矩阵瓦瑟斯坦-1距离
Matricial Wasserstein-1 Distance.
作者信息
Chen Yongxin, Georgiou Tryphon T, Ning Lipeng, Tannenbaum Allen
机构信息
Department of Medical Physics, Memorial Sloan Kettering Cancer Center, NY.
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA.
出版信息
IEEE Control Syst Lett. 2017 Jul;1(1):14-19. doi: 10.1109/LCSYS.2017.2699319. Epub 2017 Apr 28.
Abstract
We propose an extension of the Wasserstein 1-metric () for density matrices, matrix-valued density measures, and an unbalanced interpretation of mass transport. We use duality theory and, in particular, a "dual of the dual" formulation of . This matrix analogue of the Earth Mover's Distance has several attractive features including ease of computation.
摘要
我们提出了一种针对密度矩阵、矩阵值密度测度的Wasserstein 1-度量（）的扩展，以及质量传输的非平衡解释。我们使用对偶理论，特别是 的一种“对偶的对偶”公式。这种地球移动距离的矩阵类似物具有几个吸引人的特性，包括易于计算。
相似文献
1
Matricial Wasserstein-1 Distance.矩阵瓦瑟斯坦-1距离
IEEE Control Syst Lett. 2017 Jul;1(1):14-19. doi: 10.1109/LCSYS.2017.2699319. Epub 2017 Apr 28.
2
Ocean mover's distance: using optimal transport for analysing oceanographic data.海洋移动距离：运用最优传输分析海洋学数据
Proc Math Phys Eng Sci. 2022 Jun;478(2262):20210875. doi: 10.1098/rspa.2021.0875. Epub 2022 Jun 22.
3
EMBEDDING SIGNALS ON GRAPHS WITH UNBALANCED DIFFUSION EARTH MOVER'S DISTANCE.使用非平衡扩散推土机距离在图上嵌入信号
Proc IEEE Int Conf Acoust Speech Signal Process. 2022 May;2022:5647-5651. doi: 10.1109/icassp43922.2022.9746556. Epub 2022 Apr 27.
4
Nonnegative Matrix Factorization with Earth Mover's Distance Metric for Image Analysis.基于 Earth Mover's Distance Metric 的非负矩阵分解在图像分析中的应用。
IEEE Trans Pattern Anal Mach Intell. 2011 Aug;33(8):1590-602. doi: 10.1109/TPAMI.2011.18. Epub 2011 Jan 28.
5
An efficient Earth Mover's Distance algorithm for robust histogram comparison.一种用于稳健直方图比较的高效推土机距离算法。
IEEE Trans Pattern Anal Mach Intell. 2007 May;29(5):840-53. doi: 10.1109/TPAMI.2007.1058.
6
On Matrix-Valued Monge-Kantorovich Optimal Mass Transport.关于矩阵值蒙日 - 康托罗维奇最优质量传输
IEEE Trans Automat Contr. 2015 Feb;60(2):373-382. doi: 10.1109/TAC.2014.2350171. Epub 2014 Aug 21.
7
The earth mover's distance and Bayesian linear discriminant analysis for epileptic seizure detection in scalp EEG.用于头皮脑电图中癫痫发作检测的推土机距离和贝叶斯线性判别分析
Biomed Eng Lett. 2018 Aug 11;8(4):373-382. doi: 10.1007/s13534-018-0082-3. eCollection 2018 Nov.
8
On the Definiteness of Earth Mover's Distance and Its Relation to Set Intersection.关于 Earth Mover's Distance 的确定性及其与集合交集的关系。
IEEE Trans Cybern. 2018 Nov;48(11):3184-3196. doi: 10.1109/TCYB.2017.2761798. Epub 2017 Oct 30.
9
Spatial and Texture Analysis of Root System distribution with Earth mover's Distance (STARSEED).基于推土机距离的根系分布空间与纹理分析（STARSEED）
Plant Methods. 2023 Jan 5;19(1):2. doi: 10.1186/s13007-022-00974-z.
10
Aggregated Wasserstein Distance and State Registration for Hidden Markov Models.隐马尔可夫模型的聚合瓦瑟斯坦距离与状态配准
IEEE Trans Pattern Anal Mach Intell. 2020 Sep;42(9):2133-2147. doi: 10.1109/TPAMI.2019.2908635. Epub 2019 Apr 1.
引用本文的文献
1
Smooth interpolation of covariance matrices and brain network estimation: Part II.协方差矩阵的平滑插值与脑网络估计：第二部分。
IEEE Trans Automat Contr. 2020 May;65(5):1901-1910. doi: 10.1109/TAC.2019.2926854. Epub 2019 Jul 4.
本文引用的文献
1
Robust transport over networks.网络上的稳健传输。
IEEE Trans Automat Contr. 2017 Sep;62(9):4675-4682. doi: 10.1109/TAC.2016.2626796. Epub 2016 Nov 9.
2
Pediatric Sarcoma Data Forms a Unique Cluster Measured via the Earth Mover's Distance.儿科肉瘤数据通过大地移动距离形成独特的聚类。
Sci Rep. 2017 Aug 1;7(1):7035. doi: 10.1038/s41598-017-07551-8.
3
Ricci curvature: An economic indicator for market fragility and systemic risk.Ricci 曲率：市场脆弱性和系统性风险的经济指标。
Sci Adv. 2016 May 27;2(5):e1501495. doi: 10.1126/sciadv.1501495. eCollection 2016 May.
4
On Matrix-Valued Monge-Kantorovich Optimal Mass Transport.关于矩阵值蒙日 - 康托罗维奇最优质量传输
IEEE Trans Automat Contr. 2015 Feb;60(2):373-382. doi: 10.1109/TAC.2014.2350171. Epub 2014 Aug 21.
5
Graph Curvature for Differentiating Cancer Networks.用于区分癌症网络的图形曲率
Sci Rep. 2015 Jul 14;5:12323. doi: 10.1038/srep12323.
6
Optical flow estimation for flame detection in videos.视频中火焰检测的光流估计。
IEEE Trans Image Process. 2013 Jul;22(7):2786-97. doi: 10.1109/TIP.2013.2258353. Epub 2013 Apr 16.
Zotero 插件