Subspace clustering (SC) approximates high-dimensional data as a combination of low-dimensional subspaces, which is suitable for high-dimensional data analysis across various domains including image segmentation and face recognition. Existing SC methods typically obtain the global structure representation solely through the self-representation of the samples, thereby neglecting the intrinsic local connections among the samples. Moreover, due to their inherent framework design, obtaining additional a priori information in unsupervised scenarios presents a significant challenge. To address these limitations, this paper proposes a new method, named Sample-Dependent Subspace Clustering with Elastic Structure Consistency Constraints (SDSC). Firstly, we introduce a new Elastic Structure Consistency Constraints (ESCC) strategy to measure global and local structures elastically. Benefiting from this strategy, SDSC can flexibly explore the structural information within the samples to obtain a comprehensive data representation. By employing the joint regularization term, SDSC can learn effective cluster assignment information directly from the constrained structured data representation, and the cluster assignment information and representation coefficient matrix are smoothly integrated into a unified framework and learn in a mutually reinforcing manner. This learning approach contributes to comprehensive and high-quality clustering results, enhancing the robustness and utility of SDSC. Extensive experiments on several real-world benchmarks and synthetic datasets demonstrate the feasibility and effectiveness of SDSC.
ParsonsLHaqueELiuH. Subspace clustering for high dimensional data: a review. Acm Sigkdd Explorat Newslett2004; 6: 90–105.
2.
VidalR. Subspace clustering. IEEE Signal Process Mag2011; 28: 52–68.
3.
FengWWangZXiaoT, et al.Adaptive weighted dictionary representation using anchor graph for subspace clustering. Pattern Recognit2024; 151: 110350.
4.
WeiLJiFLiuH, et al.Subspace clustering via structured sparse relation representation. IEEE Trans Neur Netw Learn Syst2021; 33: 4610–4623.
5.
TsengP. Nearest q-flat to m points. J Optim Theory Appl2000; 105: 249–252.
6.
RaoSTronRVidalR, et al.Motion segmentation in the presence of outlying, incomplete, or corrupted trajectories. IEEE Trans Pattern Anal Mach Intell2009; 32: 1832–1845.
7.
FuZZhaoYChangD, et al.Latent low-rank representation with weighted distance penalty for clustering. IEEE Trans Cybern2022; 53: 6870–6882.
8.
VidalRMaYSastryS. Generalized principal component analysis (GPCA). IEEE Trans Pattern Anal Mach Intell2005; 27: 1945–1959.
9.
ChenHChenXTaoH, et al.PDRLRR: a novel low-rank representation with projection distance regularization via manifold optimization for clustering. Pattern Recognit2024; 149: 110198.
10.
WangYWuLLinX, et al.Multiview spectral clustering via structured low-rank matrix factorization. IEEE Trans Neur Netw Learn Syst2018; 29: 4833–4843.
11.
NieFLuJWuD, et al.A novel normalized-cut solver with nearest neighbor hierarchical initialization. IEEE Trans Pattern Anal Mach Intell2023; 46: 659–666.
12.
PeiSNieFWangR, et al.Efficient clustering based on a unified view of k-means and ratio-cut. In: Advances in neural information processing systems, on line, December 6–12, 2020, pp. 14855–14866.
13.
ElhamifarEVidalR. Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell2013; 35: 2765–2781.
14.
LiuGLinZYanS, et al.Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell2012; 35: 171–184.
15.
ChenYWangZBaiX. Fuzzy sparse subspace clustering for infrared image segmentation. IEEE Trans Image Process2023; 32: 2132–2146.
16.
WangSNieFWangZ, et al.Sparse robust subspace learning via boolean weight. Inf Fusion2023; 96: 224–236.
17.
GuoYTierneySGaoJ. Efficient sparse subspace clustering by nearest neighbour filtering. Signal Process2021; 185: 108082.
18.
LiuGYanS. Latent low-rank representation for subspace segmentation and feature extraction. In: 2011 international conference on computer vision, Barcelona, Spain, November 6–13, 2011, pp. 1615–1622.
19.
LiuXWangLZhangJ, et al.Global and local structure preservation for feature selection. IEEE Trans Neur Netw Learn Syst2013; 25: 1083–1095.
20.
ZhouNXuYChengH, et al.Global and local structure preserving sparse subspace learning: an iterative approach to unsupervised feature selection. Pattern Recognit2016; 53: 87–101.
21.
XuJLiTZhangD, et al.Ensemble clustering via fusing global and local structure information. Expert Syst Appl2024; 237: 121557.
22.
JiaHZhuDHuangL, et al.Global and local structure preserving nonnegative subspace clustering. Pattern Recognit2023; 138: 109388.
23.
KouSYinXWangY, et al.Structure-Aware subspace clustering. IEEE Trans Knowl Data Eng2023; 35: 10569–10582.
24.
LiuYTanYWuH, et al.Preserving local and global information: an effective metric-based subspace clustering. In: Proceedings of the 31st ACM international conference on multimedia, Ottawa, Canada, October 29 to November 3, 2023, pp. 3619–3627.
25.
BaiLLiangJYCaoF. Semi-supervised clustering with constraints of different types from multiple information sources. IEEE Trans Pattern Anal Mach Intell2020; 43: 3247–3258.
26.
HuangDWangCDWuJS, et al.Ultra-scalable spectral clustering and ensemble clustering. IEEE Trans Knowl Data Eng2019; 32: 1212–1226.
27.
FuZZhaoYChangD, et al.Auto-weighted low-rank representation for clustering. Knowl Based Syst2022; 251: 109063.
28.
XuJXuKChenK, et al.Reweighted sparse subspace clustering. Comput Vis Image Underst2015; 138: 25–37.
29.
LiCGYouCVidalR. Structured sparse subspace clustering: a joint affinity learning and subspace clustering framework. IEEE Trans Image Process2017; 26: 2988–3001.
30.
TangKLiuRSuZ, et al.Structure-constrained low-rank representation. IEEE Trans Neur Netw Learn Syst2014; 25: 2167–2179.
31.
LuXWangYYuanY. Graph-regularized low-rank representation for destriping of hyperspectral images. IEEE Trans Geosci Remote Sens2013; 51: 4009–4018.
32.
LuCFengJLinZ, et al.Subspace clustering by block diagonal representation. IEEE Trans Pattern Anal Mach Intell2018; 41: 487–501.
33.
KangZLinZZhuX, et al.Structured graph learning for scalable subspace clustering: from single view to multiview. IEEE Trans Cybern2021; 52: 8976–8986.
34.
HawkinsDM. The problem of overfitting. J Chem Inf Comput Sci2004; 44: 1–12.
35.
PengXTangHZhangL, et al.A unified framework for representation-based subspace clustering of out-of-sample and large-scale data. IEEE Trans Neur Netw Learn Syst2015; 27: 2499–2512.
36.
LuCYMinHZhaoZQ, et al.Robust and efficient subspace segmentation via least squares regression. In: Computer Vision–ECCV 2012: 12th European Conference on Computer Vision, Florence, Italy, October 7–13, 2012, pp. 347–360.
37.
MaLCrawfordMTianJ. Local manifold learning-based k-nearest-neighbor for hyperspectral image classification. IEEE Trans Geosci Remote Sens2010; 48: 4099–4109.
38.
HajizadehRAghagolzadehAEzojiM. Local distances preserving based manifold learning. Expert Syst Appl2020; 139: 112860.
LuZPengY. Exhaustive and efficient constraint propagation: a graph-based learning approach and its applications. Int J Comput Vision2013; 103: 306–325.
KimELeeMOhS. Elastic-net regularization of singular values for robust subspace learning. In: Proceedings of the IEEE conference on computer vision and pattern recognition, Boston, Massachusetts, June 7–12, 2015, pp. 915–923.
49.
GuoJSunYGaoJ. Logarithmic schatten-p norm minimization for tensorial multi-view subspace clustering. IEEE Trans Pattern Anal Mach Intell2022; 45: 3396–3410.
