scholarly journals New Modeling Approaches Based on Varimax Rotation of Functional Principal Components

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2085
Author(s):  
Christian Acal ◽  
Ana M. Aguilera ◽  
Manuel Escabias
Keyword(s):  
Principal Component Analysis ◽  
Principal Components ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
Varimax Rotation ◽  
Basis Expansion ◽  
The Matrix ◽  
Functional Principal Components ◽  
Component Scores

Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper, two new functional Varimax rotation approaches are introduced. They are based on the equivalence between FPCA of basis expansion of the sample curves and Principal Component Analysis (PCA) of a transformation of the matrix of basis coefficients. The first approach consists of a rotation of the eigenvectors that preserves the orthogonality between the eigenfunctions but the rotated principal component scores are not uncorrelated. The second approach is based on rotation of the loadings of the standardized principal component scores that provides uncorrelated rotated scores but non-orthogonal eigenfunctions. A simulation study and an application with data from the curves of infections by COVID-19 pandemic in Spain are developed to study the performance of these methods by comparing the results with other existing approaches.

scholarly journals MFPCA: Multiscale Functional Principal Component Analysis

2019 ◽  
Vol 33 ◽  
pp. 4320-4327 ◽  
Author(s):  
Zhenhua Lin ◽  
Hongtu Zhu
Keyword(s):  
Principal Component Analysis ◽  
Dimension Reduction ◽  
Principal Components ◽  
Functional Data ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
Number Of Components ◽  
Small Variance ◽  
Functional Principal Component

We consider the problem of performing dimension reduction on heteroscedastic functional data where the variance is in different scales over entire domain. The aim of this paper is to propose a novel multiscale functional principal component analysis (MFPCA) approach to address such heteroscedastic issue. The key ideas of MFPCA are to partition the whole domain into several subdomains according to the scale of variance, and then to conduct the usual functional principal component analysis (FPCA) on each individual subdomain. Both theoretically and numerically, we show that MFPCA can capture features on areas of low variance without estimating high-order principal components, leading to overall improvement of performance on dimension reduction for heteroscedastic functional data. In contrast, traditional FPCA prioritizes optimizing performance on the subdomain of larger data variance and requires a practically prohibitive number of components to characterize data in the region bearing relatively small variance.

Functional principal component analysis of glomerular filtration rate curves after kidney transplant

2017 ◽  
Vol 27 (12) ◽  
pp. 3785-3796 ◽  
Author(s):  
Jianghu J Dong ◽  
Liangliang Wang ◽  
Jagbir Gill ◽  
Jiguo Cao
Keyword(s):  
Principal Component Analysis ◽  
Glomerular Filtration Rate ◽  
Glomerular Filtration ◽  
Kidney Transplant ◽  
Filtration Rate ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
Functional Principal Component ◽  
Component Scores

This article is motivated by some longitudinal clinical data of kidney transplant recipients, where kidney function progression is recorded as the estimated glomerular filtration rates at multiple time points post kidney transplantation. We propose to use the functional principal component analysis method to explore the major source of variations of glomerular filtration rate curves. We find that the estimated functional principal component scores can be used to cluster glomerular filtration rate curves. Ordering functional principal component scores can detect abnormal glomerular filtration rate curves. Finally, functional principal component analysis can effectively estimate missing glomerular filtration rate values and predict future glomerular filtration rate values.

Stormwater inflow prediction using radar rainfall data compressed by principal component analysis

2006 ◽  
Vol 1 (1) ◽  
Author(s):  
K. Katayama ◽  
K. Kimijima ◽  
O. Yamanaka ◽  
A. Nagaiwa ◽  
Y. Ono
Keyword(s):  
Principal Component Analysis ◽  
Prediction Model ◽  
Principal Components ◽  
Prediction Method ◽  
Principal Component ◽  
Component Analysis ◽  
Rainfall Data ◽  
Radar Rainfall ◽  
Input Variables ◽  
Inflow Prediction

This paper proposes a method of stormwater inflow prediction using radar rainfall data as the input of the prediction model constructed by system identification. The aim of the proposal is to construct a compact system by reducing the dimension of the input data. In this paper, Principal Component Analysis (PCA), which is widely used as a statistical method for data analysis and compression, is applied to pre-processing radar rainfall data. Then we evaluate the proposed method using the radar rainfall data and the inflow data acquired in a certain combined sewer system. This study reveals that a few principal components of radar rainfall data can be appropriate as the input variables to storm water inflow prediction model. Consequently, we have established a procedure for the stormwater prediction method using a few principal components of radar rainfall data.

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