Weighted Euclidean Biplots
| Autor: | Michael Greenacre, Patrick J. F. Groenen |
|---|---|
| Přispěvatelé: | Econometrics |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
0106 biological sciences
Biplot correspondence analysis Distance majorization multidimensional scaling singular-value decomposition weighted least squares Biplot jel:C88 Library and Information Sciences 010603 evolutionary biology 01 natural sciences Data matrix (multivariate statistics) Combinatorics Euclidean distance 010104 statistics & probability Mathematics (miscellaneous) jel:C19 Principal component analysis Singular value decomposition Psychology (miscellaneous) Multidimensional scaling 0101 mathematics Statistics Probability and Uncertainty Stress majorization Algorithm Mathematics Principal axis theorem |
| Zdroj: | Journal of Classification, 33, 442-459. Springer New York |
| ISSN: | 1432-1343 0176-4268 |
| Popis: | We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, our approach leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots, we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|