第3期 黄雨婷，等：三角距离相关性的标签分布学习 ·457· 函数基础的KL散度；3)利用新的距离映射函数 correlations and missing labels[Cl//Proceedings of the 表示标签的相关性。 28th AAAI Conference on Artificial Intelligence.Quebec City,Canada.2014:1680-1686 参考文献： [11]HUANG Shengjun,ZHOU Zhihua.Multi-label learning by exploiting label correlations locally[C]//Proceedings of [1]GENG Xin.Label distribution learning[J].IEEE transac- the 26th AAAI Conference on Artificial Intelligence tions on knowledge and data engineering,2016,28(7): Toronto,Canada,2012:949-955 17341748. [12]GENG Xin,WANG Qin,XIA Yu.Facial age estimation [2]JIA Xiuyi,ZHENG Xiang,LI Weiwei,et al.Facial emo- by adaptive label distribution learning[C]//Proceedings of tion distribution learning by exploiting low-rank label cor- the 22nd International Conference on Pattern Recognition. relations locally[C]//Proceedings of 2019 IEEE/CVF Con- Stockholm,Sweden,2014:4465-4470 ference on Computer Vision and Pattern Recognition. [13]ZHANG Zhaoxiang,WANG Mo,GENG Xin.Crowd Long Beach,USA,2019:9841-9850. counting in public video surveillance by label distribution [3]YANG Xu,GAO Binbin,XING Chao,et al.Deep label learning[J].Neurocomputing,2015,166:151-163. distribution learning for apparent age estimation[C]//Pro- [14]GENG Xin,YIN Chao,ZHOU Zhihua.Facial age estima- ceedings of 2015 IEEE International Conference on Com- tion by learning from label distributions[J].IEEE transac- puter Vision Workshops.Santiago,Chile,2015:102-108. tions on pattern analysis and machine intelligence,2013, [4]ZHANG Hengru,HUANG Yuting,XU Yuanyuan,et al. 35(10):2401-2412 COS-LDL:label distribution learning by cosine-based dis- [15]GENG Xin,LING Miaogen.Soft video parsing by tance-mapping correlation[J].IEEE access,2020,8: label distribution learning[C].Proceedings of the 31th 63961-63970. AAAI Conference on Artificial Intelligence.San Fran- [5]邵东恒，杨文元，赵红.应用k-means算法实现标记分布 cisco,USA,2017:1331-1337. 学习[).智能系统学报，2017,12(3)：325-332 [16]JIA Xiuyi,LI Weiwei,LIU Junyu,et al.Label distribu- SHAO Dongheng,YANG Wenyuan,ZHAO Hong.Label tion learning by exploiting label correlations[C]//Proceed- distribution learning based on k-means algorithm[J].CAAI ings of the 32nd AAAI Conference on Artificial Intelli- transactions on intelligent systems,2017,12(3):325-332. gence.New Orleans,USA,2018:3310-3317. [6]刘玉杰，唐顺静，高永标，等.基于标签分布学习的视频 [17]ZHENG Xiang,JIA Xiuyi,LI Weiwei.Label distribution 摘要算法「J刀.计算机轴助设计与图形学学报，2019. learning by exploiting sample correlations locally[Cl// 31(1):104110 Proceedings of the 32nd AAAI Conference on Artificial LIU Yujie.TANG Shunjing.,GAO Yongbiao,et al.Label Intelligence.New Orleans,USA,2018:4556-4563. distribution learning for video summarization[J].Journal of [18]KULLBACK S,LEIBLER R A.On information and suf- computer-aided design&computer graphics,2019,31(1): ficiency[J].The annals of mathematical statistics,1951, 104-110. 22(179-86. [7]王一宾，田文泉，程玉胜.基于标记分布学习的异态集成 [19]DANIELSSON P E.Euclidean distance mapping[J]. 学习算法[.模式识别与人工智能，2019,32(10)： Computer graphics and image processing,1980,14(3): 945-954 227-248. WANG Yibin,TIAN Wenquan,CHENG Yusheng.Het- [20]SORENSEN T.A method of establishing groups of equal erogeneous ensemble learning algorithm based on label amplitude in plant sociology based on similarity of spe- distribution learning[J].Pattern recognition and artificial cies content,and its application to analyses of the vegeta- intelligence,.2019,32(10):945-954. tion on Danish commons[J].Kongelige danske [8]耿新，徐宁.标记分布学习与标记增强).中国科学：信 videnskabernes selskab biologiske skrifter,1948,5(4): 息科学，2018,48(5：521-530. 1-34. GENG Xin,XU Ning.Label distribution learning and la- [21]GAVIN D G.OSWALD WW.WAHL E R.et al.A stat- bel enhancement[J].Scientia sinica informationis,2018, istical approach to evaluating distance metrics and analog 48(5):521-530. assignments for pollen records[J].Quaternary research, [9]ZHANG Mingling,ZHANG Kun.Multi-label learning by 2003,60(3):356-367. exploiting label dependency[C]//Proceedings of the 16th [22]DUDA R O.HART P E.STORK D G.Pattern classifica- ACM SIGKDD International Conference on Knowledge tion[M].2nd ed.New York:Wiley,2000. Discovery and Data Mining.Washington,USA,2010: [23]DEZA E,DEZA MM.Dictionary of distances[M].Ams- 999-1007. terdam:Elsevier,2006. [10]BI Wei,KWOK JT.Multilabel classification with label [24]JEGOU H.DOUZE M,SCHMID C.Hamming embed-函数基础的 KL 散度；3) 利用新的距离映射函数 表示标签的相关性。 参考文献： GENG Xin. Label distribution learning[J]. IEEE transac￾tions on knowledge and data engineering, 2016, 28(7): 1734–1748. [1] JIA Xiuyi, ZHENG Xiang, LI Weiwei, et al. Facial emo￾tion distribution learning by exploiting low-rank label cor￾relations locally[C]//Proceedings of 2019 IEEE/CVF Con￾ference on Computer Vision and Pattern Recognition. Long Beach, USA, 2019: 9841−9850. [2] YANG Xu, GAO Binbin, XING Chao, et al. Deep label distribution learning for apparent age estimation[C]//Pro￾ceedings of 2015 IEEE International Conference on Com￾puter Vision Workshops. Santiago, Chile, 2015: 102−108. [3] ZHANG Hengru, HUANG Yuting, XU Yuanyuan, et al. COS-LDL: label distribution learning by cosine-based dis￾tance-mapping correlation[J]. IEEE access, 2020, 8: 63961–63970. [4] 邵东恒, 杨文元, 赵红. 应用 k-means 算法实现标记分布 学习 [J]. 智能系统学报, 2017, 12(3): 325–332. SHAO Dongheng, YANG Wenyuan, ZHAO Hong. Label distribution learning based on k-means algorithm[J]. CAAI transactions on intelligent systems, 2017, 12(3): 325–332. [5] 刘玉杰, 唐顺静, 高永标, 等. 基于标签分布学习的视频 摘要算法 [J]. 计算机辅助设计与图形学学报, 2019, 31(1): 104–110. LIU Yujie, TANG Shunjing, GAO Yongbiao, et al. Label distribution learning for video summarization[J]. Journal of computer-aided design & computer graphics, 2019, 31(1): 104–110. [6] 王一宾, 田文泉, 程玉胜. 基于标记分布学习的异态集成 学习算法 [J]. 模式识别与人工智能, 2019, 32(10): 945–954. WANG Yibin, TIAN Wenquan, CHENG Yusheng. Het￾erogeneous ensemble learning algorithm based on label distribution learning[J]. Pattern recognition and artificial intelligence, 2019, 32(10): 945–954. [7] 耿新, 徐宁. 标记分布学习与标记增强 [J]. 中国科学: 信 息科学, 2018, 48(5): 521–530. GENG Xin, XU Ning. Label distribution learning and la￾bel enhancement[J]. Scientia sinica informationis, 2018, 48(5): 521–530. [8] ZHANG Mingling, ZHANG Kun. Multi-label learning by exploiting label dependency[C]//Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Washington, USA, 2010: 999−1007. [9] [10] BI Wei, KWOK J T. Multilabel classification with label correlations and missing labels[C]//Proceedings of the 28th AAAI Conference on Artificial Intelligence. Québec City, Canada, 2014: 1680−1686. HUANG Shengjun, ZHOU Zhihua. Multi-label learning by exploiting label correlations locally[C]//Proceedings of the 26th AAAI Conference on Artificial Intelligence. Toronto, Canada, 2012: 949−955. [11] GENG Xin, WANG Qin, XIA Yu. Facial age estimation by adaptive label distribution learning[C]//Proceedings of the 22nd International Conference on Pattern Recognition. Stockholm, Sweden, 2014: 4465−4470. [12] ZHANG Zhaoxiang, WANG Mo, GENG Xin. Crowd counting in public video surveillance by label distribution learning[J]. Neurocomputing, 2015, 166: 151–163. [13] GENG Xin, YIN Chao, ZHOU Zhihua. Facial age estima￾tion by learning from label distributions[J]. IEEE transac￾tions on pattern analysis and machine intelligence, 2013, 35(10): 2401–2412. [14] GENG Xin, LING Miaogen. Soft video parsing by label distribution learning[C]. Proceedings of the 31th AAAI Conference on Artificial Intelligence. San Fran￾cisco, USA, 2017: 1331−1337. [15] JIA Xiuyi, LI Weiwei, LIU Junyu, et al. Label distribu￾tion learning by exploiting label correlations[C]//Proceed￾ings of the 32nd AAAI Conference on Artificial Intelli￾gence. New Orleans, USA, 2018: 3310−3317. [16] ZHENG Xiang, JIA Xiuyi, LI Weiwei. Label distribution learning by exploiting sample correlations locally[C]// Proceedings of the 32nd AAAI Conference on Artificial Intelligence. New Orleans, USA, 2018: 4556−4563. [17] KULLBACK S, LEIBLER R A. On information and suf￾ficiency[J]. The annals of mathematical statistics, 1951, 22(1): 79–86. [18] DANIELSSON P E. Euclidean distance mapping[J]. Computer graphics and image processing, 1980, 14(3): 227–248. [19] SØRENSEN T. A method of establishing groups of equal amplitude in plant sociology based on similarity of spe￾cies content, and its application to analyses of the vegeta￾tion on Danish commons[J]. Kongelige danske videnskabernes selskab biologiske skrifter, 1948, 5(4): 1–34. [20] GAVIN D G, OSWALD W W, WAHL E R, et al. A stat￾istical approach to evaluating distance metrics and analog assignments for pollen records[J]. Quaternary research, 2003, 60(3): 356–367. [21] DUDA R O, HART P E, STORK D G. Pattern classifica￾tion[M]. 2nd ed. New York: Wiley, 2000. [22] DEZA E, DEZA M M. Dictionary of distances[M]. Ams￾terdam: Elsevier, 2006. [23] [24] JEGOU H, DOUZE M, SCHMID C. Hamming embed- 第 3 期 黄雨婷，等：三角距离相关性的标签分布学习 ·457·