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                    生成式不完整多視圖數據聚類

                    趙博宇 張長青 陳蕾 劉新旺 李澤超 胡清華

                    趙博宇,  張長青,  陳蕾,  劉新旺,  李澤超,  胡清華.  生成式不完整多視圖數據聚類.  自動化學報,  2021,  47(8): 1867?1875 doi: 10.16383/j.aas.c200121
                    引用本文: 趙博宇,  張長青,  陳蕾,  劉新旺,  李澤超,  胡清華.  生成式不完整多視圖數據聚類.  自動化學報,  2021,  47(8): 1867?1875 doi: 10.16383/j.aas.c200121
                    Zhao Bo-Yu,  Zhang Chang-Qing,  Chen Lei,  Liu Xin-Wang,  Li Ze-Chao,  Hu Qing-Hua.  Generative model for partial multi-view clustering.  Acta Automatica Sinica,  2021,  47(8): 1867?1875 doi: 10.16383/j.aas.c200121
                    Citation: Zhao Bo-Yu,  Zhang Chang-Qing,  Chen Lei,  Liu Xin-Wang,  Li Ze-Chao,  Hu Qing-Hua.  Generative model for partial multi-view clustering.  Acta Automatica Sinica,  2021,  47(8): 1867?1875 doi: 10.16383/j.aas.c200121

                    生成式不完整多視圖數據聚類

                    doi: 10.16383/j.aas.c200121
                    基金項目: 國家自然科學基金(61976151, 61732011, 61872190), 南京郵電大學江蘇省大數據安全與智能處理重點實驗室資助
                    詳細信息
                      作者簡介:

                      趙博宇:天津大學智能與計算學部碩士研究生. 主要研究方向為多視圖學習. E-mail: boyuzhao@tju.edu.cn

                      張長青:天津大學智能與計算學部副教授. 主要研究方向為機器學習, 模式識別. 本文通信作者. E-mail: zhangchangqing@tju.edu.cn

                      陳蕾:南京郵電大學計算機學院教授. 主要研究方向為人工智能, 機器學習及數據挖掘應用. E-mail: chenlei@njupt.edu.cn

                      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, 特征選擇, 譜聚類和隱變量學習. E-mail: 1022xinwang.liu@gmail.com

                      李澤超:南京理工大學計算機科學與工程學院教授. 主要研究方向為大媒體分析, 計算機視覺. E-mail: zechao.li@njust.edu.cn

                      胡清華:天津大學智能與計算學部教授. 主要研究方向為多模態學習, 度量學習, 模糊集不確定性建模與推理, 粗糙集和概率論. E-mail: huqinghua@tju.edu.cn

                    • 1 http://cvc.yale.edu/projects/yalefacesB/yalefacesB.html2 http://www.uk.research.att.com/facedatabase.html3 http://www.cs.columbia.edu/CAVE/software/softlib/4 http://mlg.ucd.ie/datasets/
                    • 2http://www.uk.research.att.com/facedatabase.html
                    • 3http://www.cs.columbia.edu/CAVE/software/softlib/
                    • 4http://mlg.ucd.ie/datasets/

                    Generative Model For Partial Multi-view Clustering

                    Funds: Supported by National Natural Science Foundation of China (61976151, 61732011, 61872190), Jiangsu Key Laboratory of Big Data Security & Intelligent Processing, Nanjing University of Posts and Telecommunications
                    More Information
                      Author Bio:

                      ZHAO Bo-Yu Master student at the College of Intelligence and Computing, Tianjin University. His main research interest is multi-view learning

                      ZHANG Chang-Qing Associate professor at the College of Intelligence and Computing, Tianjin University. His research interest covers machine learning and pattern recognition. Corresponding author of this paper

                      CHEN Lei Professor at the School of Computer Science, Nanjing University of Posts and Telecommunications. His research interest covers application of artificial intelligence, machine learning and data mining

                      LIU Xin-Wang Professor at the School of Computer, National University of Defense Technology. His research interest covers kernel learning, feature selection, spectral clustering and latent variable learning

                      LI Ze-Chao Professor at the School of Computer Science and Engineering, Nanjing University of Science and Technology. His research interest covers big media analysis and computer vision

                      HU Qing-Hua Professor at the College of Intelligence and Computing, Tianjin University. His research interest covers multi-modality learning, metric learning, uncertainty modeling and reasoning with fuzzy sets, rough sets and probability theory

                    • 摘要:

                      基于自表示子空間聚類的多視圖聚類引起越來越多的關注. 大多數現有算法假設每個樣本的所有視圖都可獲得, 然而在實際應用中, 由于各種因素, 可能會導致某些視圖缺失. 為了對視圖不完整數據進行聚類, 本文提出了一種在統一框架下同時執行缺失視圖補全和多視圖子空間聚類的方法. 具體地, 缺失視圖是由已觀測視圖數據約束的隱表示生成的. 此外, 多秩張量應用于挖掘不同視圖之間的高階相關性. 這樣通過隱表示和高階張量同時挖掘了不同視圖以及所有樣本(即使是不完整視圖樣本)之間的相關性. 本文使用增廣拉格朗日交替方向最小化(AL-ADM)方法求解優化問題. 在真實數據集上的實驗結果表明, 我們的方法優于最新的多視圖聚類算法, 具有更好的聚類準確度和魯棒性.

                      1)  1 http://cvc.yale.edu/projects/yalefacesB/yalefacesB.html2 http://www.uk.research.att.com/facedatabase.html3 http://www.cs.columbia.edu/CAVE/software/softlib/4 http://mlg.ucd.ie/datasets/
                      2)  2http://www.uk.research.att.com/facedatabase.html
                      3)  3http://www.cs.columbia.edu/CAVE/software/softlib/
                      4)  4http://mlg.ucd.ie/datasets/
                    • 圖  1  同時用$P(X|H)$對隱空間$H$進行建模, 并基于隱表示生成完整特征. 根據完整的數據, GM-PMVC將子空間表示集成到一個張量中, 可以挖掘多視圖數據高階相關性

                      Fig.  1  Illustration of generative model for partial multi-view clustering (GM-PMVC). Given incomplete multi-view data, we simultaneously model latent space $H$ by $P(X|H)$ and generate complete feature based on latent representation. According to the completed data, GM-PMVC integrates subspace representation into a tensor which can effectively explores higher-order correlations equipped with low-rank constraint

                      圖  2  在四個數據集上不同缺失率的準確度(ACC)和歸一化互信息(NMI) (平均值 ± 標準差)

                      Fig.  2  Results (mean ± std) in terms of accuracy and NMI on four datasets with different missing rate

                      圖  3  YaleB數據集上缺失率為10 %時的模型分析: (a) 參數調整對NMI指標的影響; (b)迭代過程中的收斂條件數值和聚類指數曲線(收斂條件數值已歸一化)

                      Fig.  3  Model analysis on YaleB with missing rate: 10 %: (a) Performence with parameter tuning; (b) Convergence and clustering index curves during iteration (convergence values are normlized)

                      表  1  符號與定義

                      Table  1  Notations and definitions

                      $b$ 標量 $B$ 矩陣
                      ${\boldsymbol}$ 向量 ${\cal{B}}$ 張量
                      ${\cal{I}}$ 單位張量 $fft$ 快速傅里葉變換
                      ${\cal{B}}_{ijk}$ 張量${\cal{B}}$第$(i,j,k)$元素 ${\cal{Q}}$ 正交張量
                      ${\cal{B}}(i,:,:)$ 第$i$水平切片 ${\cal{B}}^{\rm T}$ ${\cal{B}}$的轉置
                      ${\cal{B}}(:,i,:)$ 第$i$側面切片 ${\cal{B}}_{f}$ $fft({\cal{B}},[],3)$
                      ${\cal{B}}(:,:,i)$ 第$i$正面切片 $B^{(i)}$ ${\cal{B}}(:,:,i)$
                      $||B||_{F}$ $\sqrt{\sum\nolimits_{i,j}|B_{ij}|^{2}}$ $||B||_{*}$ 矩陣$B$奇異值之和
                      $||{\cal{B}}||_{F}$ $\sqrt{\sum\nolimits_{i,j,k}|{\cal{B}}_{ijk}|^{2}}$ $||{\cal{B}}||_{1}$ $\sum\nolimits_{i,j,k}|{\cal{B}}_{ijk}|$
                      下載: 導出CSV

                      表  2  算法運行時間對比(秒)

                      Table  2  Algorithm running time comparison (s)

                      Algorithms ORL yaleB
                      MIC 84.67 143.30
                      IMG 83.02 169.38
                      PVC 120.68 404.82
                      DAIMC 157.76 191.27
                      SRLCs 93.21 193.36
                      t-SVD-MSC 56.77 107.03
                      Ours 180.90 288.50
                      下載: 導出CSV
                      360彩票
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                    • 收稿日期:  2020-03-11
                    • 錄用日期:  2020-05-03
                    • 網絡出版日期:  2021-02-01
                    • 刊出日期:  2021-08-20

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