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              基于加權錨點的多視圖聚類算法

              劉溯源 王思為 唐廠 周思航 王思齊 劉新旺

              劉溯源, 王思為, 唐廠, 周思航, 王思齊, 劉新旺. 基于加權錨點的多視圖聚類算法. 自動化學報, 2024, 50(6): 1000?1010 doi: 10.16383/j.aas.c220531
              引用本文: 劉溯源, 王思為, 唐廠, 周思航, 王思齊, 劉新旺. 基于加權錨點的多視圖聚類算法. 自動化學報, 2024, 50(6): 1000?1010 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): 1000?1010 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): 1000?1010 doi: 10.16383/j.aas.c220531

              基于加權錨點的多視圖聚類算法

              doi: 10.16383/j.aas.c220531
              基金項目: 國家自然科學基金(61922088, 62006236, 62006237), 國防科技大學科研計劃項目(ZK21-23, ZK20-10), 高性能計算國家重點實驗室自主課題(202101-15)資助
              詳細信息
                作者簡介:

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

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

                唐廠:中國地質大學計算機學院教授. 主要研究方向為多視圖學習. E-mail: tangchang@cug.edu.cn

                周思航:國防科技大學智能科學學院講師. 主要研究方向為機器學習, 醫學圖像分析. E-mail: sihangjoe@gmail.com

                王思齊:國防科技大學計算機學院高性能計算國家重點實驗室助理研究員. 主要研究方向為機器學習, 異常檢測. 本文通信作者. E-mail: wangsiqi10c@gmail.com

                劉新旺:國防科技大學計算機學院教授. 主要研究方向為核學習, 無監督特征學習. 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 soutlier/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: 大規模多視圖聚類旨在解決傳統多視圖聚類算法中計算速度慢、空間復雜度高, 以致無法擴展到大規模數據的問題. 其中, 基于錨點的多視圖聚類方法通過使用整體數據集合的錨點集構建后者對于前者的重構矩陣, 利用重構矩陣進行聚類, 有效地降低了算法的時間和空間復雜度. 然而, 現有的方法忽視了錨點之間的差異, 均等地看待所有錨點, 導致聚類結果受到低質量錨點的限制. 為定位更具有判別性的錨點, 加強高質量錨點對聚類的影響, 提出一種基于加權錨點的大規模多視圖聚類算法(Multi-view clustering with weighted anchors, MVC-WA). 通過引入自適應錨點加權機制, 所提方法在統一框架下確定錨點的權重, 進行錨圖的構建. 同時, 為增加錨點的多樣性, 根據錨點之間的相似度進一步調整錨點的權重. 在9個基準數據集上與現有最先進的大規模多視圖聚類算法的對比實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個數據集上學習到的錨點權重

                Fig.  1  Learned anchor weights on four datasets

                圖  2  目標函數值隨迭代次數增長的變化曲線

                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
                $n$ 數據點數量
                $k$ 類別數
                $v$ 視圖數
                $m$ 錨點數
                $d^{(p)}$ 第$p$個視圖上數據的維度
                ${\boldsymbol{X}}^{(p)} \in \mathbf{R}^{d^{(p)} \times n}$ 第$p$個視圖的數據矩陣
                ${\boldsymbol{A}}^{(p)} \in \mathbf{R}^{d^{(p)} \times m}$ 第$p$個視圖的錨點矩陣
                ${\boldsymbol{Z}}^{(p)} \in \mathbf{R}^{m \times n}$ 第$p$個視圖上的錨圖
                ${\boldsymbol{W}}^{(p)} \in \mathbf{R}^{m \times m}$ 第$p$個視圖上的權重矩陣
                ${\boldsymbol{M}}^{(p)} \in \mathbf{R}^{m \times m}$ 第$p$個視圖上錨點的相關性矩陣
                下載: 導出CSV

                表  2  實驗中使用的數據集

                Table  2  Description of datasets

                數據集 樣本數 視圖數 類別數
                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±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 0.00 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±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
                Fscore
                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  消融實驗結果 (%)

                Table  5  Results of ablation experiments (%)

                聚類指標 對比方法 數據集
                ProteinFold Mfeat BDGP Wiki CCV ALOI YTF10 YTF20
                ACC 最優單視圖 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
                Fscore 最優單視圖 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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                        出版歷程
                        • 收稿日期:  2022-06-27
                        • 錄用日期:  2022-11-12
                        • 網絡出版日期:  2022-12-19

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