多元L1中位数及相关数据深度。
The multivariate L1-median and associated data depth.
作者信息
Vardi Y, Zhang C H
机构信息
Department of Statistics, Rutgers University, New Brunswick, NJ 08854, USA.
出版信息
Proc Natl Acad Sci U S A. 2000 Feb 15;97(4):1423-6. doi: 10.1073/pnas.97.4.1423.
Abstract
This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-median of a data cloud in Rd, a problem that can be traced to Fermat and has fascinated applied mathematicians for over three centuries; (ii) a new general definition for depth functions, as functions of multivariate medians, so that different definitions of medians will, correspondingly, give rise to different dept functions; and (iii) a simple closed-form formula of the L1-depth function for a given data cloud in Rd.
摘要
本文给出了三个相关结果
（i）一种用于推导(R^d)中数据云的(L1)中位数的新的、简单、快速且单调收敛的算法，该问题可追溯到费马，并且在三个多世纪以来一直吸引着应用数学家；（ii）深度函数的一个新的通用定义，作为多元中位数的函数，这样中位数的不同定义将相应地产生不同的深度函数；以及（iii）对于(R^d)中给定数据云的(L1)深度函数的一个简单的封闭形式公式。
相似文献
1
The multivariate L1-median and associated data depth.多元L1中位数及相关数据深度。
Proc Natl Acad Sci U S A. 2000 Feb 15;97(4):1423-6. doi: 10.1073/pnas.97.4.1423.
2
Machine learning-based coding unit depth decisions for flexible complexity allocation in high efficiency video coding.基于机器学习的编码单元深度决策，用于高效视频编码中的灵活复杂度分配。
IEEE Trans Image Process. 2015 Jul;24(7):2225-38. doi: 10.1109/TIP.2015.2417498.
3
L1/2 regularization: a thresholding representation theory and a fast solver.L1/2 正则化：一种阈值表示理论和快速求解器。
IEEE Trans Neural Netw Learn Syst. 2012 Jul;23(7):1013-27. doi: 10.1109/TNNLS.2012.2197412.
4
Immunohistochemical Mapping of Sensory Nerve Endings in the Human Triangular Fibrocartilage Complex.人三角纤维软骨复合体中感觉神经末梢的免疫组织化学定位
Clin Orthop Relat Res. 2015 Oct;473(10):3245-53. doi: 10.1007/s11999-015-4357-z. Epub 2015 May 30.
5
Curve of Spee and its relationship to vertical eruption of teeth among different malocclusion groups.司皮曲线及其与不同错牙合畸形组牙齿垂直萌出的关系。
Am J Orthod Dentofacial Orthop. 2015 Mar;147(3):305-12. doi: 10.1016/j.ajodo.2014.10.031.
6
On a notion of simplicial depth.关于单纯形深度的一个概念。
Proc Natl Acad Sci U S A. 1988 Mar;85(6):1732-4. doi: 10.1073/pnas.85.6.1732.
7
Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms.使用分区可分离抛物面替代坐标上升算法的图像恢复
IEEE Trans Image Process. 2002;11(3):306-17. doi: 10.1109/83.988963.
8
Prediction of Postoperative Intraocular Lens Position with Angle-to-Angle Depth Using Anterior Segment Optical Coherence Tomography.应用前节 OCT 测量眼前节角度至角度的深度预测术后人工晶状体位置。
Ophthalmology. 2016 Dec;123(12):2474-2480. doi: 10.1016/j.ophtha.2016.09.005. Epub 2016 Oct 18.
9
Using median sets for inferring phylogenetic trees.使用中位数集推断系统发育树。
Bioinformatics. 2007 Jan 15;23(2):e129-35. doi: 10.1093/bioinformatics/btl300.
10
On the taxonomy of optimization problems under estimation of distribution algorithms.基于分布估计算法的优化问题分类。
Evol Comput. 2013 Fall;21(3):471-95. doi: 10.1162/EVCO_a_00095. Epub 2013 Jun 19.
引用本文的文献
1
High-throughput iNaturalist image analysis reveals flower color divergence in .高通量iNaturalist图像分析揭示了……中的花色差异。 （原文中“in”后面缺少具体内容）
bioRxiv. 2025 May 26:2025.05.21.655392. doi: 10.1101/2025.05.21.655392.
2
On the Wasserstein Median of Probability Measures.关于概率测度的瓦瑟斯坦中位数
J Comput Graph Stat. 2025;34(1):253-266. doi: 10.1080/10618600.2024.2374580. Epub 2024 Aug 29.
3
Methods for Brain Connectivity Analysis with Applications to Rat Local Field Potential Recordings.用于脑连接性分析的方法及其在大鼠局部场电位记录中的应用
Entropy (Basel). 2025 Mar 21;27(4):328. doi: 10.3390/e27040328.
4
High-dimensional multivariate analysis of variance via geometric median and bootstrapping.基于几何中位数和自举法的高维多元方差分析。
Biometrics. 2024 Jul 1;80(3). doi: 10.1093/biomtc/ujae088.
5
Doubly elastic net regularized online portfolio optimization with transaction costs.带交易成本的双弹性网络正则化在线投资组合优化
Sci Rep. 2023 Nov 2;13(1):18937. doi: 10.1038/s41598-023-46059-2.
6
Application of a maximal-clique based community detection algorithm to gut microbiome data reveals driver microbes during influenza A virus infection.将基于最大团的社区检测算法应用于肠道微生物组数据，揭示甲型流感病毒感染期间的驱动微生物。
Front Microbiol. 2022 Oct 20;13:979320. doi: 10.3389/fmicb.2022.979320. eCollection 2022.
7
The Mouse Action Recognition System (MARS) software pipeline for automated analysis of social behaviors in mice.鼠标动作识别系统（MARS）软件流水线，用于自动分析小鼠的社交行为。
Elife. 2021 Nov 30;10:e63720. doi: 10.7554/eLife.63720.
8
Band-based similarity indices for gene expression classification and clustering.基于带的基因表达分类和聚类相似性指数。
Sci Rep. 2021 Nov 3;11(1):21609. doi: 10.1038/s41598-021-00678-9.
9
A depth-based global envelope test for comparing two groups of functions with applications to biomedical data.一种基于深度的全局包络测试方法，用于比较两组函数，在生物医学数据中有应用。
Stat Med. 2021 Mar 30;40(7):1639-1652. doi: 10.1002/sim.8861. Epub 2021 Jan 6.
10
Machine Learning Representation of Loss of Eye Regularity in a Neurodegenerative Model.神经退行性模型中眼部规则性丧失的机器学习表征
Front Neurosci. 2020 Jun 4;14:516. doi: 10.3389/fnins.2020.00516. eCollection 2020.
Zotero 插件