Efficient and Robust MultiView Clustering With Anchor Graph Regularization

Robustness Meets Low-Rankness: Unified Entropy and Tensor Learning for Multi-View Subspace Clustering

“…Specifically, sparse representation clustering (SSC) [11] is used for each view independently to generate a sparse self-representation matrix and reports the best performance; Low-rank representation clustering (LRR) [12] is used for each view independently to generate a low-rank self-representation matrix and reports the best performance; Robust multi-view spectral clustering (RMSC) [48] recovers a shared low-rank transition probability matrix by Markov chain method. Diversity-induced clustering (DiMSC) [49] explores the complementarity of views by diversity term; Graph learning clustering (GMC) [55] fuses data graph matrices of all views to generate a unified graph matrix; Latent subspace clustering (LMSC) [36] learns latent low-rank representation by mapping the original space into a low-dimensional latent [55] 0.381±0.000 0.519±0.000 0.191±0.000 0.281±0.000 0.174±0.000 0.732±0.000 LMSC [36] 0.563±0.000 0.525±0.000 0.397±0.000 0.440 ±0.000 0.430±0.000 0.450±0.000 MLAN [56] 0.331±0.000 0.475±0.000 0.151±0.000 0.248±0.000 0.150±0.000 0.731±0.000 tSVDMSC [16] 0.812±0.007 0.858±0.007 0.771±0.003 0.788±0.001 0.743±0.006 0.839±0.003 ETLMSC [28] 0.878±0.000 0.902±0.000 0.851±0.000 0.862±0.000 0.848±0.000 0.877±0.000 LRTG [57] 0.615±0.016 0.657±0.005 0.486±0.016 0.525±0.014 0.485±0.023 0.572±0.005 GNLTA [18] 0.881±0.043 0.895±0.013 0.850±0.032 0.861±0.030 0.846±0.041 0.876±0.020 ERMC-AGR [45] 0.430±0.023 0.430±0.012 0.259±0.007 0.315±0.007 0.289±0.005 0.347±0.013 RLMSC [51] 0.551±0.000 0.730±0.000 0.477±0.000 0.513±0.000 0.516±0.000 0.511±0.000…”

“…Scene-15 WETMSC 0.904±0.011 0.929±0.007 0.891±0.009 0.899±0.008 0.887±0.011 0.911±0.006 SSC [11] 0.420±0.015 0.723±0.005 0.303±0.011 0.317±0.012 0.441±0.025 0.248±0.010 LRR [12] 0.510±0.009 0.728±0.014 0.304±0.017 0.339±0.008 0.627±0.012 0.231±0.010 RMSC [48] 0.346±0.036 0.573±0.047 0.246±0.031 0.258±0.027 0.457±0.033 0.182±0.031 DiMSC [49] 0.351±0.000 0.589±0.000 0.226±0.000 0.253±0.000 0.362±0.000 0.191±0.000 LT-MSC [15] 0.559±0.012 0.788±0.005 0.393±0.007 0.403±0.003 0.670±0.009 0.288±0.012 GMC [55] 0.331±0.000 0.544±0.000 0.031±0.000 0.081±0.000 0.044±0.000 0.470±0.000 LMSC [36] 0.566±0.012 0.818±0.004 0.383±0.010 0.392±0.010 0.710±0.014 0.271±0.008 MLAN [56] 0.579±0.024 0.748±0.020 0.222±0.015 0.265±0.015 0.173±0.009 0.560±0.016 tSVDMSC [16] 0.607±0.005 0.858±0.003 0.430±0.005 0.440±0.010 0.742±0.007 0.323±0.009 ETLMSC [28] 0.639±0.019 0.899±0.007 0.456±0.017 0.465±0.017 0.825±0.029 0.324±0.012 LRTG [57] 0.490±0.000 0.750±0.000 0.340±0.000 0.350±0.000 0.547±0.000 0.260±0.000 GNLTA [18] 0.604±0.016 0.875±0.005 0.444±0.017 0.453±0.016 0.776±0.018 0.320±0.015 ERMC-AGR [45] 0.169±0.000 0.307±0.000 0.153±0.000 0.179±0.000 0.166±0.000 0.194±0.000 RLMSC [51] 0.512±0.000 0.837±0.000 0.419±0.000 0.429±0.000 0.669±0.000 0.316±0.000 Caltech101 WETMSC 0.673±0.028 0.902±0.018 0.497±0.033 0.500±0.025 0.817±0.029 0.360±0.029 space. Adaptive neighbors clustering (MLAN) [56] adaptively updates the graph for MVC; Anchor graph regularization (ERMC-AGR) [45] learns the embedded anchor graph under matrix factorization framework and introduces CIM to encode noise. Robust localized multi-view subspace clustering (RLMSC) [51] learns the robust consensus representation by fusing the noiseless structures of views.…”

“…Their aim is to factorize multi-view data into common representations with smaller dimension by minimizing the overall loss function for different views. The recent works in [14], [45]- [47] proposed anchor graphs to handle large-scale datasets. Their difference is that methods in [14], [45] directly obtained the anchors through the cluster center of k-means, while methods in [46], [47] learned the public graph through the projected unified anchors, avoiding the isolation of the fixed anchors and the graph construction.…”

“…We investigate the clustering performance of the proposed WETMSC on six real-world datasets including text and image [55] 0.736±0.000 0.815±0.000 0.678±0.000 0.713±0.000 0.644±0.000 0.799±0.000 LMSC [36] 0.893±0.000 0.815±0.000 0.783±0.000 0.805±0.000 0.798±0.000 0.812±0.000 MLAN [56] 0.874±0.000 0.910±0.000 0.847±0.000 0.864±0.000 0.797±0.000 0.943±0.000 tSVDMSC [16] 0.955±0.000 0.932±0.000 0.924±0.000 0.932±0.000 0.930±0.000 0.934±0.000 ETLMSC [28] 0.958±0.078 0.977±0.028 0.953±0.069 0.958±0.062 0.940±0.088 0.980±0.029 LRTG [57] 0.981±0.000 0.953±0.000 0.957±0.000 0.961±0.000 0.961±0.000 0.962±0.000 GNLTA [18] 0.981±0.036 0.979±0.012 0.972±0.036 0.975±0.032 0.968±0.052 0.983±0.008 ERMC-AGR [45] 0.746±0.063 0.675±0.035 0.582±0.060 0.625±0.053 0.607±0.065 0.645±0.040 RLMSC [51] 0.754±0.000 0.759±0.000 0.608±0.000 0.648±0.000 0.637±0.000 0.659±0.000 UCI-3views WETMSC 0.996±0.000 0.989±0.000 0.991±0.000 0.992±0.000 0.992±0.000 0.992±0.000 SSC [11] 0.791±0.007 0.750±0.005 0.651±0.006 0.701±0.005 0.670±0.008 0.736±0.003 LRR [12] 0.695±0.000 0.590±0.000 0.491±0.000 0.562±0.000 0.560±0.000 0.564±0.000 RMSC [48] 0.761±0.054 0.673±0.032 0.587±0.041 0.646±0.035 0.633±0.041 0.660±0.031 DiMSC [49] 0.759±0.009 0.622±0.015 0.548±0.015 0.611±0.013 0.606±0.013 0.616±0.012 LT-MSC [15] 0.831±0.003 0.743±0.004 0.665±0.004 0.712±0.004 0.699±0.004 0.725±0.003 GMC [55] 0.748±0.000 0.771±0.000 0.640±0.000 0.697±0.000 0.612±0.000 0.809±0.000 LMSC [36] 0.770±0.022 0.679±0.025 0.596±0.028 0.654±0.024 0.635±0.025 0.673±0.023 MLAN [56] 0.859±0.003 0.751±0.003 0.709±0.004 0.750±0.003 0.727±0.004 0.776±0.002 tSVDMSC [16] 0.991±0.000 0.982±0.000 0.978±0.000 0.981 ±0.000 0.980±0.000 0.982±0.000 ETLMSC [28] 0.872±0.082 0.805±0.053 0.764±0.083 0.797±0.071 0.784±0.082 0.812±0.059 LRTG [57] 0.895±0.000 0.829±0.000 0.775±0.000 0.807±0.000 0.794±0.000 0.821±0.000 GNLTA [18] 0…”

The methods for improving large-scale multi-view clustering efficiency: a survey

“…Since anchors can substantially reduce the time complexity and spatial complexity of graph construction, it has been widely used in graph-based large-scale data processing since Liu et al (2010) proposed it (Liu et al 2010;Guo and Ye 2019;Deng et al 2016;Yang et al 2020;Chen and Cai 2011;Cai and Chen 2014;Li et al 2015Li et al , 2016Hong et al 2023;Han et al 2017). Especially after the improvement of anchors-based methods proposed by Nie et al (2016b) and Wang et al (2016) later, there are more and more large-scale multiview data clustering algorithms proposed based on anchors (Shen et al 2022;He et al 2020He et al , 2019Shi et al 2021a;Zhang and Sun 2022;Sun and Zhang 2022;Affeldt et al 2020;Qiang et al 2021;Zhang et al 2020a;Yang et al 2022a, b;Wang et al 2019b;Shu et al 2022). To facilitate the understanding, this section first presents the concept of graph construction, then introduces the anchors-based method and its improvement based on the problems in graph construction, and finally gives a brief description of the anchors-based algorithms.…”