Principal Components Analysis deals mainly with the analysis of large data sets with multivariate structure in an observational context for exploraty purposes. The factorial planes produced will show the main oppositions between variables and individuals. However, we may be interested in going further by controlling the effect of some latent or third variable which expresses some well-defined phenomenon. We go through this by means of a graph among individuals, following the same idea of instrumental variables as Rao, or partial correlation analysis. We call such analysis Local Principal Components Analysis, which consists of defining a semi-metric upon the variable spaces. Finally, we illustrate this with an example.
@article{urn:eudml:doc:40335,
title = {Local Principal Components Analysis.},
journal = {Q\"uestii\'o},
volume = {15},
year = {1991},
pages = {267-278},
zbl = {1167.62306},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40335}
}
Aluja Banet, Tomàs.; Nonell Torrent, Ramón. Local Principal Components Analysis.. Qüestiió, Tome 15 (1991) pp. 267-278. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40335/