Comparing methods for dimensionality reduction when data are density functions
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Functional Data Analysis (FDA) deals with samples where a whole function is observed
for each individual. A particular case of FDA is when the observed functions are density
functions, that are also an example of infinite dimensional compositional data. In this
work we compare several methods for dimensionality reduction for this particular type
of data: functional principal components analysis (PCA) with or without a previous
data transformation and multidimensional scaling (MDS) for diferent inter-densities
distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households
income distributions)
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