13 Theory of multidimensional scaling
作者： Jan de Leeuw , Willem Heiser
DOI: 10.1016/S0169-7161(82)02016-1
关键词: Discrete mathematics 、 Gauss 、 Mathematics 、 Kruskal's algorithm 、 Combinatorics 、 Multidimensional scaling
摘要: Publisher Summary This chapter discusses the theory of Multidimensional Scaling (MDS). MDS is quite old. The closely-related methods have been used by surveyors and geographers since Gauss, Kruskal has discovered a crude method in systematic zoology Boyden around 1930, algorithms for mapping chromosomes from crossing-over frequencies can already be found an interesting paper Fisher. development MDS, however, almost completely taken place psychometrics. first important contribution to not methods, probably Stumpf's (1880). broad sense includes various forms cluster analysis linear multivariate analysis. narrow sense, represents dissimilarity data low-dimensional space.
elsevier.com
sci-hub.se 参考文章(106)
J. Seidel, MATHEMATICSAngles and distances in N-dimensional euclidean and noneuclidean geometry. III Indagationes Mathematicae (Proceedings). ,vol. 58, ,(1955) , 10.1016/S1385-7258(55)50073-4
R. D. Luce, Detection and recognition Handbook of mathematical psychology. ,vol. 1, pp. 103- 189 ,(1963)
Samuel J. Messick, Some Recent Theoretical Developments in Multidimensional Scaling1 Educational and Psychological Measurement. ,vol. 16, pp. 82- 100 ,(1956) , 10.1177/001316445601600107
Leonard M. Blumenthal, Four-point properties and norm postulates Lecture Notes in Mathematics. pp. 1- 13 ,(1975) , 10.1007/BFB0081126
P. Lancaster, A Review of Numerical Methods for Eigenvalue Problems Nonlinear in the Parameter Numerik und Anwendungen von Eigenwertaufgaben und Verzweigungsproblemen. pp. 43- 67 ,(1977) , 10.1007/978-3-0348-5579-2_2
R. M. Cormack, A Review of Classification Journal of the Royal Statistical Society: Series A (General). ,vol. 134, pp. 321- 353 ,(1971) , 10.2307/2344237
Robin Sibson, Order Invariant Methods for Data Analysis Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 34, pp. 311- 338 ,(1972) , 10.1111/J.2517-6161.1972.TB00910.X
Erich Goldmeier, Über Ähnlichkeit bei gesehenen Figuren Psychologische Forschung. ,vol. 21, pp. 146- 208 ,(1937) , 10.1007/BF02441206
E. Andalafte, L. Blumenthal, Metric characterizations of Banach and Euclidean spaces Fundamenta Mathematicae. ,vol. 55, pp. 23- 55 ,(1964) , 10.4064/FM-55-1-23-55
Leonard Mascot Blumenthal, Theory and Applications of Distance Geometry ,(1970)