DSpace Collection:
http://hdl.handle.net/10908/633
2024-03-29T13:10:20ZPrincipal components for multivariate functional data
http://hdl.handle.net/10908/635
Title: Principal components for multivariate functional data
Abstract: A principal component method for multivariate functional data is proposed.
Data can be arranged in a matrix whose elements are functions so that for each
individual a vector of p functions is observed. This set of p curves is reduced to a
small number of transformed functions, retaining as much information as possible.
The criterion to measure the information loss is the integrated variance. Under
mild regular conditions, it is proved that if the original functions are smooth
this property is inherited by the principal components. A numerical procedure
to obtain the smooth principal components is proposed and the goodness of the
dimension reduction is assessed by two new measures of the proportion of explained
variability. The method performs as expected in various controlled simulated data
sets and provides interesting conclusions when it is applied to real data sets.
Description: Fil: Barrendero, J.R. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.; Fil: Justel, Ana. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.; Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.2011-01-01T00:00:00ZInterpretable Clustering using Unsupervised Binary Trees
http://hdl.handle.net/10908/636
Title: Interpretable Clustering using Unsupervised Binary Trees
Abstract: We herein introduce a new method of interpretable clustering that uses unsu-
pervised binary trees. It is a three-stage procedure, the rst stage of which entails
a series of recursive binary splits to reduce the heterogeneity of the data within
the new subsamples. During the second stage (pruning), consideration is given to
whether adjacent nodes can be aggregated. Finally, during the third stage (join-
ing), similar clusters are joined together, even if they do not share the same parent
originally. Consistency results are obtained, and the procedure is used on simulated
and real data sets.
Description: Fil: Fraiman, Ricardo. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.; Fil: Ghattas, Badih. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.; Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.2011-01-01T00:00:00ZResistant estimates for high dimensional and functional data based on random projections
http://hdl.handle.net/10908/637
Title: Resistant estimates for high dimensional and functional data based on random projections
Abstract: We herein propose a new robust estimation method based on random pro-
jections that is adaptive and, automatically produces a robust estimate, while
enabling easy computations for high or in nite dimensional data. Under some re-
stricted contamination models, the procedure is robust and attains full e ciency.
We tested the method using both simulated and real data.
Description: Fil: Fraiman, Ricardo. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.; Fil: Svarc, Marcela. Universidad de San Andrés. Departamento de Matemática y Ciencias; Argentina.2011-01-01T00:00:00Z