Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (1): 115-122.DOI: 10.11772/j.issn.1001-9081.2021071181
• Data science and technology • Previous Articles Next Articles
Lili FAN, Guifu LU(), Ganyi TANG, Dan YANG
Received:
2021-07-08
Revised:
2021-09-03
Accepted:
2021-09-06
Online:
2021-09-16
Published:
2022-01-10
Contact:
Guifu LU
About author:
FAN Lili, born in 1982, M. S., lecturer. Her research interests include machine learning, pattern recognition.Supported by:
通讯作者:
卢桂馥
作者简介:
范莉莉(1982—),女,山东莱芜人,讲师,硕士,CCF会员,主要研究方向:机器学习、模式识别基金资助:
CLC Number:
Lili FAN, Guifu LU, Ganyi TANG, Dan YANG. Low-rank representation subspace clustering method based on Hessian regularization and non-negative constraint[J]. Journal of Computer Applications, 2022, 42(1): 115-122.
范莉莉, 卢桂馥, 唐肝翌, 杨丹. 基于Hessian正则化和非负约束的低秩表示子空间聚类算法[J]. 《计算机应用》唯一官方网站, 2022, 42(1): 115-122.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2021071181
聚类数目 | 算法 | AC | NMI |
---|---|---|---|
5 | K-means | 48.73 | 36.17 |
NMF | 49.82 | 40.60 | |
PCA | 29.10 | 11.64 | |
Ncut | 61.45 | 53.36 | |
LRR ALRR | 67.27 67.45 | 56.00 59.03 | |
LRR-HN | 80.00 | 62.53 | |
8 | K-means | 48.86 | 44.69 |
NMF | 48.64 | 43.25 | |
PCA | 20.91 | 13.91 | |
Ncut | 56.14 | 57.77 | |
LRR ALRR | 65.91 62.50 | 58.16 57.61 | |
LRR-HN | 69.32 | 60.15 | |
12 | K-means | 43.18 | 46.19 |
NMF | 43.18 | 45.04 | |
PCA | 20.45 | 19.48 | |
Ncut | 50.91 | 56.39 | |
LRR ALRR | 56.44 59.85 | 55.36 62.10 | |
LRR-HN | 60. 61 | 59.60 | |
15 | K-means | 40.74 | 46.92 |
NMF | 38.73 | 45.82 | |
PCA | 23.39 | 24.32 | |
Ncut | 45.52 | 54.55 | |
LRR ALRR | 52.67 52.12 | 53.69 57.56 | |
LRR-HN | 55.58 | 56.35 |
Tab.1 Clustering results of different algorithms on Yale dataset
聚类数目 | 算法 | AC | NMI |
---|---|---|---|
5 | K-means | 48.73 | 36.17 |
NMF | 49.82 | 40.60 | |
PCA | 29.10 | 11.64 | |
Ncut | 61.45 | 53.36 | |
LRR ALRR | 67.27 67.45 | 56.00 59.03 | |
LRR-HN | 80.00 | 62.53 | |
8 | K-means | 48.86 | 44.69 |
NMF | 48.64 | 43.25 | |
PCA | 20.91 | 13.91 | |
Ncut | 56.14 | 57.77 | |
LRR ALRR | 65.91 62.50 | 58.16 57.61 | |
LRR-HN | 69.32 | 60.15 | |
12 | K-means | 43.18 | 46.19 |
NMF | 43.18 | 45.04 | |
PCA | 20.45 | 19.48 | |
Ncut | 50.91 | 56.39 | |
LRR ALRR | 56.44 59.85 | 55.36 62.10 | |
LRR-HN | 60. 61 | 59.60 | |
15 | K-means | 40.74 | 46.92 |
NMF | 38.73 | 45.82 | |
PCA | 23.39 | 24.32 | |
Ncut | 45.52 | 54.55 | |
LRR ALRR | 52.67 52.12 | 53.69 57.56 | |
LRR-HN | 55.58 | 56.35 |
聚类数目 | 算法 | AC | NMI |
---|---|---|---|
10 | K-means | 56.30 | 63.24 |
NMF | 56.60 | 63.11 | |
PCA | 24.60 | 22.55 | |
Ncut | 58.60 | 63.90 | |
LRR ALRR | 63.60 68.00 | 70.06 77.47 | |
LRR-HN | 68.73 | 78.31 | |
20 | K-means | 52.05 | 67.18 |
NMF | 52.85 | 68.45 | |
PCA | 27.70 | 38.54 | |
Ncut | 56.40 | 70.53 | |
LRR ALRR | 63.50 69.50 | 76.23 84.92 | |
LRR-HN | 74.50 | 85.97 | |
30 | K-means | 52.97 | 71.74 |
NMF | 53.10 | 71.87 | |
PCA | 40.77 | 59.18 | |
Ncut | 53.57 | 72.41 | |
LRR ALRR | 65.90 66.67 | 78.77 81.42 | |
LRR-HN | 67.80 | 82.76 | |
40 | K-means | 51.53 | 72.76 |
NMF | 50.08 | 72.58 | |
PCA | 44.85 | 65.30 | |
Ncut | 53.58 | 75.00 | |
LRR ALRR | 66.30 67.75 | 81.07 82.16 | |
LRR-HN | 68.30 | 81.66 |
Tab.2 Clustering results of different algorithms on ORL dataset
聚类数目 | 算法 | AC | NMI |
---|---|---|---|
10 | K-means | 56.30 | 63.24 |
NMF | 56.60 | 63.11 | |
PCA | 24.60 | 22.55 | |
Ncut | 58.60 | 63.90 | |
LRR ALRR | 63.60 68.00 | 70.06 77.47 | |
LRR-HN | 68.73 | 78.31 | |
20 | K-means | 52.05 | 67.18 |
NMF | 52.85 | 68.45 | |
PCA | 27.70 | 38.54 | |
Ncut | 56.40 | 70.53 | |
LRR ALRR | 63.50 69.50 | 76.23 84.92 | |
LRR-HN | 74.50 | 85.97 | |
30 | K-means | 52.97 | 71.74 |
NMF | 53.10 | 71.87 | |
PCA | 40.77 | 59.18 | |
Ncut | 53.57 | 72.41 | |
LRR ALRR | 65.90 66.67 | 78.77 81.42 | |
LRR-HN | 67.80 | 82.76 | |
40 | K-means | 51.53 | 72.76 |
NMF | 50.08 | 72.58 | |
PCA | 44.85 | 65.30 | |
Ncut | 53.58 | 75.00 | |
LRR ALRR | 66.30 67.75 | 81.07 82.16 | |
LRR-HN | 68.30 | 81.66 |
1 | ZHANG X, SUN F C, LIU G C, et al. Fast low-rank subspace segmentation[J]. IEEE Transactions on Knowledge and Data Engineering, 2014, 26(5): 1293-1297. 10.1109/tkde.2013.114 |
2 | PATEL V M, NGUYEN H VAN, VIDAL R. Latent space sparse and low-rank subspace clustering[J]. IEEE Journal of Selected Topics in Signal Processing, 2015, 9(4): 691-701. 10.1109/jstsp.2015.2402643 |
3 | BRBIĆ M, KOPRIVA I. Multi-view low-rank sparse subspace clustering[J]. Pattern Recognition, 2018, 73: 247-258. 10.1016/j.patcog.2017.08.024 |
4 | CHEN J, MAO H, WANG Z, et al. Low-rank representation with adaptive dictionary learning for subspace clustering[J]. Knowledge-Based Systems, 2021, 223: No.107053. 10.1016/j.knosys.2021.107053 |
5 | VIDAL R. Subspace clustering[J]. IEEE Signal Processing, 2011, 28(2): 52-68. 10.1109/msp.2010.939739 |
6 | LUXBURG U VON. A tutorial on spectral clustering[J]. Statistics and Computing, 2007, 17(4): 395-416. 10.1007/s11222-007-9033-z |
7 | LAUER F, SCHNÖRR C. Spectral clustering of linear subspaces for motion segmentation[C]// Proceedings of the IEEE 12th International Conference on Computer Vision. Piscataway: IEEE, 2009: 678-685. 10.1109/iccv.2009.5459173 |
8 | ELHAMIFAR E, VIDAL R. Sparse subspace clustering: algorithm, theory, and applications[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(11): 2765-2781. 10.1109/tpami.2013.57 |
9 | LIU G C, LIN Z C, YU Y. Robust subspace segmentation by low-rank representation[C]// Proceedings of the 27th International Conference on Machine Learning. Madison, WI: Omnipress, 2010: 663-670. 10.1109/iccv.2011.6126422 |
10 | LIU G C, LIN Z C, YAN S C, et al. Robust recovery of subspace structures by low-rank representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(1): 171-184. 10.1109/tpami.2012.88 |
11 | LU C Y, MIN H, ZHAO Z Q, et al. Robust and efficient subspace segmentation via least squares regression[C]// Proceedings of the 2012 European Conference on Computer Vision, LNCS7578. Berlin: Springer, 2012: 347-360. |
12 | JI P, SALZMANN M, LI H D. Efficient dense subspace clustering[C]// Proceedings of the 2014 IEEE Winter Conference on Applications of Computer Vision. Piscataway: IEEE, 2014: 461-468. 10.1109/wacv.2014.6836065 |
13 | CHEN J, MAO H, SANG Y S, et al. Subspace clustering using a symmetric low-rank representation[J]. Knowledge-Based Systems, 2017, 127: 46-57. 10.1016/j.knosys.2017.02.031 |
14 | ZHU X F, ZHANG S C, LI Y G, et al. Low-rank sparse subspace for spectral clustering[J]. IEEE Transactions on Knowledge and Data Engineering, 2019, 31(8): 1532-1543. 10.1109/tkde.2018.2858782 |
15 | LIU J M, CHEN Y J, ZHANG J S, et al. Enhancing low-rank subspace clustering by manifold regularization[J]. IEEE Transactions on Image Processing, 2014, 23(9): 4022-4030. 10.1109/tip.2014.2343458 |
16 | YIN M, GAO J B, LIN Z C. Laplacian regularized low-rank representation and its applications[J]. IEEE Transactions Pattern Analysis and Machine Intelligence, 2016, 38(3): 504-517. 10.1109/tpami.2015.2462360 |
17 | HE W, CHEN J X, ZHANG W H. Low-rank representation with graph regularization for subspace clustering[J]. Soft Computing, 2017, 21(6): 1569-1581. 10.1007/s00500-015-1869-0 |
18 | CHEN Y Y, WANG S Q, ZHENG F Y, et al. Graph-regularized least squares regression for multi-view subspace clustering[J]. Knowledge-Based Systems, 2020, 194: No.105482. 10.1016/j.knosys.2020.105482 |
19 | KIM K I, STEINKE F, HEIN M. Semi-supervised regression using Hessian energy with an application to semi-supervised dimensionality reduction[C]// Proceedings of the 22nd International Conference on Neural Information Processing Systems. Red Hook, NY: Curran Associates Inc., 2009: 979-987. |
20 | ZHANG J H, WAN Y, CHEN Z P, et al. Non-negative and local sparse coding based on l2-norm and Hessian regularization[J]. Information Sciences, 2019, 486: 88-100. 10.1016/j.ins.2019.02.024 |
21 | XIE J Y, GIRSHICK R, FARHADI A. Unsupervised deep embedding for clustering analysis[C]// Proceedings of the 33rd International Conference on Machine Learning. New York: JMLR.org, 2016: 478-487. |
22 | JI P, ZHANG T, LI H D, et al. Deep subspace clustering networks[C]// Proceedings of the 31st International Conference on Neural Information Processing Systems. Red Hook, NY: Curran Associates Inc., 2017: 23-32. |
23 | LAW M T, URTASUN R, ZEMEL R S. Deep spectral clustering learning[C]// Proceedings of the 34th International Conference on Machine Learning. New York: JMLR.org, 2017: 1985-1994. 10.1109/cvpr.2017.630 |
24 | PENG X, FENG J S, ZHOU J T Y, et al. Deep subspace clustering[J]. IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(12): 5509-5521. 10.1109/tnnls.2020.2968848 |
25 | ZHENG M, BU J J, CHEN C. Hessian sparse coding[J]. Neurocomputing, 2014, 123: 247-254. 10.1016/j.neucom.2013.08.001 |
26 | 卢桂馥,万鸣华. Hessian正则化的低秩矩阵分解算法[J]. 小型微型计算机系统, 2016, 37(10): 2296-2299. 10.3969/j.issn.1000-1220.2016.10.029 |
LU G F, WAN M H. Hessian regularized low-rank matrix factorization[J]. Journal of Chinese Computer Systems, 2016, 37(10): 2296-2299. 10.3969/j.issn.1000-1220.2016.10.029 | |
27 | LIN Z C, LIU R S, SU Z X. Linearized alternating direction method with adaptive penalty for low-rank representation[C]// Proceedings of the 24th International Conference on Neural Information Processing Systems. Red Hook, NY: Curran Associates Inc., 2011: 612-620. |
28 | CAI J F, CANDÈS E J, SHEN Z W. A singular value thresholding algorithm for matrix completion[J]. SIAM Journal on Optimization, 2010, 20(4): 1956-1982. 10.1137/080738970 |
29 | LIN Z C, CHEN M M, WU L Q, et al. The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices: UILU-ENG-09-2215, DC-247[R]. Urbana, IL: University of Illinois at Urbana-Champaign, Coordinated Science Laboratory, 2009:10. |
30 | HARTIGAN J A, WONG M A. A K-means clustering algorithm[J]. Journal of the Royal Statistical Society, Series C (Applied Statistics), 1979, 28(1): 100-108. 10.2307/2346830 |
31 | LEE D D, SEUNG H S. Algorithms for non-negative matrix factorization[C]// Proceedings of the 13th International Conference on Neural Information Processing Systems. Cambridge: MIT Press, 2000: 535-541. |
32 | ABDI H, WILLIAMS L J. Principal component analysis[J]. Wiley Interdisciplinary Reviews: Computational Statistics, 2010, 2(4): 433-459. 10.1002/wics.101 |
33 | SHI J B, MALIK J. Normalized cuts and image segmentation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(8): 888-905. 10.1109/34.868688 |
34 | CAI D, HE X F, WANG X H, et al. Locality preserving nonnegative matrix factorization[C]// Proceedings of the 21st International Joint Conferences on Artificial Intelligence. Palo Alto, CA: AAAI Press, 2009: 1010-1015. |
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