scholarly journals Erratum to “Data‐driven dimension reduction in functional principal component analysis identifying the change‐point in functional data”

2021 ◽  
Keyword(s):  
Principal Component Analysis ◽  
Dimension Reduction ◽  
Functional Data ◽  
Change Point ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
Data Driven ◽  
Functional Principal Component

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 FOR RECOGNITION OF ARM GESTURES AND HUMANOID IMITATION

2013 ◽  
Vol 10 (04) ◽  
pp. 1350033 ◽  
Author(s):  
JACOPO ALEOTTI ◽  
STEFANO CASELLI
Keyword(s):  
Principal Component Analysis ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Recognition Rate ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
Finite Dimensional Space ◽  
Functional Principal Component

This paper investigates the use of functional principal component analysis (FPCA) for automatic recognition of dynamic human arm gestures and robot imitation. FPCA is a statistical technique of functional data analysis that generalizes standard multivariate principal component analysis. Functional data analysis signals (e.g., gestures) are functions that are considered as observations of a random variable on a functional space. In particular, FPCA reduces the dimensionality of the input data by projecting them onto a finite-dimensional space spanned by a few prominent eigenfunctions. The main contribution of this work is the proposal of a novel technique for unsupervised clustering of training data and dynamic gesture recognition based on FPCA. FPCA has not been considered in previous studies on humanoid learning. The proposed approach has been evaluated in two experimental settings for motion capture. In the first setup single arm gestures are recognized from inertial sensors attached to the arm of the user. In the second setup the method is extended to two-arm gestures acquired from a range sensor. Recognized gestures are reproduced by a small humanoid robot. The FPCA method has also been compared to a high performance algorithm for gesture classification based on dynamic time warping (DTW). The FPCA algorithm achieves comparable results in both recognition rate and robustness to missing data, while it outperforms DTW in terms of efficiency in execution time.

scholarly journals Functional principal component analysis of fMRI data

2004 ◽  
Vol 24 (2) ◽  
pp. 109-129 ◽  
Author(s):  
Roberto Viviani ◽  
Georg Grön ◽  
Manfred Spitzer
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Functional Principal Component Analysis ◽  
Fmri Data ◽  
Functional Principal Component
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