 1±0.026 9	0.263 5±0.027 2	0.268 1±0.025 8	0.258 6±0.024 9	0.246 2±0.029 5	0.254 9±0.022 6

Coverage(↓)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	3.907 8±0.458 0	1.074 6±0.231 7	2.793 8±0.475 7	2.820 8±0.405 1	2.851 1±0.374 3	2.810 7±0.409 3
Cal500	138.659 1±1.945 6	86.374 3±3.427 6	144.799 6±2.470 5	144.950 9±3.038 8	147.130 3±2.659 7	144.871 8±2.685 4
Emotions	1.845 6±0.186 7	0.332 7±0.085 1	1.968 1±0.158 2	2.052 4±0.117 0	2.048 7±0.127 1	2.089 5±0.137 0
Flags	3.776 8±0.425 0	0.977 4±0.292 8	3.639 5±0.424 7	3.679 7±0.290 6	3.616 6±0.318 7	3.616 6±0.318 7
Scene	0.656 0±0.054 4	0.302 4±0.059 6	1.039 0±0.048 7	1.017 4±0.050 1	1.006 6±0.050 6	0.991 7±0.082 9
Yeast	6.837 8±0.254 5	2.553 9±0.162 1	6.917 5±0.223 7	7.126 1±0.182 0	6.839 5±0.212 6	6.782 4±0.202 4

Average Precision(↑)
Dataset	Original	CMSVP	IG-BR	IG-LP	RF-BR	RF-LP
Birds	0.455 7±0.050 5	0.595 9±0.080 8	0.607 6±0.058 4	0.615 3±0.058 6	0.598 1±0.056 9	0.605 9±0.061 9
Cal500	0.476 7±0.011 8	0.306 8±0.014 0	0.475 5±0.014 1	0.467 0±0.014 2	0.466 6±0.011 6	0.466 3±0.014 3
Emotions	0.788 4±0.033 0	0.891 1±0.030 2	0.761 4±0.028 8	0.743 7±0.025 8	0.739 6±0.025 3	0.741 6±0.024 1
Flags	0.815 2±0.024 8	0.706 2±0.049 1	0.837 7±0.032 1	0.835 1±0.030 3	0.839 6±0.021 8	0.839 6±0.021 8
Scene	0.814 7±0.015 6	0.800 5±0.029 0	0.704 3±0.024 4	0.714 6±0.020 6	0.716 8±0.020 7	0.719 1±0.025 3
Yeast	0.732 2±0.019 8	0.766 9±0.017 3	0.723 7±0.019 8	0.713 8±0.0195	0.730 7±0.019 6	0.733 9±0.016 6

表12

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U	A		L
U	a₁	a₂	l₁	l₂	l₃
x₁	0	6	1	0	1
x₂	1	1	0	0	1
x₃	5	3	0	1	0
x₄	2	1	1	1	0
x₅	1	2	1	0	1
x₆	3	0	0	1	1
x₇	4	5	1	1	1
x₈	6	4	1	1	0

U	A^P		L
U	a₁^P	a₂^P	l₁	l₂	l₃
x₁	{0, 1, 4}	{2, 5, 6}	1	0	1
x₂	{0, 1, 4}	{0, 1}	0	0	1
x₃	{5, 6}	{3, 4}	0	1	0
x₄	{2, 3}	{0, 1}	1	1	0
x₅	{0, 1, 4}	{2, 5, 6}	1	0	1
x₆	{2, 3}	{0, 1}	0	1	1
x₇	{0, 1, 4}	{2, 5, 6}	1	1	1
x₈	{5, 6}	{3, 4}	1	1	0

符号	定义说明
N	U中实例的个数
q	L中标签的个数
M	A中属性的个数
CN	记录相同属性值的个数
D_{a_i}	关于属性a_i的决策子表
V′_i	D_{a_i}中去重后的属性值域
P_j	V′_i中第j个属性值的概率
G_i	属性a_i的无向加权图
v_t	G_i中的节点t
M^G_i	关于G_i的相关转移矩阵

U	A		L′
U	a₁	a₂	{l₁, l₃}	{l₂}
x₁	0	6	1	0
x₂	1	1	0	0
x₃	5	3	0	1
x₄	2	1	0	1
x₅	1	2	1	0
x₆	3	0	0	1
x₇	4	5	1	1
x₈	6	4	0	1

步骤描述	复杂度
标签聚类	O(qN)
构建无向加权图	O(qMN²)
随机游走聚类	O(RMN²)
总复杂度	O((q+R)MN²)