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              基于加權錨點(diǎn)的多視圖聚類(lèi)算法

              劉溯源 王思為 唐廠(chǎng) 周思航 王思齊 劉新旺

              劉溯源, 王思為, 唐廠(chǎng), 周思航, 王思齊, 劉新旺. 基于加權錨點(diǎn)的多視圖聚類(lèi)算法. 自動(dòng)化學(xué)報, 2024, 50(6): 1160?1170 doi: 10.16383/j.aas.c220531
              引用本文: 劉溯源, 王思為, 唐廠(chǎng), 周思航, 王思齊, 劉新旺. 基于加權錨點(diǎn)的多視圖聚類(lèi)算法. 自動(dòng)化學(xué)報, 2024, 50(6): 1160?1170 doi: 10.16383/j.aas.c220531
              Liu Su-Yuan, Wang Si-Wei, Tang Chang, Zhou Si-Hang, Wang Si-Qi, Liu Xin-Wang. Multi-view clustering with weighted anchors. Acta Automatica Sinica, 2024, 50(6): 1160?1170 doi: 10.16383/j.aas.c220531
              Citation: Liu Su-Yuan, Wang Si-Wei, Tang Chang, Zhou Si-Hang, Wang Si-Qi, Liu Xin-Wang. Multi-view clustering with weighted anchors. Acta Automatica Sinica, 2024, 50(6): 1160?1170 doi: 10.16383/j.aas.c220531

              基于加權錨點(diǎn)的多視圖聚類(lèi)算法

              doi: 10.16383/j.aas.c220531
              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
              詳細信息
                作者簡(jiǎn)介:

                劉溯源:國防科技大學(xué)計算機學(xué)院碩士研究生. 主要研究方向為多視圖學(xué)習. E-mail: suyuanliu@nudt.edu.cn

                王思為:國防科技大學(xué)計算機學(xué)院博士研究生. 主要研究方向為無(wú)監督多視圖學(xué)習, 大規模聚類(lèi)和深度無(wú)監督學(xué)習. E-mail: wangsiwei13@nudt.edu.cn

                唐廠(chǎng):中國地質(zhì)大學(xué)計算機學(xué)院教授. 主要研究方向為多視圖學(xué)習. E-mail: tangchang@cug.edu.cn

                周思航:國防科技大學(xué)智能科學(xué)學(xué)院講師. 主要研究方向為機器學(xué)習, 醫學(xué)圖像分析. E-mail: sihangjoe@gmail.com

                王思齊: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)驗室助理研究員. 主要研究方向為機器學(xué)習, 異常檢測. 本文通信作者. E-mail: wangsiqi10c@gmail.com

                劉新旺:國防科技大學(xué)計算機學(xué)院教授. 主要研究方向為核學(xué)習, 無(wú)監督特征學(xué)習. E-mail: xinwangliu@nudt.edu.cn

              Multi-view Clustering With Weighted Anchors

              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)
              More Information
                Author Bio:

                LIU Su-Yuan Master student at the College of Computer, National University of Defense Technology. His main research interest is multi-view learning

                WANG Si-Wei Ph.D. candidate at the College of Computer, National University of Defense Technology. His research interest covers unsupervised multi-view learning, scalable clustering, and deep unsupervised learning

                TANG Chang Professor at the College of Computer, China University of Geosciences. His main research interest is multi-view learning

                ZHOU Si-Hang Lecturer at the College of Intelligent Science and Technology, National University of Defense Technology. His research interest covers machine learning and medical image analysis

                WANG Si-Qi Assistant professor at the State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology. His research interest covers machine learning and outlier/anomaly detection. Corresponding author of this paper

                LIU Xin-Wang Professor at the College of Computer, National University of Defense Technology. His research interest covers kernel learning and unsupervised feature learning

              • 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.
                1)  11 http://mkl.ucsd.edu/dataset/protein-fold-prediction/2 http://archive.ics.uci.edu/ml/datasets/Multiple+Features3 https://www.fruitfly.org/4 http://svcl.ucsd.edu/projects/crossmodal/5 https://www.ee.columbia.edu/ln/dvmm/CCV/6 http://staff.science.uva.nl/aloi/7 https://www.cs.tau.ac.il/wolf/ytfaces/
                2)  2http://archive.ics.uci.edu/ml/datasets/Multiple+Features
                3)  3https://www.fruitfly.org/
                4)  4http://svcl.ucsd.edu/projects/crossmodal/
                5)  5https://www.ee.columbia.edu/ln/dvmm/CCV/
                6)  6http://staff.science.uva.nl/aloi/
                7)  7https://www.cs.tau.ac.il/wolf/ytfaces/
              • 圖  1  4個(gè)數據集上學(xué)習到的錨點(diǎn)權重

                Fig.  1  Learned anchor weights on four datasets

                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
                下載: 導出CSV

                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
                下載: 導出CSV

                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
                下載: 導出CSV

                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
                下載: 導出CSV

                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
                下載: 導出CSV
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                        • 收稿日期:  2022-06-27
                        • 錄用日期:  2022-11-12
                        • 網(wǎng)絡(luò )出版日期:  2022-12-19
                        • 刊出日期:  2024-06-27

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