scholarly journals Functional Data Analysis in Sport Science: Example of Swimmers’ Progression Curves Clustering

2018 ◽  
Vol 8 (10) ◽  
pp. 1766 ◽  
Author(s):  
Arthur Leroy ◽  
Andy MARC ◽  
Olivier DUPAS ◽  
Jean Lionel REY ◽  
Servane Gey
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Clustering Algorithms ◽  
Principal Component ◽  
Continuous Functions ◽  
Functional Principal Component Analysis ◽  
Data Set ◽  
Functional Clustering ◽  
Sport Science

Many data collected in sport science come from time dependent phenomenon. This article focuses on Functional Data Analysis (FDA), which study longitudinal data by modelling them as continuous functions. After a brief review of several FDA methods, some useful practical tools such as Functional Principal Component Analysis (FPCA) or functional clustering algorithms are presented and compared on simulated data. Finally, the problem of the detection of promising young swimmers is addressed through a curve clustering procedure on a real data set of performance progression curves. This study reveals that the fastest improvement of young swimmers generally appears before 16 years old. Moreover, several patterns of improvement are identified and the functional clustering procedure provides a useful detection tool.

scholarly journals A functional data analysis approach for the monitoring of ship CO2 emissions

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Christian Capezza ◽  
Fabio Centofanti ◽  
Antonio Lepore ◽  
Biagio Palumbo
Keyword(s):  
Data Analysis ◽  
Co2 Emissions ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Control Charts ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Unknown Parameters ◽  
Statistical Process ◽  
Data Set

Abstract Sensing networks provide nowadays massive amounts of data that in many applications provide information about curves, surfaces and vary over a continuum, usually time, and thus, can be suitably modelled as functional data. Their proper modelling by means of functional data analysis approaches naturally addresses new challenges also arising in the statistical process monitoring (SPM). Motivated by an industrial application, the objective of the present paper is to provide the reader with a very transparent set of steps for the SPM of functional data in real-world case studies: i) identifying a finite dimensional model for the functional data, based on functional principal component analysis; ii) estimating the unknown parameters; iii) designing control charts on the estimated parameters, in a nonparametric framework. The proposed SPM procedure is applied to a real-case study from the maritime field in monitoring CO2 emissions from real navigation data of a roll-on/roll-off passenger cruise ship, i.e., a ship designed to carry both passengers and wheeled vehicles that are driven on and off the ship on their own wheels. We show different scenarios highlighting clear and interpretable indications that can be extracted from the data set and support the detection of anomalous voyages.

The Oxford Handbook of Functional Data Analysis

2018 ◽  
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Principal Component ◽  
Regression Modeling ◽  
Functional Principal Component Analysis ◽  
Functional Regression ◽  
Vector Integration ◽  
Wide Range

This handbook presents the state-of-the-art of the statistics dealing with functional data analysis. With contributions from international experts in the field, it discusses a wide range of the most important statistical topics (classification, inference, factor-based analysis, regression modeling, resampling methods, time series, random processes) while also taking into account practical, methodological, and theoretical aspects of the problems. The book is organised into three sections. Part I deals with regression modeling and covers various statistical methods for functional data such as linear/nonparametric functional regression, varying coefficient models, and linear/nonparametric functional processes (i.e. functional time series). Part II considers related benchmark methods/tools for functional data analysis, including curve registration methods for preprocessing functional data, functional principal component analysis, and resampling/bootstrap methods. Finally, Part III examines some of the fundamental mathematical aspects of the infinite-dimensional setting, with a focus on the stochastic background and operatorial statistics: vector-valued function integration, spectral and random measures linked to stationary processes, operator geometry, vector integration and stochastic integration in Banach spaces, and operatorial statistics linked to quantum statistics.

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 Sparse functional data analysis accounts for missing information in single-cell epigenomics

2018 ◽  
Author(s):  
Pedro Madrigal ◽  
Xiongtao Dai ◽  
Pantelis Z. Hadjipantelis
Keyword(s):  
Data Analysis ◽  
Missing Data ◽  
Single Cell ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Principal Component ◽  
R Package ◽  
Chromatin Accessibility ◽  
Functional Principal Component Analysis ◽  
Sampled Data

Single-cell epigenome assays produce sparsely sampled data, leading to coverage pooling across cells to increase resolution. Imputation of missing data using deep learning is available but requires intensive computation, and it has been applied only to DNA methylation obtained by single cell bisulfite sequencing. Here, sparsity in chromatin accessibility obtained by scNMT-seq is addressed using functional data analysis to fit sparsely sampled GpC coverage profiles of individual cells taking into account all the cells of the same cell-type or condition. For that, sparse functional principal component analysis (S-FPCA) is applied, and the principal components are used to estimate chromatin accessibility coverage in individual cells. This methodology can potentially be used with other single-cell assays with missing data such as scBS-seq, scNOME-seq, or scATAC-seq. The R package fdapace is available in CRAN, and R code used in this manuscript can be found at: http://github.com/pmb59/sparseSingleCell.

Functional data analysis techniques for the study of structural parameters in polymer composites

2016 ◽  
Vol 49 (2) ◽  
pp. 594-605 ◽  
Author(s):  
Thejas Gopal Krishne Urs ◽  
Karthik Bharath ◽  
Sangappa Yallappa ◽  
Somashekar Rudrappa
Keyword(s):  
Data Analysis ◽  
Polymer Composites ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Dopant Concentration ◽  
Structural Parameters ◽  
Principal Component ◽  
Global Features ◽  
Casting Technique ◽  
Microstructural Parameters

This article presents a novel method, based on functional data analysis, to analyse measurements of structural parameters of polymers and polymer composites. The method is demonstrated using newly developed biodegradable conducting polymer composites prepared via a solution casting technique. The measurements of the macro- and microstructural parameters that are used in the characterization of these films are obtained using X-ray diffraction, an impedance analyser and a UV–vis spectrometer. A functional representation of the measured values of the parameters at different dopant concentrations is adopted by viewing them as realizations of a continuous-time stochastic process observed with measurement error. This allows one to estimate the mean functional relationship between a parameter and the dopant concentration. A functional version of principal component analysis is performed, by which the major modes of variation are discovered and the correlations of parameter values at different concentrations are estimated. This provides insight into local and global features of the relationship between these parameters. Some comments are made on how the parameters vary as a function of dopant concentration.

scholarly journals Subpopulation identification for single-cell RNA-sequencing data using functional data analysis

2019 ◽  
Author(s):  
Kyungmin Ahn ◽  
Hironobu Fujiwara
Keyword(s):  
Gene Expression ◽  
Data Analysis ◽  
Single Cell ◽  
Gene Expression Data ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Clustering Algorithms ◽  
Expression Data ◽  
Clustering Methods ◽  
Single Cell Rna Sequencing

AbstractBackgroundIn single-cell RNA-sequencing (scRNA-seq) data analysis, a number of statistical tools in multivariate data analysis (MDA) have been developed to help analyze the gene expression data. This MDA approach is typically focused on examining discrete genomic units of genes that ignores the dependency between the data components. In this paper, we propose a functional data analysis (FDA) approach on scRNA-seq data whereby we consider each cell as a single function. To avoid a large number of dropouts (zero or zero-closed values) and reduce the high dimensionality of the data, we first perform a principal component analysis (PCA) and assign PCs to be the amplitude of the function. Then we use the index of PCs directly from PCA for the phase components. This approach allows us to apply FDA clustering methods to scRNA-seq data analysis.ResultsTo demonstrate the robustness of our method, we apply several existing FDA clustering algorithms to the gene expression data to improve the accuracy of the classification of the cell types against the conventional clustering methods in MDA. As a result, the FDA clustering algorithms achieve superior accuracy on simulated data as well as real data such as human and mouse scRNA-seq data.ConclusionsThis new statistical technique enhances the classification performance and ultimately improves the understanding of stochastic biological processes. This new framework provides an essentially different scRNA-seq data analytical approach, which can complement conventional MDA methods. It can be truly effective when current MDA methods cannot detect or uncover the hidden functional nature of the gene expression dynamics.

Identifying and Classifying Aberrant Response Patterns Through Functional Data Analysis

2020 ◽  
Vol 45 (6) ◽  
pp. 719-749
Author(s):  
Eduardo Doval ◽  
Pedro Delicado
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Simulated Data ◽  
Real Data ◽  
Response Patterns ◽  
Fit Indices ◽  
Person Fit ◽  
Data Set ◽  
Aberrant Response Patterns

We propose new methods for identifying and classifying aberrant response patterns (ARPs) by means of functional data analysis. These methods take the person response function (PRF) of an individual and compare it with the pattern that would correspond to a generic individual of the same ability according to the item-person response surface. ARPs correspond to atypical difference functions. The ARP classification is done with functional data clustering applied to the PRFs identified as ARP. We apply these methods to two sets of simulated data (the first is used to illustrate the ARP identification methods and the second demonstrates classification of the response patterns flagged as ARP) and a real data set (a Grade 12 science assessment test, SAT, with 32 items answered by 600 examinees). For comparative purposes, ARPs are also identified with three nonparametric person-fit indices (Ht, Modified Caution Index, and ZU3). Our results indicate that the ARP detection ability of one of our proposed methods is comparable to that of person-fit indices. Moreover, the proposed classification methods enable ARP associated with either spuriously low or spuriously high scores to be distinguished.

Functional Data Analysis and Wave Profiles During a Storm

2011 ◽  
Author(s):  
Joaqui´n Ortega ◽  
Cristina Gorrostieta ◽  
George H. Smith
Keyword(s):  
Data Analysis ◽  
Wave Height ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Significant Wave Height ◽  
Functional Principal Component Analysis ◽  
Time Interval ◽  
Significant Wave ◽  
Wave Profiles ◽  
The Waves

Functional Data Analysis is a set of statistical tools developed to perform statistical analysis on data having a functional form. In our case we consider the one-dimensional wave profiles registered during a North-Sea storm as functional data. The waves are defined as the surface height between two consecutive downcrossings. Data is split into 20-minute periods and after registration of the waves to the interval [0,1], the mean wave is obtained along with the first two derivatives of this mean profile. We analyze the shape of these mean waves and their derivatives and show how they change as a function of the significant wave height for the corresponding time interval. We also look at the evolution of the energy, as represented by the phase diagram, as a function of significant wave height. The results show the asymmetry in vertical and horizontal scales for real data. To consider how the individual waves vary we perform a Functional Principal Component Analysis of wave profiles, dividing previously the waves into groups according to their height and comparing with waves measured during a non-storm period. The results suggest that the modes of variation of wave profiles do not depend on wave height or sea condition.

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