Matrix computations (3rd ed.)
Independent component analysis: algorithms and applications
Neural Networks
Another look at principal curves and surfaces
Journal of Multivariate Analysis
Functional PLS logit regression model
Computational Statistics & Data Analysis
Principal component analysis of measures, with special emphasis on grain-size curves
Computational Statistics & Data Analysis
Editorial: Statistics for Functional Data
Computational Statistics & Data Analysis
An overview to modelling functional data
Computational Statistics
A Projection Pursuit Algorithm for Exploratory Data Analysis
IEEE Transactions on Computers
Variational Bayesian functional PCA
Computational Statistics & Data Analysis
Additive prediction and boosting for functional data
Computational Statistics & Data Analysis
Structural components in functional data
Computational Statistics & Data Analysis
Dimensionality reduction when data are density functions
Computational Statistics & Data Analysis
Identifying cluster number for subspace projected functional data clustering
Computational Statistics & Data Analysis
Model-based clustering for multivariate functional data
Computational Statistics & Data Analysis
| Hi-index | 0.03 |
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.