Functional Data Analysis of Amplitude and Phase Variation

@article{Marron2015FunctionalDA,
  title={Functional Data Analysis of Amplitude and Phase Variation},
  author={J. S. Marron and James O. Ramsay and Laura M. Sangalli and Anuj Srivastava},
  journal={arXiv: Methodology},
  year={2015}
}
The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces, observation noise, and so on. However, there is another interesting phenomena that creates problems in FDA. The functional data often comes with lateral displacements/deformations in curves, a phenomenon which is different from the height or amplitude… 
A general framework for multivariate functional principal component analysis of amplitude and phase variation
Functional data typically contain amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain
Registration for exponential family functional data
TLDR
A novel method for separating amplitude and phase variability in exponential family functional data is introduced, andSimulations designed to mimic the application indicate that the proposed methods outperform competing approaches in terms of estimation accuracy and computational efficiency.
Registration for Incomplete Non-Gaussian Functional Data
TLDR
This work extends and refine a framework for joint likelihood-based registration and latent Gaussian process-based generalized functional principal component analysis that is able to handle incomplete curves and registers data from a seismological application comprising spatially indexed, incomplete ground velocity time series with a highly volatile Gamma structure.
Principal Nested Spheres for Time-Warped Functional Data Analysis
ABSTRACT There are often two important types of variation in functional data: the horizontal (or phase) variation and the vertical (or amplitude) variation. These two types of variation have been
A geometric approach for computing tolerance bounds for elastic functional data
TLDR
A generative, probabilistic model is defined for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data, and two different types of tolerance bounds are defined that are able to measure both types of variability.
Shape Analysis of Functional Data
TLDR
This work summarizes recent developments in the field of elastic shape analysis of functional data, with a perspective on statistical inferences, and introduces square-root representations of functions to help simplify computations and facilitate efficient algorithms for large-scale data analysis.
Variograms for spatial functional data with phase variation.
Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace variogram, which quantifies spatial variation, can be misleading when
A Geometric Approach to Visualization of Variability in Functional Data
TLDR
This work uses a recent functional data analysis framework, based on a representation of functions called square-root slope functions, to decompose observed variation in functional data into three main components: amplitude, phase, and vertical translation.
Spatially Penalised Registration of Multivariate Functional Data
Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general
A Geometric Approach to Visualization of Variability in Univariate and Multivariate Functional Data
TLDR
This dissertation describes a new method for the construction and visualization of geometrically-motivated displays for univariate functional data and multivariate curve data, and proposes to separately identify outliers based on each of the main components after decomposition.
...
...

References

SHOWING 1-10 OF 39 REFERENCES
On the definition of phase and amplitude variability in functional data analysis
We introduce a modeling and mathematical framework in which the problem of registering a functional data set can be consistently set. In detail, we show that the introduction, in a functional data
Registration of Functional Data Using Fisher-Rao Metric
TLDR
A novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis using the Fisher-Rao Riemannian metric and a convenient square-root velocity function representation.
Principal Nested Spheres for Time-Warped Functional Data Analysis
ABSTRACT There are often two important types of variation in functional data: the horizontal (or phase) variation and the vertical (or amplitude) variation. These two types of variation have been
Pairwise curve synchronization for functional data
Data collected by scientists are increasingly in the form of trajectories or curves. Often these can be viewed as realizations of a composite process driven by both amplitude and time variation. We
Simultaneous curve registration and clustering for functional data
Statistics of time warpings and phase variations
Many methods exist for one dimensional curve registration, and how methods compare has not been made clear in the literature. This special section is a summary of a detailed comparison of a number of
Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese
TLDR
A joint multivariate mixed effect model can be formulated, which gives insights into the relationship between the different modes of variation as well as their dependence on linguistic and nonlinguistic covariates.
Combining Registration and Fitting for Functional Models
A registration method can be defined as a process of aligning features of a sample of curves by monotone transformations of their domain. The aligned curves exhibit only amplitude variation, and the
Core Shape modelling of a set of curves
...
...