电子学报 ›› 2022, Vol. 50 ›› Issue (11): 2730-2737.DOI: 10.12263/DZXB.20211273
赵嘉, 王刚, 吕莉, 樊棠怀
收稿日期:
2021-09-17
修回日期:
2022-01-01
出版日期:
2022-11-25
作者简介:
基金资助:
ZHAO Jia, WANG Gang, LÜ Li, FAN Tang-huai
Received:
2021-09-17
Revised:
2022-01-01
Online:
2022-11-25
Published:
2022-11-19
摘要:
密度峰值聚类算法倾向在球形分布数据中选择密度峰值,而流形数据多呈非球形分布,导致不能准确找到数据的类簇中心.该算法的分配策略优先对类簇中心附近的样本进行链式分配,而流形数据大量样本远离其类簇中心,导致本应属于同一类簇的样本被错误分配.为此,本文提出一种面向流形数据的测地距离与余弦互逆近邻密度峰值聚类算法.将K近邻与测地距离结合并重新定义局部密度,凸显密度峰值与非密度峰值的差异,准确找到类簇中心;将互逆近邻和余弦相似性相结合,得到基于余弦互逆近邻的样本相似度矩阵,为流形类簇准确分配样本.实验结果表明,本算法能有效发现流形数据集的几何形状并准确聚类,对真实数据集和图像数据集的聚类效果优秀.
中图分类号:
赵嘉, 王刚, 吕莉, 樊棠怀. 面向流形数据的测地距离与余弦互逆近邻密度峰值聚类算法[J]. 电子学报, 2022, 50(11): 2730-2737.
ZHAO Jia, WANG Gang, LÜ Li, FAN Tang-huai. Density Peaks Clustering Algorithm Based on Geodesic Distance and Cosine Mutual Reverse Nearest Neighbors for Manifold Datasets[J]. Acta Electronica Sinica, 2022, 50(11): 2730-2737.
数据集 | 样本规模 | 样本维度 | 类簇个数 |
---|---|---|---|
Db | 630 | 2 | 4 |
Jain | 373 | 2 | 2 |
Spiral | 312 | 2 | 3 |
Pathbased | 300 | 2 | 3 |
Lineblobs | 266 | 2 | 3 |
Sticks | 512 | 2 | 4 |
Cth | 1016 | 2 | 4 |
Circle | 1897 | 2 | 3 |
Iris | 150 | 4 | 3 |
Seeds | 210 | 7 | 3 |
Wine | 178 | 13 | 3 |
WDBC | 569 | 30 | 2 |
Libras | 360 | 90 | 15 |
Ecoli | 336 | 8 | 8 |
Dermatology | 366 | 33 | 6 |
Glass | 214 | 11 | 39 |
表1 流形和真实数据集的基本特征
数据集 | 样本规模 | 样本维度 | 类簇个数 |
---|---|---|---|
Db | 630 | 2 | 4 |
Jain | 373 | 2 | 2 |
Spiral | 312 | 2 | 3 |
Pathbased | 300 | 2 | 3 |
Lineblobs | 266 | 2 | 3 |
Sticks | 512 | 2 | 4 |
Cth | 1016 | 2 | 4 |
Circle | 1897 | 2 | 3 |
Iris | 150 | 4 | 3 |
Seeds | 210 | 7 | 3 |
Wine | 178 | 13 | 3 |
WDBC | 569 | 30 | 2 |
Libras | 360 | 90 | 15 |
Ecoli | 336 | 8 | 8 |
Dermatology | 366 | 33 | 6 |
Glass | 214 | 11 | 39 |
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Db | 1 | 0.6675 | 1 | 0.6526 | 0.5107 | 0.4136 | 0.5098 | 0.5185 |
Spiral | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Jain | 1 | 0.5398 | 0.6183 | 1 | 0.7092 | 0.2167 | 0.5961 | 0.6183 |
Pathbased | 0.9027 | 0.537 | 0.5294 | 0.8442 | 0.9305 | 0.7073 | 0.5751 | 0.5212 |
Lineblobs | 1 | 1 | 1 | 0.8375 | 1 | 1 | 0.6386 | 0.7799 |
Sticks | 1 | 1 | 1 | 1 | 1 | 0.7634 | 0.7634 | 0.8094 |
Cth | 1 | 0.6555 | 1 | 0.8482 | 1 | 0.7891 | 0.8758 | 0.682 |
Circle | 1 | 0.7788 | 1 | 0.1927 | 0.7063 | 0.295 | 0.4236 | 0.2747 |
表2 8种算法在流形数据集上的AMI值
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Db | 1 | 0.6675 | 1 | 0.6526 | 0.5107 | 0.4136 | 0.5098 | 0.5185 |
Spiral | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Jain | 1 | 0.5398 | 0.6183 | 1 | 0.7092 | 0.2167 | 0.5961 | 0.6183 |
Pathbased | 0.9027 | 0.537 | 0.5294 | 0.8442 | 0.9305 | 0.7073 | 0.5751 | 0.5212 |
Lineblobs | 1 | 1 | 1 | 0.8375 | 1 | 1 | 0.6386 | 0.7799 |
Sticks | 1 | 1 | 1 | 1 | 1 | 0.7634 | 0.7634 | 0.8094 |
Cth | 1 | 0.6555 | 1 | 0.8482 | 1 | 0.7891 | 0.8758 | 0.682 |
Circle | 1 | 0.7788 | 1 | 0.1927 | 0.7063 | 0.295 | 0.4236 | 0.2747 |
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Db | 1 | 0.5368 | 1 | 0.5033 | 0.2718 | 0.1096 | 0.2714 | 0.2794 |
Spiral | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Jain | 1 | 0.6728 | 0.7146 | 1 | 0.8224 | 0.0442 | 0.7257 | 0.7146 |
Pathbased | 0.9292 | 0.5329 | 0.4797 | 0.8593 | 0.9499 | 0.6133 | 0.5067 | 0.4717 |
Lineblobs | 1 | 1 | 1 | 0.8237 | 1 | 1 | 0.5769 | 0.721 |
Sticks | 1 | 1 | 1 | 1 | 1 | 0.636 | 0.639 | 0.7534 |
Cth | 1 | 0.671 | 1 | 0.7729 | 1 | 0.6538 | 0.8327 | 0.5017 |
Circle | 1 | 0.8497 | 1 | 0.1319 | 0.6139 | 0.0833 | 0.2732 | 0.0554 |
表3 8种算法在流形数据集上的ARI值
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Db | 1 | 0.5368 | 1 | 0.5033 | 0.2718 | 0.1096 | 0.2714 | 0.2794 |
Spiral | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Jain | 1 | 0.6728 | 0.7146 | 1 | 0.8224 | 0.0442 | 0.7257 | 0.7146 |
Pathbased | 0.9292 | 0.5329 | 0.4797 | 0.8593 | 0.9499 | 0.6133 | 0.5067 | 0.4717 |
Lineblobs | 1 | 1 | 1 | 0.8237 | 1 | 1 | 0.5769 | 0.721 |
Sticks | 1 | 1 | 1 | 1 | 1 | 0.636 | 0.639 | 0.7534 |
Cth | 1 | 0.671 | 1 | 0.7729 | 1 | 0.6538 | 0.8327 | 0.5017 |
Circle | 1 | 0.8497 | 1 | 0.1319 | 0.6139 | 0.0833 | 0.2732 | 0.0554 |
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Db | 1 | 0.725 | 1 | 0.6999 | 0.5793 | 0.4689 | 0.5803 | 0.5853 |
Spiral | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Jain | 1 | 0.8896 | 0.8819 | 1 | 0.9359 | 0.5924 | 0.9051 | 0.8819 |
Pathbased | 0.9529 | 0.7538 | 0.6703 | 0.9067 | 0.9665 | 0.7511 | 0.7065 | 0.6664 |
Lineblobs | 1 | 1 | 1 | 0.8842 | 1 | 1 | 0.7218 | 0.8166 |
Sticks | 1 | 1 | 1 | 1 | 1 | 0.7443 | 0.7467 | 0.8235 |
Cth | 1 | 0.7868 | 1 | 0.835 | 1 | 0.7547 | 0.8786 | 0.6397 |
Circle | 1 | 0.9152 | 1 | 0.4857 | 0.779 | 0.5242 | 0.5863 | 0.5005 |
表4 8种算法在流形数据集上的FMI值
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Db | 1 | 0.725 | 1 | 0.6999 | 0.5793 | 0.4689 | 0.5803 | 0.5853 |
Spiral | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Jain | 1 | 0.8896 | 0.8819 | 1 | 0.9359 | 0.5924 | 0.9051 | 0.8819 |
Pathbased | 0.9529 | 0.7538 | 0.6703 | 0.9067 | 0.9665 | 0.7511 | 0.7065 | 0.6664 |
Lineblobs | 1 | 1 | 1 | 0.8842 | 1 | 1 | 0.7218 | 0.8166 |
Sticks | 1 | 1 | 1 | 1 | 1 | 0.7443 | 0.7467 | 0.8235 |
Cth | 1 | 0.7868 | 1 | 0.835 | 1 | 0.7547 | 0.8786 | 0.6397 |
Circle | 1 | 0.9152 | 1 | 0.4857 | 0.779 | 0.5242 | 0.5863 | 0.5005 |
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Db | 6 | - | 6/2.0 | - | 19 | - | 0.09 | 4 |
Spiral | 11 | - | 10/2.0 | - | 6 | - | 0.07 | 1.8 |
Jain | 27 | - | 10/0.5 | - | 43 | - | 0.47 | 0.8 |
Pathbased | 7 | - | 6/6.0 | - | 9 | - | 0.01 | 3.8 |
Lineblobs | 7 | - | 10/6.0 | - | 12 | - | 0.21 | 3.7 |
Sticks | 15 | - | 10/2.0 | - | 6 | - | 0.16 | 2.1 |
Cth | 10 | - | 10/2.0 | - | 22 | - | 0.45 | 1.1 |
Circle | 13 | - | 10/2.0 | - | 32 | - | 0.29 | 3.3 |
表5 8种算法在流形数据集上获得最优聚类结果的参数取值
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Db | 6 | - | 6/2.0 | - | 19 | - | 0.09 | 4 |
Spiral | 11 | - | 10/2.0 | - | 6 | - | 0.07 | 1.8 |
Jain | 27 | - | 10/0.5 | - | 43 | - | 0.47 | 0.8 |
Pathbased | 7 | - | 6/6.0 | - | 9 | - | 0.01 | 3.8 |
Lineblobs | 7 | - | 10/6.0 | - | 12 | - | 0.21 | 3.7 |
Sticks | 15 | - | 10/2.0 | - | 6 | - | 0.16 | 2.1 |
Cth | 10 | - | 10/2.0 | - | 22 | - | 0.45 | 1.1 |
Circle | 13 | - | 10/2.0 | - | 32 | - | 0.29 | 3.3 |
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Iris | 0.8828 | 0.8831 | 0.7277 | 0.8623 | 0.8831 | 0.8831 | 0.8831 | 0.7247 |
Seeds | 0.7441 | 0.5452 | 0.7172 | 0.7299 | 0.7118 | 0.6609 | 0.7136 | 0.7298 |
Wine | 0.8210 | 0.6455 | 0.7575 | 0.7675 | 0.8481 | 0.748 | 0.7898 | 0.7065 |
WDBC | 0.6575 | 0.1345 | 0.6518 | 0.6237 | 0.6423 | 0.3361 | 0.6076 | 0.4366 |
Libras | 0.6171 | 0.4367 | 0.5609 | 0.5733 | 0.5554 | 0.5388 | 0.5494 | 0.5358 |
Ecoli | 0.5236 | 0.5603 | 0.5103 | 0.6638 | 0.5878 | 0.4406 | 0.4833 | 0.4978 |
Dermatology | 0.9401 | 0.7468 | 0.8029 | 0.8638 | 0.8066 | 0.7451 | 0.7898 | 0.7615 |
Glass | 0.5345 | 0.2666 | 0.4337 | 0.4511 | 0.4308 | 0.2404 | 0.4701 | 0.5260 |
表6 8种算法在真实数据集上的AMI值
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Iris | 0.8828 | 0.8831 | 0.7277 | 0.8623 | 0.8831 | 0.8831 | 0.8831 | 0.7247 |
Seeds | 0.7441 | 0.5452 | 0.7172 | 0.7299 | 0.7118 | 0.6609 | 0.7136 | 0.7298 |
Wine | 0.8210 | 0.6455 | 0.7575 | 0.7675 | 0.8481 | 0.748 | 0.7898 | 0.7065 |
WDBC | 0.6575 | 0.1345 | 0.6518 | 0.6237 | 0.6423 | 0.3361 | 0.6076 | 0.4366 |
Libras | 0.6171 | 0.4367 | 0.5609 | 0.5733 | 0.5554 | 0.5388 | 0.5494 | 0.5358 |
Ecoli | 0.5236 | 0.5603 | 0.5103 | 0.6638 | 0.5878 | 0.4406 | 0.4833 | 0.4978 |
Dermatology | 0.9401 | 0.7468 | 0.8029 | 0.8638 | 0.8066 | 0.7451 | 0.7898 | 0.7615 |
Glass | 0.5345 | 0.2666 | 0.4337 | 0.4511 | 0.4308 | 0.2404 | 0.4701 | 0.5260 |
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Iris | 0.886 | 0.9038 | 0.6634 | 0.8857 | 0.9038 | 0.9038 | 0.9038 | 0.7037 |
Seeds | 0.788 | 0.555 | 0.7341 | 0.767 | 0.7303 | 0.6873 | 0.7545 | 0.767 |
Wine | 0.8516 | 0.6332 | 0.7562 | 0.7713 | 0.8839 | 0.7414 | 0.8025 | 0.6724 |
WDBC | 0.7736 | 0.1634 | 0.7607 | 0.7423 | 0.7613 | 0.3771 | 0.7305 | 0.4964 |
Libras | 0.4187 | 0.2428 | 0.4174 | 0.3816 | 0.3459 | 0.3095 | 0.329 | 0.3193 |
Ecoli | 0.5929 | 0.5551 | 0.4551 | 0.7561 | 0.5894 | 0.4593 | 0.5618 | 0.4465 |
Dermatology | 0.9437 | 0.7376 | 0.784 | 0.8772 | 0.8361 | 0.6062 | 0.7995 | 0.6923 |
Glass | 0.4705 | 0.2316 | 0.3573 | 0.4049 | 0.437 | 0.1982 | 0.4711 | 0.3562 |
表7 8种算法在真实数据集上的ARI值
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Iris | 0.886 | 0.9038 | 0.6634 | 0.8857 | 0.9038 | 0.9038 | 0.9038 | 0.7037 |
Seeds | 0.788 | 0.555 | 0.7341 | 0.767 | 0.7303 | 0.6873 | 0.7545 | 0.767 |
Wine | 0.8516 | 0.6332 | 0.7562 | 0.7713 | 0.8839 | 0.7414 | 0.8025 | 0.6724 |
WDBC | 0.7736 | 0.1634 | 0.7607 | 0.7423 | 0.7613 | 0.3771 | 0.7305 | 0.4964 |
Libras | 0.4187 | 0.2428 | 0.4174 | 0.3816 | 0.3459 | 0.3095 | 0.329 | 0.3193 |
Ecoli | 0.5929 | 0.5551 | 0.4551 | 0.7561 | 0.5894 | 0.4593 | 0.5618 | 0.4465 |
Dermatology | 0.9437 | 0.7376 | 0.784 | 0.8772 | 0.8361 | 0.6062 | 0.7995 | 0.6923 |
Glass | 0.4705 | 0.2316 | 0.3573 | 0.4049 | 0.437 | 0.1982 | 0.4711 | 0.3562 |
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Iris | 0.9237 | 0.9355 | 0.7824 | 0.9233 | 0.9355 | 0.9355 | 0.9355 | 0.8032 |
Seeds | 0.8581 | 0.7101 | 0.8231 | 0.8444 | 0.8029 | 0.7918 | 0.8361 | 0.8444 |
Wine | 0.9013 | 0.7672 | 0.838 | 0.8478 | 0.9229 | 0.8283 | 0.8686 | 0.7835 |
WDBC | 0.8956 | 0.7164 | 0.8914 | 0.8829 | 0.8894 | 0.7595 | 0.8758 | 0.7941 |
Libras | 0.4654 | 0.3397 | 0.4581 | 0.4247 | 0.4044 | 0.3791 | 0.3869 | 0.3717 |
Ecoli | 0.7198 | 0.6724 | 0.5843 | 0.8284 | 0.7027 | 0.6467 | 0.7178 | 0.5775 |
Dermatology | 0.955 | 0.8077 | 0.8311 | 0.9018 | 0.8709 | 0.6896 | 0.8418 | 0.7545 |
Glass | 0.6055 | 0.5554 | 0.5403 | 0.5552 | 0.5924 | 0.5448 | 0.5973 | 0.5267 |
表8 8种算法在真实数据集上的FMI值
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Iris | 0.9237 | 0.9355 | 0.7824 | 0.9233 | 0.9355 | 0.9355 | 0.9355 | 0.8032 |
Seeds | 0.8581 | 0.7101 | 0.8231 | 0.8444 | 0.8029 | 0.7918 | 0.8361 | 0.8444 |
Wine | 0.9013 | 0.7672 | 0.838 | 0.8478 | 0.9229 | 0.8283 | 0.8686 | 0.7835 |
WDBC | 0.8956 | 0.7164 | 0.8914 | 0.8829 | 0.8894 | 0.7595 | 0.8758 | 0.7941 |
Libras | 0.4654 | 0.3397 | 0.4581 | 0.4247 | 0.4044 | 0.3791 | 0.3869 | 0.3717 |
Ecoli | 0.7198 | 0.6724 | 0.5843 | 0.8284 | 0.7027 | 0.6467 | 0.7178 | 0.5775 |
Dermatology | 0.955 | 0.8077 | 0.8311 | 0.9018 | 0.8709 | 0.6896 | 0.8418 | 0.7545 |
Glass | 0.6055 | 0.5554 | 0.5403 | 0.5552 | 0.5924 | 0.5448 | 0.5973 | 0.5267 |
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Iris | 21 | - | 8/2.0 | - | 22 | - | 0.11 | 0.2 |
Seeds | 5 | - | 10/2.0 | - | 4 | - | 0.07 | 0.7 |
Wine | 24 | - | 10/6.0 | - | 8 | - | 0.26 | 4 |
WDBC | 11 | - | 6/6.0 | - | 2 | - | 0.05 | 0.5 |
Libras | 8 | - | 10/2.0 | - | 10 | - | 0.17 | 0.3 |
Ecoli | 30 | - | 10/0.5 | - | 2 | - | 0.35 | 0.4 |
Dermatology | 7 | - | 6/6.0 | - | 35 | - | 0.17 | 1.6 |
Glass | 20 | - | 6/0.2 | - | 14 | - | 0.16 | 4 |
表9 8种算法在真实数据集上获得最优聚类结果的参数取值
数据集 | DPC-GDCN | RDPC-DSS | DPC-GD | IDPC-FA | FKNN-DPC | DPCSA | FNDPC | DPC |
---|---|---|---|---|---|---|---|---|
Iris | 21 | - | 8/2.0 | - | 22 | - | 0.11 | 0.2 |
Seeds | 5 | - | 10/2.0 | - | 4 | - | 0.07 | 0.7 |
Wine | 24 | - | 10/6.0 | - | 8 | - | 0.26 | 4 |
WDBC | 11 | - | 6/6.0 | - | 2 | - | 0.05 | 0.5 |
Libras | 8 | - | 10/2.0 | - | 10 | - | 0.17 | 0.3 |
Ecoli | 30 | - | 10/0.5 | - | 2 | - | 0.35 | 0.4 |
Dermatology | 7 | - | 6/6.0 | - | 35 | - | 0.17 | 1.6 |
Glass | 20 | - | 6/0.2 | - | 14 | - | 0.16 | 4 |
算法 | AMI | ARI | FMI | 参数值 |
---|---|---|---|---|
DPC-GDCN | 0.8308 | 0.7035 | 0.7159 | 4 |
RDPC-DSS | 0.6612 | 0.4354 | 0.4845 | - |
DPC-GD | 0.8260 | 0.7029 | 0.7132 | 6/1.0 |
IDPC-FA | 0.8093 | 0.6924 | 0.7029 | - |
FKNN-DPC | 0.7989 | 0.6784 | 0.6885 | 5 |
DPCSA | 0.8254 | 0.7025 | 0.7127 | - |
FNDPC | 0.7965 | 0.6652 | 0.6778 | 0.44 |
DPC | 0.7891 | 0.6549 | 0.6701 | 3.0 |
表10 8种算法在Olivetti Faces数据集的聚类结果
算法 | AMI | ARI | FMI | 参数值 |
---|---|---|---|---|
DPC-GDCN | 0.8308 | 0.7035 | 0.7159 | 4 |
RDPC-DSS | 0.6612 | 0.4354 | 0.4845 | - |
DPC-GD | 0.8260 | 0.7029 | 0.7132 | 6/1.0 |
IDPC-FA | 0.8093 | 0.6924 | 0.7029 | - |
FKNN-DPC | 0.7989 | 0.6784 | 0.6885 | 5 |
DPCSA | 0.8254 | 0.7025 | 0.7127 | - |
FNDPC | 0.7965 | 0.6652 | 0.6778 | 0.44 |
DPC | 0.7891 | 0.6549 | 0.6701 | 3.0 |
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