Weighted Bidimensional Regression. 加权二维回归
2011; Wiley; Volume: 43; Issue: 1 Linguagem: Inglês
10.1111/j.1538-4632.2010.00805.x
ISSN1538-4632
AutoresKendra K. Schmid, David B. Marx, Ashok Samal,
Tópico(s)Genetic and phenotypic traits in livestock
ResumoGeographical AnalysisVolume 43, Issue 1 p. 1-13 Weighted Bidimensional Regression. 加权二维回归 Kendra K. Schmid, Kendra K. Schmid Department of Biostatistics, College of Public Health, University of Nebraska Medical Center, Omaha, NESearch for more papers by this authorDavid B. Marx, David B. Marx Department of Statistics, University of Nebraska-Lincoln, Lincoln, NESearch for more papers by this authorAshok Samal, Ashok Samal Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, NESearch for more papers by this author Kendra K. Schmid, Kendra K. Schmid Department of Biostatistics, College of Public Health, University of Nebraska Medical Center, Omaha, NESearch for more papers by this authorDavid B. Marx, David B. Marx Department of Statistics, University of Nebraska-Lincoln, Lincoln, NESearch for more papers by this authorAshok Samal, Ashok Samal Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, NESearch for more papers by this author First published: 04 January 2011 https://doi.org/10.1111/j.1538-4632.2010.00805.xCitations: 3 Kendra K. Schmid, Department of Biostatistics, College of Public Health, University of Nebraska Medical Center, Omaha, NE 68198-4375e-mail: [email protected] Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstracten Shape analysis is useful for a wide variety of disciplines and has many applications. One of the many approaches to shape analysis focuses on shapes that are represented by predefined landmarks on an object. Some landmarks may be measured with greater precision, exhibit more natural variation, or be more important than others to an analysis. This article introduces a method for including this information when estimating mapping relations or assessing the degree of similarity between two objects that are represented by a set of two-dimensional landmarks. Weighted bidimensional regression combines aspects of weighted least squares regression and bidimensional regression as a way to weight variables that are represented by a set of two-dimensional spatial coordinates. One possible weighting scheme is suggested, and the effect of weighting is demonstrated through a face-matching application. Results indicate that appropriate weighting increases the ability to correctly match two faces and that weighting has the largest effect when used with a projective transformation. Abstractes El análisis de formas (shape anlysis) es útil y aplicable a una amplia variedad de disciplinas y aplicaciones. Uno de los muchos enfoques para dicho análisis se centra en las formas que están representadas por puntos de referencia predefinidos en un objeto. No todos los puntos de referencia son iguales: unos pueden medirse con mayor precisión, otros presentan una mayor variación natural, y algunos pueden ser más importantes que dependiendo del tipo análisis a realizarse. Este artículo presenta un método para incluir esta información en la estimación de relaciones de mapeo o evaluar el grado de similitud entre dos objetos que están representados por un conjunto de puntos de referencia en dos dimensiones. La regresión ponderada bidimensional combina aspectos de una regresión por mínimos cuadrados ponderados (weighted least square regression), y una regresión bidimensional (bidimensional regression), las cuales sirven como estrategias de ponderar variables que están representados por un conjunto de coordenadas espaciales en dos dimensiones. El artículo propone el uso de un sistema de ponderación y demuestra el efecto de la ponderación en una aplicación de emparejamiento (face-matching) Los resultados indican que la selección de una ponderación adecuada aumenta la capacidad del modelo para emparejar correctamente y que la ponderación tiene el mayor efecto cuando se usa con una transformación proyectiva (projective transformation). Abstractzh 形态分析在多个学科中得到了广泛的应用。形态分析的诸多方法之一是关注对象上预标定标记所表征的形状特征。一些可能具有更高观测精度的标记,可更好地揭示目标对象的自身变化,或者相对于其他方面对分析更为重要。本文引入一种对一组二维标记表达的两对象,可包含标定信息的空间关系估计或相似性度量新方法。加权二维回归法整合了最小二乘加权回归和二元回归对变量进行加权,并利用一组二维空间坐标描述加权变量。论文提出了一种可能的加权模式,并利用面匹配应用演示了加权的效果。结果显示,合理的权重有助于增加两个面匹配的正确率,经投影变换后其权重效应最大。 References Bates, D. M., and D. G. Watts. (1988). Nonlinear Regression Analysis and Its Applications. New York: Wiley. Campbell, J. (1998). Map Use and Analysis, 3rd ed. Boston: WCB/McGraw-Hill. Conover, W. J. (1999). Practical Nonparametric Statistics, 3rd ed. New York: Wiley. Dent, B. D. (1993). Cartography: Thematic Map Design, 3rd ed. Dubuque, IA: Wm. C. Brown Publishers. Draper, N. R., and H. Smith. (1998). Applied Regression Analysis, 3rd ed. New York: Wiley. Dryden, I. L., and K. B. Mardia. (1998). Statistical Shape Analysis. New York: Wiley. Foley, J. D., A. van Dam, S. K. Feiner, and J. F. Hughes. (1995). Computer Graphics: Principles and Practice in C, 2nd ed. Boston: Addison-Wesley. Friedman, A., and B. Kohler. (2003). "Bidimensional Regression: Assessing the Configural Similarity and Accuracy of Cognitive Maps and Other Two-Dimensional Data Sets. Psychological Methods 8 (4), 468–91. Greene, W. H. (1997). Econometric Analysis, 3rd ed. Upper Saddle River, NJ: Prentice-Hall. Iman, R. L. (1974). "Use of a t-Statistic as an Approximation to the Exact Distribution of the Wilcoxon Signed Ranks Test Statistic. Communications in Statistics 3, 795–806. Kare, S., A. Samal, and D. Marx. (2008). "Using Bidimensional Regression to Assess Face Similarity. Machine Vision and Applications 21, 261–74. Nakaya, T. (1997). "Statistical Inferences in Bidimensional Regression Models. Geographical Analysis 29, 169–86. Phillips, P. J., H. Moon, S. A. Rizvi, and P. J. Rauss. (2000). "The FERET Evaluation Methodology for Face-Recognition Algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence 22, 1090–104. Schmid, K., D. Marx, and A. Samal. (2007). "Tridimensional Regression." In Proceedings of the Kansas State University Conference on Applied Statistics in Agriculture, Manhattan, KS, April 2007. Shi, J., A. Samal, and D. Marx. (2005). "Face Recognition Using Landmark-based Bidimensional Regression." In IEEE Computer Society Proceedings on Data Mining, Houston, TX, November 2005, 765–68. Shi, J., A. Samal, and D. Marx. (2006). "How Effective Are Landmarks and Their Geometry for Face Recognition? Computer Vision and Image Understanding 102, 117–33. Symington, A., M. E. Charlton, and C. F. Brunsdon. (2002). "Using Bidimensional Regression to Explore Map Lineage. Computers, Environment and Urban Systems 26, 201–18. Tobler, W. (1994). "Bidimensional Regression. Geographical Analysis 26, 187–212. Citing Literature Volume43, Issue1January 2011Pages 1-13 ReferencesRelatedInformation
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