Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (5): 1323-1329.DOI: 10.11772/j.issn.1001-9081.2022030419
Special Issue: 第九届中国数据挖掘会议(CCDM 2022)
• China Conference on Data Mining 2022 (CCDM 2022) • Next Articles
Haitao TANG1,2, Hongjun WANG1,2(), Tianrui LI1,2
Received:
2022-04-01
Revised:
2022-05-16
Accepted:
2022-05-19
Online:
2023-05-08
Published:
2023-05-10
Contact:
Hongjun WANG
About author:
TANG Haitao, born in 1999, M. S. candidate. His research interests include feature learning, clustering.Supported by:
通讯作者:
王红军
作者简介:
唐海涛(1999—),男,四川南充人,硕士研究生,CCF会员,主要研究方向:特征学习、聚类基金资助:
CLC Number:
Haitao TANG, Hongjun WANG, Tianrui LI. Discriminative multidimensional scaling for feature learning[J]. Journal of Computer Applications, 2023, 43(5): 1323-1329.
唐海涛, 王红军, 李天瑞. 判别多维标度特征学习[J]. 《计算机应用》唯一官方网站, 2023, 43(5): 1323-1329.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2022030419
符号 | 含义 | 符号 | 含义 |
---|---|---|---|
数据点个数 | 原始数据矩阵 | ||
原始数据表示的维数 | 投影后的数据矩阵 | ||
学习到的低维数据表示维数 | 投影矩阵 | ||
簇个数 | 非负对称的权重矩阵 | ||
模糊指数权重 | 隶属度矩阵 | ||
E1项损失的权重 | 簇中心矩阵 | ||
E2项损失的权重 | D =[ | 原始数据的距离矩阵 | |
低维数据表示的距离矩阵 |
Tab. 1 Symbol notations
符号 | 含义 | 符号 | 含义 |
---|---|---|---|
数据点个数 | 原始数据矩阵 | ||
原始数据表示的维数 | 投影后的数据矩阵 | ||
学习到的低维数据表示维数 | 投影矩阵 | ||
簇个数 | 非负对称的权重矩阵 | ||
模糊指数权重 | 隶属度矩阵 | ||
E1项损失的权重 | 簇中心矩阵 | ||
E2项损失的权重 | D =[ | 原始数据的距离矩阵 | |
低维数据表示的距离矩阵 |
数据集 | 索引 | 样本数 | 特征数 | 类簇数 | 数据集 | 索引 | 样本数 | 特征数 | 类簇数 |
---|---|---|---|---|---|---|---|---|---|
voituretuning | 01 | 879 | 899 | 3 | bubble | 07 | 879 | 892 | 3 |
border | 02 | 840 | 892 | 3 | banana | 08 | 840 | 892 | 3 |
bicycle | 03 | 844 | 892 | 3 | bus | 09 | 910 | 892 | 3 |
building | 04 | 911 | 892 | 3 | vistawallpaper | 10 | 799 | 899 | 3 |
banner | 05 | 860 | 892 | 3 | CNAE-9 | 11 | 1 080 | 856 | 9 |
wallpaper2 | 06 | 919 | 899 | 3 | QSAR_AR | 12 | 1 687 | 1 024 | 2 |
Tab. 2 Experimental datasets
数据集 | 索引 | 样本数 | 特征数 | 类簇数 | 数据集 | 索引 | 样本数 | 特征数 | 类簇数 |
---|---|---|---|---|---|---|---|---|---|
voituretuning | 01 | 879 | 899 | 3 | bubble | 07 | 879 | 892 | 3 |
border | 02 | 840 | 892 | 3 | banana | 08 | 840 | 892 | 3 |
bicycle | 03 | 844 | 892 | 3 | bus | 09 | 910 | 892 | 3 |
building | 04 | 911 | 892 | 3 | vistawallpaper | 10 | 799 | 899 | 3 |
banner | 05 | 860 | 892 | 3 | CNAE-9 | 11 | 1 080 | 856 | 9 |
wallpaper2 | 06 | 919 | 899 | 3 | QSAR_AR | 12 | 1 687 | 1 024 | 2 |
索引 | KM | AP | DP | PMDS-KM | PMDS-AP | PMDS-DP | DMDS-KM | DMDS-AP | DMDS-DP | Avg | PMDS-Avg | DMDS-Avg |
---|---|---|---|---|---|---|---|---|---|---|---|---|
01 | 0.450 5 | 0.538 1 | 0.466 4 | 0.442 3 | 0.526 8 | 0.453 0 | 0.484 6 | 0.568 1 | 0.564 9 | 0.485 0 | 0.474 0 | 0.539 2 |
02 | 0.504 7 | 0.444 0 | 0.442 8 | 0.509 2 | 0.437 5 | 0.413 4 | 0.542 1 | 0.559 6 | 0.560 7 | 0.463 8 | 0.453 4 | 0.554 1 |
03 | 0.432 4 | 0.542 6 | 0.409 9 | 0.472 6 | 0.538 8 | 0.412 7 | 0.520 8 | 0.514 9 | 0.522 9 | 0.461 6 | 0.474 7 | 0.519 5 |
04 | 0.517 0 | 0.619 1 | 0.462 1 | 0.407 7 | 0.478 7 | 0.446 8 | 0.565 3 | 0.632 6 | 0.534 1 | 0.532 7 | 0.444 4 | 0.577 3 |
05 | 0.466 2 | 0.460 4 | 0.818 6 | 0.452 5 | 0.571 1 | 0.778 4 | 0.565 0 | 0.776 7 | 0.795 3 | 0.581 7 | 0.600 7 | 0.712 3 |
06 | 0.420 0 | 0.463 5 | 0.457 0 | 0.417 9 | 0.478 2 | 0.458 9 | 0.442 8 | 0.492 9 | 0.509 9 | 0.446 8 | 0.451 7 | 0.481 9 |
07 | 0.420 9 | 0.456 2 | 0.464 1 | 0.426 3 | 0.480 3 | 0.464 9 | 0.432 3 | 0.490 3 | 0.439 1 | 0.447 0 | 0.457 2 | 0.453 9 |
08 | 0.476 1 | 0.403 5 | 0.421 4 | 0.474 7 | 0.427 2 | 0.413 0 | 0.484 5 | 0.438 0 | 0.434 5 | 0.433 7 | 0.438 3 | 0.452 3 |
09 | 0.452 7 | 0.654 9 | 0.445 0 | 0.447 6 | 0.459 8 | 0.444 3 | 0.437 3 | 0.671 4 | 0.600 0 | 0.517 5 | 0.450 6 | 0.569 5 |
10 | 0.470 5 | 0.390 4 | 0.488 1 | 0.475 8 | 0.464 2 | 0.461 8 | 0.490 6 | 0.438 2 | 0.534 4 | 0.449 7 | 0.467 2 | 0.487 7 |
11 | 0.463 9 | 0.118 5 | 0.337 0 | 0.450 9 | 0.119 4 | 0.300 0 | 0.529 6 | 0.188 0 | 0.335 2 | 0.306 5 | 0.290 1 | 0.350 9 |
12 | 0.665 7 | 0.572 6 | 0.725 0 | 0.660 3 | 0.619 4 | 0.718 4 | 0.684 6 | 0.823 4 | 0.637 2 | 0.654 4 | 0.666 0 | 0.715 1 |
Tab. 3 Average clustering accuracy under different data representations
索引 | KM | AP | DP | PMDS-KM | PMDS-AP | PMDS-DP | DMDS-KM | DMDS-AP | DMDS-DP | Avg | PMDS-Avg | DMDS-Avg |
---|---|---|---|---|---|---|---|---|---|---|---|---|
01 | 0.450 5 | 0.538 1 | 0.466 4 | 0.442 3 | 0.526 8 | 0.453 0 | 0.484 6 | 0.568 1 | 0.564 9 | 0.485 0 | 0.474 0 | 0.539 2 |
02 | 0.504 7 | 0.444 0 | 0.442 8 | 0.509 2 | 0.437 5 | 0.413 4 | 0.542 1 | 0.559 6 | 0.560 7 | 0.463 8 | 0.453 4 | 0.554 1 |
03 | 0.432 4 | 0.542 6 | 0.409 9 | 0.472 6 | 0.538 8 | 0.412 7 | 0.520 8 | 0.514 9 | 0.522 9 | 0.461 6 | 0.474 7 | 0.519 5 |
04 | 0.517 0 | 0.619 1 | 0.462 1 | 0.407 7 | 0.478 7 | 0.446 8 | 0.565 3 | 0.632 6 | 0.534 1 | 0.532 7 | 0.444 4 | 0.577 3 |
05 | 0.466 2 | 0.460 4 | 0.818 6 | 0.452 5 | 0.571 1 | 0.778 4 | 0.565 0 | 0.776 7 | 0.795 3 | 0.581 7 | 0.600 7 | 0.712 3 |
06 | 0.420 0 | 0.463 5 | 0.457 0 | 0.417 9 | 0.478 2 | 0.458 9 | 0.442 8 | 0.492 9 | 0.509 9 | 0.446 8 | 0.451 7 | 0.481 9 |
07 | 0.420 9 | 0.456 2 | 0.464 1 | 0.426 3 | 0.480 3 | 0.464 9 | 0.432 3 | 0.490 3 | 0.439 1 | 0.447 0 | 0.457 2 | 0.453 9 |
08 | 0.476 1 | 0.403 5 | 0.421 4 | 0.474 7 | 0.427 2 | 0.413 0 | 0.484 5 | 0.438 0 | 0.434 5 | 0.433 7 | 0.438 3 | 0.452 3 |
09 | 0.452 7 | 0.654 9 | 0.445 0 | 0.447 6 | 0.459 8 | 0.444 3 | 0.437 3 | 0.671 4 | 0.600 0 | 0.517 5 | 0.450 6 | 0.569 5 |
10 | 0.470 5 | 0.390 4 | 0.488 1 | 0.475 8 | 0.464 2 | 0.461 8 | 0.490 6 | 0.438 2 | 0.534 4 | 0.449 7 | 0.467 2 | 0.487 7 |
11 | 0.463 9 | 0.118 5 | 0.337 0 | 0.450 9 | 0.119 4 | 0.300 0 | 0.529 6 | 0.188 0 | 0.335 2 | 0.306 5 | 0.290 1 | 0.350 9 |
12 | 0.665 7 | 0.572 6 | 0.725 0 | 0.660 3 | 0.619 4 | 0.718 4 | 0.684 6 | 0.823 4 | 0.637 2 | 0.654 4 | 0.666 0 | 0.715 1 |
索引 | KM | AP | DP | PMDS-KM | PMDS-AP | PMDS-DP | DMDS-KM | DMDS-AP | DMDS-DP | Avg | PMDS-Avg | DMDS-Avg |
---|---|---|---|---|---|---|---|---|---|---|---|---|
01 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 |
02 | 0.564 2 | 0.445 2 | 0.447 6 | 0.564 8 | 0.445 1 | 0.446 0 | 0.560 9 | 0.565 9 | 0.561 9 | 0.485 7 | 0.485 3 | 0.562 9 |
03 | 0.545 0 | 0.547 3 | 0.545 0 | 0.545 1 | 0.548 4 | 0.545 0 | 0.560 0 | 0.545 0 | 0.546 2 | 0.545 8 | 0.546 2 | 0.550 4 |
04 | 0.714 5 | 0.715 6 | 0.714 5 | 0.714 5 | 0.714 7 | 0.714 5 | 0.714 5 | 0.714 5 | 0.714 5 | 0.714 9 | 0.714 6 | 0.714 5 |
05 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 |
06 | 0.570 1 | 0.577 8 | 0.562 5 | 0.562 5 | 0.563 0 | 0.565 0 | 0.575 6 | 0.573 4 | 0.562 5 | 0.570 1 | 0.563 5 | 0.570 5 |
07 | 0.500 5 | 0.497 1 | 0.496 0 | 0.509 7 | 0.514 2 | 0.496 0 | 0.558 5 | 0.500 1 | 0.496 0 | 0.497 9 | 0.506 6 | 0.518 2 |
08 | 0.484 5 | 0.432 1 | 0.427 3 | 0.483 8 | 0.439 5 | 0.428 9 | 0.492 8 | 0.440 4 | 0.470 2 | 0.448 0 | 0.450 7 | 0.467 8 |
09 | 0.625 2 | 0.654 9 | 0.624 1 | 0.624 8 | 0.624 1 | 0.624 3 | 0.652 7 | 0.674 7 | 0.624 1 | 0.634 7 | 0.624 4 | 0.650 5 |
10 | 0.644 5 | 0.632 0 | 0.632 0 | 0.649 1 | 0.632 5 | 0.633 1 | 0.664 5 | 0.632 0 | 0.634 5 | 0.636 2 | 0.638 2 | 0.643 7 |
11 | 0.490 7 | 0.119 4 | 0.344 4 | 0.489 8 | 0.119 4 | 0.310 2 | 0.555 6 | 0.191 7 | 0.344 4 | 0.318 2 | 0.306 5 | 0.363 9 |
12 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 |
Tab. 4 Average clustering purity under different data representations
索引 | KM | AP | DP | PMDS-KM | PMDS-AP | PMDS-DP | DMDS-KM | DMDS-AP | DMDS-DP | Avg | PMDS-Avg | DMDS-Avg |
---|---|---|---|---|---|---|---|---|---|---|---|---|
01 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 | 0.639 3 |
02 | 0.564 2 | 0.445 2 | 0.447 6 | 0.564 8 | 0.445 1 | 0.446 0 | 0.560 9 | 0.565 9 | 0.561 9 | 0.485 7 | 0.485 3 | 0.562 9 |
03 | 0.545 0 | 0.547 3 | 0.545 0 | 0.545 1 | 0.548 4 | 0.545 0 | 0.560 0 | 0.545 0 | 0.546 2 | 0.545 8 | 0.546 2 | 0.550 4 |
04 | 0.714 5 | 0.715 6 | 0.714 5 | 0.714 5 | 0.714 7 | 0.714 5 | 0.714 5 | 0.714 5 | 0.714 5 | 0.714 9 | 0.714 6 | 0.714 5 |
05 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 | 0.937 2 |
06 | 0.570 1 | 0.577 8 | 0.562 5 | 0.562 5 | 0.563 0 | 0.565 0 | 0.575 6 | 0.573 4 | 0.562 5 | 0.570 1 | 0.563 5 | 0.570 5 |
07 | 0.500 5 | 0.497 1 | 0.496 0 | 0.509 7 | 0.514 2 | 0.496 0 | 0.558 5 | 0.500 1 | 0.496 0 | 0.497 9 | 0.506 6 | 0.518 2 |
08 | 0.484 5 | 0.432 1 | 0.427 3 | 0.483 8 | 0.439 5 | 0.428 9 | 0.492 8 | 0.440 4 | 0.470 2 | 0.448 0 | 0.450 7 | 0.467 8 |
09 | 0.625 2 | 0.654 9 | 0.624 1 | 0.624 8 | 0.624 1 | 0.624 3 | 0.652 7 | 0.674 7 | 0.624 1 | 0.634 7 | 0.624 4 | 0.650 5 |
10 | 0.644 5 | 0.632 0 | 0.632 0 | 0.649 1 | 0.632 5 | 0.633 1 | 0.664 5 | 0.632 0 | 0.634 5 | 0.636 2 | 0.638 2 | 0.643 7 |
11 | 0.490 7 | 0.119 4 | 0.344 4 | 0.489 8 | 0.119 4 | 0.310 2 | 0.555 6 | 0.191 7 | 0.344 4 | 0.318 2 | 0.306 5 | 0.363 9 |
12 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 | 0.882 0 |
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