山东大学学报 (工学版) ›› 2022, Vol. 52 ›› Issue (2): 57-66.doi: 10.6040/j.issn.1672-3961.0.2021.317
• • 上一篇
程业超,刘惊雷*
CHENG Yechao, LIU Jinglei*
摘要： 针对子空间聚类算法中相似性学习和谱聚类相互分离的问题,提出自适应图正则的单步子空间聚类(one-step subspace clustering with adaptive graph regularization, OSCAGR)算法。利用Frobenius范数鼓励分组效应,根据局部连通性为每个数据点分配自适应的最优邻域学习系数矩阵;考虑全局结构和局部结构,保证数据空间中相近的点拥有较大的表示系数;通过量化范数将子空间聚类两个独立的阶段整合到一个统一的优化框架中。试验结果表明,OSCAGR算法在UCI数据集和3个图像数据集上比其他对比方法的精度高1%~7%,OSCAGR算法的聚类正确率和归一化互信息优于其他对比方法。
中图分类号:
| [1] ABAVISANI M, PATEL V M. Multimodal sparse and low-rank subspace clustering[J]. Information Fusion, 2018, 39:168-177. [2] FENG J, LIN Z, XU H. Robust subspace segmentation with block-diagonal prior[C] //Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Columbus, USA: IEEE, 2014: 3818-3825. [3] LI J, CHEN C, HOU X. Laplacian Regularized non-negative sparse low-rank representation classification[C] //Proceedings of the Chinese Conference on Biometric Recognition. Shenzhen, China: Springer, 2017: 683-690. [4] WEI L, WANG X, WU A. Robust subspace segmentation by self-representation constrained low-rank representation[J]. Neural Processing Letters, 2018, 48(3):1671-1691. [5] BRADLEY P S, MANGASARIAN O L. K-plane clustering[J]. Journal of Global Optimization, 2000, 16(1):23-32. [6] ZHANG T, SZLAM A, WANG Y. Hybrid linear modeling via local best-fit flats[J]. International Journal of Computer Vision, 2012, 100(3):217-240. [7] MA Y, YANG A Y, DERKSEN H. Estimation of subspace arrangements with applications in modeling and segmenting mixed data[J]. SIAM Review, 2008, 50(3):413-458. [8] TSAKIRIS M C, VIDAL R. Algebraic clustering of affine subspaces[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, 40(2):482-489. [9] VIDAL R, MA Y, SASTRY S. Generalized principal component analysis(GPCA)[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(12):1945-1959. [10] DERKSEN H, MA Y, HONG W. Segmentation of multivariate mixed data via lossy coding and compression[C] //Proceedings of the Visual Communications and Image Processing 2007. San Jose, USA: IEEE, 2007. [11] YANG A Y, RAO S R, Ma Y. Robust statistical estimation and segmentation of multiple subspaces[C] //Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop(CVPRW'06). New York, USA: IEEE, 2006: 99-99. [12] CHEN G, LERMAN G. Spectral curvature clustering(SCC)[J]. International Journal of Computer Vision, 2009, 81(3):317-330. [13] FAN Z, ZHOU J, WU Y. Multibody grouping by inference of multiple subspaces from high-dimensional data using oriented-frames[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 28(1):91-105. [14] FAVARO P, VIDAL R, RAVICHANDRAN A. A closed form solution to robust subspace estimation and clustering[C] //Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Colorado Springs, USA: IEEE, 2011:1801-1807. [15] 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. [16] LIU G, LIN Z, YU Y. Robust subspace segmentation by low-rank representation[C] //Proceedings of the International Conference on Machine Learning. Haifa, Israel: ACM, 2010. [17] VIDAL R, FAVARO P. Low rank subspace clustering(LRSC)[J]. Pattern Recognition Letters, 2014, 43:47-61. [18] LU C Y, MIN H, ZHAO Z Q. Robust and efficient subspace segmentation via least squares regression[C] //Proceedings of the European Conference on Computer Vision. Berlin, Germany: Springer, 2012: 347-360. [19] ZHENG Y, ZHANG X, YANG S. Low-rank representation with local constraint for graph construction[J]. Neurocomputing, 2013, 122:398-405. [20] LI C G, YOU C, VIDAL R. Structured sparse subspace clustering: A joint affinity learning and subspace clustering framework[J]. IEEE Transactions on Image Processing, 2017, 26(6):2988-3001. [21] NIE F, WANG X, HUANG H. Clustering and projected clustering with adaptive neighbors[C] //Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, USA: ACM, 2014: 977-986. [22] WANG L, HUANG J, YIN M. Block diagonal representation learning for robust subspace clustering[J]. Information Sciences, 2020, 526:54-67. [23] ZHUANG L, WANG J, LIN Z. Locality-preserving low-rank representation for graph construction from nonlinear manifolds [J]. Neurocomputing, 2016, 175:715-722. [24] NIE F, DONG X, LI X. Unsupervised and semi-supervised projection with graph optimization[J]. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(4):1547-1559. [25] WANG Q, QIN Z, NIE F. Spectral embedded adaptive neighbors clustering[J]. IEEE Transactions on Neural Networks and Learning Systems, 2018, 30(4):1265-1271. [26] LIU W, POKHAREL P P, PRINCIPE J C. Correntropy: properties and applications in non-Gaussian signal processing[J]. IEEE Transactions on Signal Processing, 2007, 55(11):5286-5298. [27] TONG L, ZHOU J, QIAN B. Adaptive graph regularized multilayer nonnegative matrix factorization for hyperspectral unmixing[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2020, 13:434-447. [28] ZHOU T, TAO D. Godec: randomized low-rank & sparse matrix decomposition in noisy case[C] //Proceedings of the 28th International Conference on Machine Learning.Washington, USA: ACM, 2011. [29] KUMAR K M, REDDY A R M. An efficient k-means clustering filtering algorithm using density based initial cluster centers [J]. Information Sciences, 2017, 418-419(1):286-301. [30] LU C, FENG J, LIN Z. Correlation adaptive subspace segmentation by trace lasso[C] //Proceedings of the IEEE international conference on computer vision. Sydney, Australia: IEEE, 2013:1345-1352. [31] LIU G, YAN S. Latent low-rank representation for subspace segmentation and feature extraction[C] //Proceedings of the 2011 International Conference on Computer Vision. Barcelona, Spain: IEEE, 2011:1615-1622. [32] MAO Q, WANG L, TSANG I W. Principal graph and structure learning based on reversed graph embedding[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016, 39(11):2227-2241. |
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