计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (12): 2809-2819.DOI: 10.3778/j.issn.1673-9418.2104019
收稿日期:
2021-04-08
修回日期:
2021-05-26
出版日期:
2022-12-01
发布日期:
2021-05-18
通讯作者:
+E-mail: ghw8601@163.com作者简介:
宋鹏(1996—),男,辽宁丹东人,硕士研究生,CCF学生会员,主要研究方向为模式识别、机器学习。基金资助:
SONG Peng1,2, GE Hongwei1,2,+()
Received:
2021-04-08
Revised:
2021-05-26
Online:
2022-12-01
Published:
2021-05-18
About author:
SONG Peng, born in 1996, M.S. candidate, stu-dent member of CCF. His research interests include pattern recognition and machine learning.Supported by:
摘要:
基于动态图的密度峰值聚类标签传播算法(DPC-DLP)是密度峰值聚类算法(DPC)的一种改进算法,该算法涉及的相关参数过于复杂,并且算法在每次迭代时都会使用标签数据,会出现标签错误扩大化现象,存在迭代次数过多导致聚类效果恶化等问题。针对上述问题,提出了一种最近邻的密度峰值聚类标签传播算法(DPC-NLP)。该算法主要有三个步骤:首先利用局部密度和最小距离对样本点进行打分,根据分数确定聚类中心,然后使用聚类中心的标签在其最近邻内形成簇骨干,最后使用最近邻的标签传播方法将簇骨干的标签传播到剩余样本上,并形成最终的聚类结果。最近邻标签传播算法充分考虑数据间的结构关联性情况,并在传播的过程中不断更新数据的状态,利用更充分的信息提高分配正确率。在人工和真实数据集上对算法进行验证,并与目前主流的聚类算法进行比较,实验结果表明,DPC-NLP在性能和鲁棒性方面表现优越,并可以处理流形和非线性等复杂数据。
中图分类号:
宋鹏, 葛洪伟. 最近邻的密度峰值聚类标签传播算法[J]. 计算机科学与探索, 2022, 16(12): 2809-2819.
SONG Peng, GE Hongwei. Nearest Neighbor Label Propagation for Density Peak Clustering[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(12): 2809-2819.
数据集名称 | 样本数量 | 簇个数 |
---|---|---|
Aggregation | 788 | 7 |
CMC | 1 002 | 3 |
Flame | 515 | 2 |
Spiral | 312 | 3 |
表1 人工数据集
Table 1 Synthetic datasets
数据集名称 | 样本数量 | 簇个数 |
---|---|---|
Aggregation | 788 | 7 |
CMC | 1 002 | 3 |
Flame | 515 | 2 |
Spiral | 312 | 3 |
数据集 | 样本数 | 属性 | 类数 | 应用 |
---|---|---|---|---|
Iris | 150 | 4 | 3 | 植物生物学 |
Parkinson | 195 | 22 | 2 | 医学 |
Sonar | 208 | 60 | 2 | 物理学 |
Seeds | 210 | 7 | 3 | 农业物理学 |
Thyroid | 215 | 5 | 3 | 医学 |
Ecoli | 336 | 7 | 8 | 分子生物学 |
WDBC | 569 | 30 | 2 | 医学 |
Diabetes | 768 | 8 | 2 | 医学 |
Vehicle | 846 | 18 | 4 | 车辆识别 |
表2 低维数据基本情况
Table 2 Low-dimensional datasets
数据集 | 样本数 | 属性 | 类数 | 应用 |
---|---|---|---|---|
Iris | 150 | 4 | 3 | 植物生物学 |
Parkinson | 195 | 22 | 2 | 医学 |
Sonar | 208 | 60 | 2 | 物理学 |
Seeds | 210 | 7 | 3 | 农业物理学 |
Thyroid | 215 | 5 | 3 | 医学 |
Ecoli | 336 | 7 | 8 | 分子生物学 |
WDBC | 569 | 30 | 2 | 医学 |
Diabetes | 768 | 8 | 2 | 医学 |
Vehicle | 846 | 18 | 4 | 车辆识别 |
数据集 | 样本数 | 属性 | 类数 | 应用 |
---|---|---|---|---|
Drivface | 606 | 6 400 | 3 | 头部姿态估计 |
Coil20 | 1 440 | 1 024 | 20 | 物体识别 |
Yeast | 1 483 | 8 | 10 | 细胞生物学 |
Mfeat | 2 000 | 649 | 10 | 手写数字识别 |
Segment | 2 310 | 19 | 7 | 图像处理 |
Abalone | 4 177 | 8 | 28 | 种群生物学 |
Waveform | 5 000 | 21 | 3 | 物理学 |
USPS | 9 298 | 256 | 10 | 手写数字识别 |
表3 高维数据基本情况
Table 3 High-dimensional datasets
数据集 | 样本数 | 属性 | 类数 | 应用 |
---|---|---|---|---|
Drivface | 606 | 6 400 | 3 | 头部姿态估计 |
Coil20 | 1 440 | 1 024 | 20 | 物体识别 |
Yeast | 1 483 | 8 | 10 | 细胞生物学 |
Mfeat | 2 000 | 649 | 10 | 手写数字识别 |
Segment | 2 310 | 19 | 7 | 图像处理 |
Abalone | 4 177 | 8 | 28 | 种群生物学 |
Waveform | 5 000 | 21 | 3 | 物理学 |
USPS | 9 298 | 256 | 10 | 手写数字识别 |
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Iris | 0.819 6 | 0.866 8 | 0.900 4 | 0.947 8 | 0.947 9 |
Parkinson | 0.770 7 | 0.649 5 | 0.732 2 | 0.800 5 | 0.824 5 |
Sonar | 0.502 7 | 0.527 9 | 0.544 0 | 0.574 0 | 0.659 7 |
Seeds | 0.810 6 | 0.817 7 | 0.839 6 | 0.849 5 | 0.900 4 |
Thyroid | 0.806 1 | 0.636 9 | 0.636 9 | 0.774 3 | 0.923 1 |
Ecoli | 0.621 1 | 0.785 8 | 0.785 8 | 0.800 8 | 0.822 0 |
WDBC | 0.786 0 | 0.665 3 | 0.728 0 | 0.844 1 | 0.925 2 |
Diabetes | 0.612 5 | 0.601 6 | 0.601 6 | 0.633 3 | 0.705 6 |
Vehicle | 0.307 5 | 0.347 0 | 0.354 8 | 0.396 5 | 0.431 9 |
Average | 0.670 8 | 0.655 4 | 0.680 4 | 0.735 3 | 0.793 4 |
表4 低维数据集上的F-measure指标结果
Table 4 F-measure index results on low-dimensional datasets
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Iris | 0.819 6 | 0.866 8 | 0.900 4 | 0.947 8 | 0.947 9 |
Parkinson | 0.770 7 | 0.649 5 | 0.732 2 | 0.800 5 | 0.824 5 |
Sonar | 0.502 7 | 0.527 9 | 0.544 0 | 0.574 0 | 0.659 7 |
Seeds | 0.810 6 | 0.817 7 | 0.839 6 | 0.849 5 | 0.900 4 |
Thyroid | 0.806 1 | 0.636 9 | 0.636 9 | 0.774 3 | 0.923 1 |
Ecoli | 0.621 1 | 0.785 8 | 0.785 8 | 0.800 8 | 0.822 0 |
WDBC | 0.786 0 | 0.665 3 | 0.728 0 | 0.844 1 | 0.925 2 |
Diabetes | 0.612 5 | 0.601 6 | 0.601 6 | 0.633 3 | 0.705 6 |
Vehicle | 0.307 5 | 0.347 0 | 0.354 8 | 0.396 5 | 0.431 9 |
Average | 0.670 8 | 0.655 4 | 0.680 4 | 0.735 3 | 0.793 4 |
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Iris | 0.879 7 | 0.912 4 | 0.934 1 | 0.965 6 | 0.965 6 |
Parkinson | 0.626 9 | 0.592 9 | 0.648 7 | 0.703 9 | 0.745 5 |
Sonar | 0.503 2 | 0.522 2 | 0.534 0 | 0.564 7 | 0.557 8 |
Seeds | 0.874 3 | 0.879 5 | 0.893 9 | 0.900 4 | 0.934 2 |
Thyroid | 0.790 7 | 0.606 4 | 0.606 4 | 0.701 1 | 0.914 6 |
Ecoli | 0.819 9 | 0.868 1 | 0.868 1 | 0.877 0 | 0.895 3 |
WDBC | 0.747 8 | 0.650 7 | 0.652 6 | 0.827 9 | 0.919 1 |
Diabetes | 0.549 8 | 0.583 0 | 0.583 0 | 0.596 3 | 0.595 2 |
Vehicle | 0.653 2 | 0.657 9 | 0.657 3 | 0.680 7 | 0.686 4 |
Average | 0.716 2 | 0.697 0 | 0.708 7 | 0.757 5 | 0.801 5 |
表5 低维数据集上的RI指标结果
Table 5 RI index results on low-dimensional datasets
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Iris | 0.879 7 | 0.912 4 | 0.934 1 | 0.965 6 | 0.965 6 |
Parkinson | 0.626 9 | 0.592 9 | 0.648 7 | 0.703 9 | 0.745 5 |
Sonar | 0.503 2 | 0.522 2 | 0.534 0 | 0.564 7 | 0.557 8 |
Seeds | 0.874 3 | 0.879 5 | 0.893 9 | 0.900 4 | 0.934 2 |
Thyroid | 0.790 7 | 0.606 4 | 0.606 4 | 0.701 1 | 0.914 6 |
Ecoli | 0.819 9 | 0.868 1 | 0.868 1 | 0.877 0 | 0.895 3 |
WDBC | 0.747 8 | 0.650 7 | 0.652 6 | 0.827 9 | 0.919 1 |
Diabetes | 0.549 8 | 0.583 0 | 0.583 0 | 0.596 3 | 0.595 2 |
Vehicle | 0.653 2 | 0.657 9 | 0.657 3 | 0.680 7 | 0.686 4 |
Average | 0.716 2 | 0.697 0 | 0.708 7 | 0.757 5 | 0.801 5 |
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Iris | 0.729 4 | 0.801 5 | 0.851 2 | 0.922 2 | 0.922 2 |
Parkinson | 0 | 0.171 3 | 0.224 8 | 0.276 6 | 0.413 5 |
Sonar | 0.006 4 | 0.044 3 | 0.068 0 | 0.129 3 | 0.115 6 |
Seeds | 0.716 6 | 0.727 7 | 0.760 4 | 0.775 1 | 0.851 2 |
Thyroid | 0.579 0 | 0.207 7 | 0.207 7 | 0.207 7 | 0.827 6 |
Ecoli | 0.505 9 | 0.692 5 | 0.692 5 | 0.714 4 | 0.748 1 |
WDBC | 0.486 2 | 0.300 3 | 0.283 0 | 0.652 6 | 0.837 1 |
Diabetes | 0.080 4 | 0.165 9 | 0.165 9 | 0.184 4 | 0.167 9 |
Vehicle | 0.076 2 | 0.116 0 | 0.122 6 | 0.180 4 | 0.201 7 |
Average | 0.353 3 | 0.358 6 | 0.375 1 | 0.449 2 | 0.801 5 |
表6 低维数据集上的ARI指标结果
Table 6 ARI index results on low-dimensional datasets
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Iris | 0.729 4 | 0.801 5 | 0.851 2 | 0.922 2 | 0.922 2 |
Parkinson | 0 | 0.171 3 | 0.224 8 | 0.276 6 | 0.413 5 |
Sonar | 0.006 4 | 0.044 3 | 0.068 0 | 0.129 3 | 0.115 6 |
Seeds | 0.716 6 | 0.727 7 | 0.760 4 | 0.775 1 | 0.851 2 |
Thyroid | 0.579 0 | 0.207 7 | 0.207 7 | 0.207 7 | 0.827 6 |
Ecoli | 0.505 9 | 0.692 5 | 0.692 5 | 0.714 4 | 0.748 1 |
WDBC | 0.486 2 | 0.300 3 | 0.283 0 | 0.652 6 | 0.837 1 |
Diabetes | 0.080 4 | 0.165 9 | 0.165 9 | 0.184 4 | 0.167 9 |
Vehicle | 0.076 2 | 0.116 0 | 0.122 6 | 0.180 4 | 0.201 7 |
Average | 0.353 3 | 0.358 6 | 0.375 1 | 0.449 2 | 0.801 5 |
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Drivface | 0.428 3 | 0.561 5 | 0.693 9 | 0.816 4 | 0.814 1 |
Coil20 | 0.646 5 | 0.854 7 | 0.847 5 | 0.850 7 | 0.927 8 |
Yeast | 0.716 2 | 0.648 2 | 0.722 0 | 0.725 7 | 0.733 6 |
Mfeat | 0.887 7 | 0.837 7 | 0.750 7 | 0.786 7 | 0.889 0 |
Segment | 0.879 2 | 0.837 4 | 0.885 9 | 0.884 9 | 0.890 1 |
Abalone | 0.868 4 | 0.826 7 | 0.848 4 | 0.830 2 | 0.848 1 |
Waveform | 0.660 0 | 0.707 2 | 0.775 4 | 0.779 4 | 0.869 4 |
USPS | 0.558 5 | 0.873 7 | 0.843 5 | 0.835 0 | 0.923 3 |
Average | 0.627 2 | 0.589 9 | 0.707 5 | 0.723 2 | 0.766 2 |
表7 在高维数据集上的RI指标结果
Table 7 RI index results on high-dimensional datasets
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Drivface | 0.428 3 | 0.561 5 | 0.693 9 | 0.816 4 | 0.814 1 |
Coil20 | 0.646 5 | 0.854 7 | 0.847 5 | 0.850 7 | 0.927 8 |
Yeast | 0.716 2 | 0.648 2 | 0.722 0 | 0.725 7 | 0.733 6 |
Mfeat | 0.887 7 | 0.837 7 | 0.750 7 | 0.786 7 | 0.889 0 |
Segment | 0.879 2 | 0.837 4 | 0.885 9 | 0.884 9 | 0.890 1 |
Abalone | 0.868 4 | 0.826 7 | 0.848 4 | 0.830 2 | 0.848 1 |
Waveform | 0.660 0 | 0.707 2 | 0.775 4 | 0.779 4 | 0.869 4 |
USPS | 0.558 5 | 0.873 7 | 0.843 5 | 0.835 0 | 0.923 3 |
Average | 0.627 2 | 0.589 9 | 0.707 5 | 0.723 2 | 0.766 2 |
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Drivface | 0.014 3 | 0.123 3 | 0.193 9 | 0.296 2 | 0.304 2 |
Coil20 | 0.090 8 | 0.192 1 | 0.172 1 | 0.230 3 | 0.467 0 |
Yeast | 0.095 0 | 0.107 2 | 0.138 7 | 0.187 5 | 0.171 4 |
Mfeat | 0.418 1 | 0.286 0 | 0.251 7 | 0.350 7 | 0.538 7 |
Segment | 0.506 3 | 0.489 6 | 0.603 7 | 0.585 7 | 0.601 4 |
Abalone | 0.035 2 | 0.065 1 | 0.069 1 | 0.073 3 | 0.068 2 |
Waveform | 0.236 4 | 0.354 2 | 0.508 6 | 0.516 4 | 0.514 2 |
USPS | 0.118 3 | 0.425 3 | 0.243 4 | 0.428 7 | 0.663 0 |
Average | 0.189 3 | 0.255 4 | 0.272 7 | 0.333 6 | 0.365 0 |
表8 在高维数据集上的ARI指标结果
Table 8 ARI index results on high-dimensional datasets
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Drivface | 0.014 3 | 0.123 3 | 0.193 9 | 0.296 2 | 0.304 2 |
Coil20 | 0.090 8 | 0.192 1 | 0.172 1 | 0.230 3 | 0.467 0 |
Yeast | 0.095 0 | 0.107 2 | 0.138 7 | 0.187 5 | 0.171 4 |
Mfeat | 0.418 1 | 0.286 0 | 0.251 7 | 0.350 7 | 0.538 7 |
Segment | 0.506 3 | 0.489 6 | 0.603 7 | 0.585 7 | 0.601 4 |
Abalone | 0.035 2 | 0.065 1 | 0.069 1 | 0.073 3 | 0.068 2 |
Waveform | 0.236 4 | 0.354 2 | 0.508 6 | 0.516 4 | 0.514 2 |
USPS | 0.118 3 | 0.425 3 | 0.243 4 | 0.428 7 | 0.663 0 |
Average | 0.189 3 | 0.255 4 | 0.272 7 | 0.333 6 | 0.365 0 |
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Drivface | 0.058 4 | 0.116 9 | 0.165 3 | 0.227 8 | 0.231 8 |
Coil20 | 0.388 3 | 0.479 5 | 0.437 9 | 0.604 4 | 0.797 5 |
Yeast | 0.173 9 | 0.194 0 | 0.246 8 | 0.311 2 | 0.275 0 |
Mfeat | 0.558 5 | 0.499 6 | 0.471 7 | 0.604 9 | 0.732 0 |
Segment | 0.610 2 | 0.682 0 | 0.715 7 | 0.713 3 | 0.744 5 |
Abalone | 0.160 5 | 0.178 0 | 0.177 8 | 0.213 8 | 0.223 4 |
Waveform | 0.320 9 | 0.376 8 | 0.500 7 | 0.504 1 | 0.664 1 |
USPS | 0.230 5 | 0.506 6 | 0.354 2 | 0.642 4 | 0.752 4 |
Average | 0.312 7 | 0.379 2 | 0.383 8 | 0.477 7 | 0.491 2 |
表9 在高维数据集上的NMI指标结果
Table 9 NMI index results on high-dimensional datasets
Dataset | FCM | DPC-KNN | IDPC | DPC-DLP | Ours |
---|---|---|---|---|---|
Drivface | 0.058 4 | 0.116 9 | 0.165 3 | 0.227 8 | 0.231 8 |
Coil20 | 0.388 3 | 0.479 5 | 0.437 9 | 0.604 4 | 0.797 5 |
Yeast | 0.173 9 | 0.194 0 | 0.246 8 | 0.311 2 | 0.275 0 |
Mfeat | 0.558 5 | 0.499 6 | 0.471 7 | 0.604 9 | 0.732 0 |
Segment | 0.610 2 | 0.682 0 | 0.715 7 | 0.713 3 | 0.744 5 |
Abalone | 0.160 5 | 0.178 0 | 0.177 8 | 0.213 8 | 0.223 4 |
Waveform | 0.320 9 | 0.376 8 | 0.500 7 | 0.504 1 | 0.664 1 |
USPS | 0.230 5 | 0.506 6 | 0.354 2 | 0.642 4 | 0.752 4 |
Average | 0.312 7 | 0.379 2 | 0.383 8 | 0.477 7 | 0.491 2 |
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