Abstract
Local formalism deals with weighted unoriented networks, specified by an exchange matrix, determining the selection probabilities of pairs of vertices. It permits to define local inertia and local autocorrelation relatively to arbitrary networks. In particular, free partitioned exchanges amount in defining a categorical variable (hard membership), together with canonical spectral scores, identical to Fisher’s discriminant functions. One demonstrates how to extend the construction of the latter to any unoriented network, and how to assess the similarity between canonical and original configurations, as illustrated on four datasets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bavaud, F. (2008). Local concentrations. Papers in Regional Science, 87, 357–370.
Bavaud, F. (2010). Euclidean distances, soft and spectral clustering on weighted graphs. In Proceedings of the ECML PKDD’10. Lecture notes in computer science (Vol. 6321, pp. 103–118). Berlin: Springer.
Bavaud, F. (2013). Testing spatial autocorrelation in weighted networks: The modes permutation test. Journal of Geographical Systems, 15, 233–247.
Berger, J., & Snell, J. L. (1957). On the concept of equal exchange. Behavioral Science, 2, 111–118.
Chung, F. R. K. (1997). Spectral graph theory. In CBMS Regional Conference Series in Mathematics 92. Washington: American Mathematical Society.
Cliff, A. D., & Ord, J. K., (1973). Spatial autocorrelation. London: Pion.
Flury, B. (1997). A first course in multivariate statistics. New York: Springer.
Geary, R. (1954). The contiguity ratio and statistical mapping. The Incorporated Statistician, 5, 115–145.
Le Foll, Y. (1982). Pondération des distances en analyse factorielle. Statistique et Analyse des Données, 7, 13–31.
Lebart, L. (1969). Analyse statistique de la contiguïté. Publications de l’Institut de Statistique des Universités de Paris, XVIII, 81–112.
Lebart, L. (2005). Contiguity analysis and classification. In W. Gaul, O. Opitz, & M. Schader (Eds.), Data analysis (pp. 233–244). Berlin: Springer.
Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate analysis. London: Academic Press.
Meot, A., Chessel, D., & Sabatier, R. (1993). Opérateurs de voisinage et analyse des données spatio-temporelles. In D. Lebreton & B. Asselain (Eds.), Biométrie et environnement (pp. 45–71). Paris: Masson.
Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37, 17–23.
Robert, P., & Escoufier, Y. (1976). A unifying tool for linear multivariate statistical methods: The RV -coefficient. Applied Statistics, 25, 257–265.
Saporta, G. (2006). Probabilités, analyse des données et statistique. Paris: Technip.
Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and testing independence by correlation of distances. Annals of Statistics, 35, 2769–2794.
Thioulouse, J., Chessel, D., & Champely, S. (1995). Multivariate analysis of spatial patterns - A unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1–14.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bavaud, F., Cocco, C. (2015). Factor Analysis of Local Formalism. In: Lausen, B., Krolak-Schwerdt, S., Böhmer, M. (eds) Data Science, Learning by Latent Structures, and Knowledge Discovery. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44983-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-44983-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44982-0
Online ISBN: 978-3-662-44983-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)