基于加權錨點(diǎn)的多視圖聚類(lèi)算法
doi: 10.16383/j.aas.c220531
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國防科技大學(xué)計算機學(xué)院 長(cháng)沙 410073
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中國地質(zhì)大學(xué)計算機學(xué)院 武漢 430074
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國防科技大學(xué)智能科學(xué)學(xué)院 長(cháng)沙 410073
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國防科技大學(xué)計算機學(xué)院高性能計算國家重點(diǎn)實(shí)驗室 長(cháng)沙 410073
基金項目: 國家自然科學(xué)基金(61922088, 62006236, 62006237), 國防科技大學(xué)科研計劃項目(ZK21-23, ZK20-10), 高性能計算國家重點(diǎn)實(shí)驗室自主課題(202101-15)資助
Multi-view Clustering With Weighted Anchors
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College of Computer, National University of Defense Technology, Changsha 410073
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College of Computer, China University of Geosciences, Wuhan 430074
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College of Intelligent Science and Technology, National University of Defense Techno-logy, Changsha 410073
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State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology, Changsha 410073
Funds: Supported by National Natural Science Foundation of China (61922088, 62006236, 62006237), Research Project of National University of Defense Technology (ZK21-23, ZK20-10), and Autonomous Project of State Key Laboratory of High Performance Computing (202101-15)
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摘要: 大規模多視圖聚類(lèi)旨在解決傳統多視圖聚類(lèi)算法中計算速度慢、空間復雜度高, 以致無(wú)法擴展到大規模數據的問(wèn)題. 其中, 基于錨點(diǎn)的多視圖聚類(lèi)方法通過(guò)使用整體數據集合的錨點(diǎn)集構建后者對于前者的重構矩陣, 利用重構矩陣進(jìn)行聚類(lèi), 有效地降低了算法的時(shí)間和空間復雜度. 然而, 現有的方法忽視了錨點(diǎn)之間的差異, 均等地看待所有錨點(diǎn), 導致聚類(lèi)結果受到低質(zhì)量錨點(diǎn)的限制. 為定位更具有判別性的錨點(diǎn), 加強高質(zhì)量錨點(diǎn)對聚類(lèi)的影響, 提出一種基于加權錨點(diǎn)的大規模多視圖聚類(lèi)算法(Multi-view clustering with weighted anchors, MVC-WA). 通過(guò)引入自適應錨點(diǎn)加權機制, 所提方法在統一框架下確定錨點(diǎn)的權重, 進(jìn)行錨圖的構建. 同時(shí), 為增加錨點(diǎn)的多樣性, 根據錨點(diǎn)之間的相似度進(jìn)一步調整錨點(diǎn)的權重. 在9個(gè)基準數據集上與現有最先進(jìn)的大規模多視圖聚類(lèi)算法的對比實(shí)驗結果驗證了所提方法的高效性與有效性.
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關(guān)鍵詞:
- 多視圖聚類(lèi) /
- 大規模聚類(lèi) /
- 錨點(diǎn) /
- 權重學(xué)習
Abstract: Large-scale multi-view clustering aims to solve the problem that traditional methods cannot scale to large-scale data due to slow computational speed and high complexity. Among them, the anchor-based multi-view clustering method constructs a reconstruction matrix for the entire dataset by utilizing a set of anchor points. Clustering with the reconstruction matrix effectively reduces the time and space complexity of the algorithm. However, existing methods ignore the differences among anchor points and treat them equally, resulting in clustering results limited by low-quality anchor points. In order to identify more discriminative anchor points and enhance the influence of high-quality anchors on clustering, a large-scale multi-view clustering algorithm based on weighted anchors (MVC-WA) was proposed. By introducing an adaptive anchor weighting mechanism, the proposed method determine the weights of anchors in a unified framework for the construction of anchor graphs. Meanwhile, in order to increase the diversity among anchors, the weights of anchors were further adjusted according to the similarity between them. Experimental results comparing with existing state-of-the-art large-scale multi-view clustering algorithms on nine benchmark datasets validate the efficiency and effectiveness of the proposed method.-
Key words:
- Multi-view clustering /
- large-scale clustering /
- anchor /
- weight learning
1)1 1http://mkl.ucsd.edu/dataset/protein-fold-prediction/ 2http://archive.ics.uci.edu/ml/datasets/Multiple+Features 3https://www.fruitfly.org/ 4http://svcl.ucsd.edu/projects/crossmodal/ 5https://www.ee.columbia.edu/ln/dvmm/CCV/ 6http://staff.science.uva.nl/aloi/ 7https://www.cs.tau.ac.il/wolf/ytfaces/ 2)2 http://archive.ics.uci.edu/ml/datasets/Multiple+Features3)3 https://www.fruitfly.org/4)4 http://svcl.ucsd.edu/projects/crossmodal/5)5 https://www.ee.columbia.edu/ln/dvmm/CCV/6)6 http://staff.science.uva.nl/aloi/7)7 https://www.cs.tau.ac.il/wolf/ytfaces/ -
圖 2 目標函數值隨迭代次數增長(cháng)的變化曲線(xiàn)
Fig. 2 The variation curves the objective function value with the increase of the number of iterations
圖 3 參數調整對聚類(lèi)性能的影響
Fig. 3 The influence of parameter tuning on clustering performance
表 1 本文使用的主要符號
Table 1 Summary of notations
符號 定義 $n$ 數據點(diǎn)數量 $k$ 類(lèi)別數 $v$ 視圖數 $m$ 錨點(diǎn)數 $d^{(p)}$ 第$p$個(gè)視圖上數據的維度 ${\boldsymbol{X}}^{(p)} \in \mathbf{R}^{d^{(p)} \times n}$ 第$p$個(gè)視圖的數據矩陣 ${\boldsymbol{A}}^{(p)} \in \mathbf{R}^{d^{(p)} \times m}$ 第$p$個(gè)視圖的錨點(diǎn)矩陣 ${\boldsymbol{Z}}^{(p)} \in \mathbf{R}^{m \times n}$ 第$p$個(gè)視圖上的錨圖 ${\boldsymbol{W}}^{(p)} \in \mathbf{R}^{m \times m}$ 第$p$個(gè)視圖上的權重矩陣 ${\boldsymbol{M}}^{(p)} \in \mathbf{R}^{m \times m}$ 第$p$個(gè)視圖上錨點(diǎn)的相關(guān)性矩陣 
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表 2 實(shí)驗中使用的數據集
Table 2 Description of datasets
數據集 樣本數 視圖數 類(lèi)別數 ProteinFold 694 12 27 Mfeat 2 000 6 10 BDGP 2 500 3 5 Wiki 2 866 2 10 CCV 6 773 3 20 ALOI 10 800 4 100 YTF10 38 654 4 10 YTF20 63 896 4 20 YTF50 126 054 4 50
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表 3 對比算法在所有數據集上的聚類(lèi)性能 (%)
Table 3 Clustering performance of compared methods on all datasets (%)
數據集 MSC-IAS PMSC MVSC FMR SFMC MLRSSC AMGL RMKM BMVC LMVSC SMVSC FPMVS 本文算法 ACC ProteinFold 28.45±1.31 12.06±0.41 24.83±1.35 32.85±1.75 26.22±0 11.10±0 10.96±1.23 23.63±0 26.22±0 28.29±1.57 29.26±1.52 30.03±1.06 32.57±1.88 Mfeat 85.95±6.81 32.48±2.11 45.40±3.03 59.63±3.21 85.85±0 20.00±0 83.08±7.58 67.10±0 58.45±0 81.50±5.30 67.64±3.86 46.34±3.11 88.97±6.42 BDGP 52.10±4.59 26.44±0.19 35.36±2.45 24.93±0.28 20.08±0 36.12±0 32.33±1.82 41.44±0 29.48±0 50.16±0.29 37.22±2.03 32.62±0.71 60.04±1.89 Wiki 23.91±0.58 49.93±3.46 20.99±0.50 41.97±1.26 35.45±0 15.77±0 12.21±0.16 17.34±0 15.11±0 56.05±2.65 52.47±3.53 51.18±2.54 56.55±2.03 CCV — — — 11.93±0.26 12.52±0 10.44±0 13.71±0.31 11.94±0 15.50±0 20.28±0.60 22.98±0.58 22.88±0.74 22.60±0.67 ALOI — — — — — 1.01±0 60.26±1.69 33.74±0 59.67±0 40.27±1.55 48.34±1.49 21.72±0.65 71.29±1.80 YTF10 — — — — — — — 75.68±0 60.43±0 66.74±3.69 72.93±3.96 67.09±2.80 79.15±8.39 YTF20 — — — — — — — 57.62±0 60.09±0 60.64±4.18 67.13±4.20 63.08±2.39 68.16±4.82 YTF50 — — — — — — — — 66.00±0 68.32±2.45 67.13±3.68 64.24±2.97 66.97±3.08 NMI ProteinFold 36.91±0.89 6.71±0.58 34.45±1.58 40.69±1.13 31.02±0 0±0 20.02±2.19 34.83±0 29.53±0 37.43±1.14 39.94±1.40 37.75±0.99 43.34±1.19 Mfeat 87.68±2.85 40.14±2.76 42.49±3.30 49.19±1.37 91.77±0 28.63±0 87.29±3.84 65.33±0 68.88±0 79.35±1.95 62.18±1.77 56.46±1.81 86.74±2.26 BDGP 33.07±2.81 3.70±0.20 10.25±2.15 0.99±0.08 2.25±0 26.33±0 13.42±2.29 28.12±0 4.60±0 25.41±0.15 9.85±1.22 10.02±0.38 33.78±0.43 Wiki 8.65±0.27 52.01±1.51 7.28±0.67 33.09±1.09 34.18±0 0.08±0 0.82±0.10 4.34±0 2.46±0 51.57±2.17 50.05±3.79 49.34±2.95 49.47±1.77 CCV — — — 7.04±0.32 5.44±0 0±0 12.52±0.40 7.76±0 11.70±0 16.28±0.46 17.55±0.32 16.96±0.68 17.02±0.49 ALOI — — — — — 0.02±0 75.29±0.90 63.55±0 75.67±0 54.38±1.88 72.51±0.50 55.39±0.29 83.15±0.53 YTF10 — — — — — — — 80.22±0 58.91±0 73.75±2.25 78.57±4.61 76.11±5.78 83.15±4.01 YTF20 — — — — — — — 73.84±0 71.67±0 75.57±1.88 78.36±3.96 74.30±5.99 78.63±1.90 YTF50 — — — — — — — — 81.90±0 82.43±0.78 82.56±1.42 82.08±1.07 83.19±0.90 Purity ProteinFold 32.99±1.37 14.37±0.41 31.26±1.19 38.46±1.60 28.96±0 11.10±0 11.71±1.20 33.86±0 28.53±0 35.90±1.63 36.00±1.16 34.95±0.66 39.21±1.56 Mfeat 87.20±6.10 33.27±2.29 47.92±3.08 60.99±2.47 88.25±0 20.00±0 83.94±6.13 75.95±0 74.98±0 82.08±4.59 68.80±2.87 49.44±2.92 89.97±5.26 BDGP 53.52±3.70 28.59±0.23 35.67±3.06 25.17±0.21 21.12±0 36.12±0 33.46±2.10 51.00±0 29.48±0 50.17±0.23 37.80±1.17 34.82±1.33 60.13±1.24 Wiki 26.68±0.76 51.85±2.91 24.03±0.94 46.06±1.31 37.68±0 15.77±0 12.46±0.19 24.08±0 17.62±0 60.45±2.69 57.63±4.19 55.97±3.30 59.54±1.68 CCV — — — 15.92±0.31 13.04±0 10.44±0 14.12±0.33 17.04±0 19.18±0 23.62±0.47 25.91±0.51 25.09±0.78 25.34±0.67 ALOI — — — — — 1.01±0 63.92±1.26 64.02±0 62.35±0 42.32±1.55 51.46±1.41 23.67±0.72 73.81±1.42 YTF10 — — — — — — — 80.70±0 60.43±0 71.52±3.25 77.35±5.70 69.43±3.06 83.57±5.78 YTF20 — — — — — — — 68.78±0 64.83±0 68.20±3.02 72.40±3.79 64.92±1.95 74.40±3.32 YTF50 — — — — — — — — 73.64±0 73.21±2.18 70.09±3.61 66.84±3.02 73.65±2.50 F-score ProteinFold 14.07±0.62 9.44±0.01 14.28±0.85 18.57±1.38 11.68±0 9.64±0 7.84±0.79 12.92±0 16.41±0 15.58±1.17 16.76±0.96 17.09±0.94 19.61±1.62 Mfeat 83.66±6.35 26.94±1.09 37.46±2.69 41.49±1.51 85.52±0 27.39±0 81.39±7.35 59.22±0 62.59±0 74.42±4.13 56.50±2.45 46.57±1.33 85.05±5.09 BDGP 40.44±2.22 29.55±0.10 29.08±0.61 21.00±0.07 33.15±0 41.19±0 32.62±0.81 36.28±0 26.51±0 37.81±0.06 28.81±1.23 28.79±0.58 45.31±0.50 Wiki 15.44±0.25 41.83±2.91 14.91±0.54 30.34±0.78 21.38±0 19.46±0 12.48±0.69 13.04±0 11.15±0 48.71±2.18 45.76±4.69 44.91±3.43 47.17±1.64 CCV — — — 7.50±0.07 10.81±0 10.84±0 10.93±0.41 8.66±0 9.79±0 11.43±0.31 12.93±0.21 13.16±0.31 12.51±0.30 ALOI — — — — — 1.96±0 13.58±2.28 28.82±0 48.29±0 29.91±1.49 31.22±0.85 10.21±0.13 61.96±1.48 YTF10 — — — — — — — 73.27±0 53.15±0 62.24±3.70 68.34±5.88 66.10±5.06 75.78±8.28 YTF20 — — — — — — — 53.89±0 48.06±0 55.39±4.25 61.68±3.83 57.81±4.00 63.66±4.34 YTF50 — — — — — — — — 57.09±0 62.49±2.45 57.97±5.08 56.89±3.18 60.54±3.26
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表 4 對比算法在所有數據集上的運行時(shí)間 (s)
Table 4 Running time of compared methods on all datasets (s)
數據集 MSC-IAS PMSC MVSC FMR SFMC MLRSSC AMGL RMKM BMVC LMVSC SMVSC FPMVS 本文算法 ProteinFold 2.44 1 512.10 408.89 16.43 6.86 2.12 1.66 1.21 12.64 2.55 2.82 3.97 6.91 Mfeat 16.81 3 300.30 11 528.00 251.03 88.62 27.94 19.62 3.95 0.43 2.96 1.38 1.43 9.20 BDGP 13.26 15 215.00 34 800.00 1 070.40 39.00 26.89 73.71 7.53 0.35 2.86 1.63 3.38 7.18 Wiki 15.92 14 386.00 9 991.70 1 068.80 9.84 30.72 180.62 6.27 0.11 3.57 3.15 20.16 4.89 CCV — — — 10 287.00 39.51 486.68 1 250.00 25.00 0.88 20.46 13.79 10.54 47.37 ALOI — — — — — 3 358.90 10 594.00 202.32 8.41 68.53 66.24 61.46 581.28 YTF10 — — — — — — — 675.42 108.22 196.70 253.21 998.23 495.83 YTF20 — — — — — — — 1 780.50 80.53 513.52 720.15 1 680.34 1 516.70 YTF50 — — — — — — — — 65.71 3 535.72 2 254.48 9 175.31 4 868.40
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表 5 消融實(shí)驗結果 (%)
Table 5 Results of ablation experiments (%)
聚類(lèi)指標 對比方法 數據集 ProteinFold Mfeat BDGP Wiki CCV ALOI YTF10 YTF20 ACC 最優(yōu)單視圖 31.48±1.22 77.62±5.85 49.98±2.95 52.01±3.70 20.03±0.32 55.79±1.40 72.08±5.27 63.52±3.80 未加權 27.83±1.66 82.55±6.64 46.32±3.19 52.05±2.38 18.10±0.53 70.14±2.04 70.72±8.29 66.36±4.72 無(wú)正則化項 30.57±1.57 86.54±7.40 47.37±2.16 47.49±2.35 21.75±0.74 66.26±1.82 68.95±8.83 62.18±4.49 本文方法 32.57±1.88 88.97±6.42 60.04±1.89 56.55±2.03 22.60±0.67 71.29±1.80 79.15±8.39 68.16±4.82 NMI 最優(yōu)單視圖 41.08±0.82 74.73±2.25 27.61±2.33 50.01±3.12 16.67±0.40 73.59±0.44 74.87±2.52 69.70±1.55 未加權 36.98±1.18 84.10±2.64 24.28±3.34 49.25±1.88 13.90±0.36 83.17±0.51 76.34±4.74 75.09±1.74 無(wú)正則化項 42.10±1.08 87.26±2.59 26.89±2.87 36.51±2.07 16.83±0.49 79.91±0.51 76.77±4.39 75.65±1.70 本文方法 43.34±1.19 86.74±2.26 33.78±0.43 49.47±1.77 17.02±0.49 83.15±0.53 83.15±4.01 78.63±1.90 Purity 最優(yōu)單視圖 36.97±0.97 79.67±4.38 51.69±2.83 57.39±3.90 23.59±0.32 58.86±1.22 76.85±3.66 68.07±2.33 未加權 35.17±1.46 84.32±5.43 47.12±3.11 58.34±2.52 21.10±0.40 72.77±1.71 76.89±6.26 71.52±3.27 無(wú)正則化項 38.73±1.27 88.55±5.55 47.45±2.04 50.37±1.98 24.76±0.63 69.02±1.47 76.11±6.23 70.25±3.64 本文方法 39.21±1.56 89.97±5.26 60.13±1.24 59.54±1.68 25.34±0.67 73.81±1.42 83.57±5.78 74.40±3.32 F-score 最優(yōu)單視圖 19.63±1.10 69.72±4.28 37.83±2.14 45.07±3.62 11.50±0.20 43.10±1.38 67.00±4.92 52.49±3.96 未加權 15.68±1.38 78.80±5.59 35.78±2.64 44.79±2.01 10.64±0.23 60.72±1.60 66.43±8.78 58.07±4.43 無(wú)正則化項 18.65±1.24 83.90±5.96 38.61±2.13 37.17±1.75 12.06±0.32 54.92±1.47 67.00±8.70 54.88±3.74 本文方法 19.61±1.62 85.05±5.09 45.31±0.50 47.17±1.64 12.51±0.30 61.96±1.48 75.78±8.28 63.66±4.34
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