Functional Data Analysis: Transition from Daily Observation of COVID-19 Prevalence in France to Functional Curves

AbstractIn this paper we use the technique of functional data analysis to model daily hospitalized, deceased, ICU cases and return home patient numbers along the COVID-19 outbreak, considered as functional data across different departments in France while our response variables are numbers of vaccinations, deaths, infected, recovered and tests in France. These sets of data were considered before and after vaccination started in France. We used some smoothing techniques to smooth our data set, then analysis based on functional principal components method was performed, clustering using k-means techniques was done to understand the dynamics of the pandemic in different French departments according to their geographical location on France map and we also performed canonical correlations analysis between variables. Finally, we made some predictions to assess the accuracy of the method using functional linear regression models.

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Functional data analysis: Application to daily observation of COVID-19 prevalence in France

AIMS Mathematics ◽

10.3934/math.2022298 ◽

2022 ◽

Vol 7 (4) ◽

pp. 5347-5385

Author(s):

Kayode Oshinubi ◽

◽

Firas Ibrahim ◽

Mustapha Rachdi ◽

Jacques Demongeot

Keyword(s):

Data Analysis ◽

Functional Data Analysis ◽

Functional Data ◽

Geographical Location ◽

Linear Regression Models ◽

Data Set ◽

Canonical Correlations ◽

Before And After ◽

Functional Principal Components ◽

Functional Linear Regression

<abstract> <p>In this paper we use the technique of functional data analysis to model daily hospitalized, deceased, Intensive Care Unit (ICU) cases and return home patient numbers along the COVID-19 outbreak, considered as functional data across different departments in France while our response variables are numbers of vaccinations, deaths, infected, recovered and tests in France. These sets of data were considered before and after vaccination started in France. After smoothing our data set, analysis based on functional principal components method was performed. Then, a clustering using k-means techniques was done to understand the dynamics of the pandemic in different French departments according to their geographical location on France map. We also performed canonical correlations analysis between variables. Finally, we made some predictions to assess the accuracy of the method using functional linear regression models.</p> </abstract>

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

Applied Sciences ◽

10.3390/app8101766 ◽

2018 ◽

Vol 8 (10) ◽

pp. 1766 ◽

Cited By ~ 2

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.

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Identifying and Classifying Aberrant Response Patterns Through Functional Data Analysis

Journal of Educational and Behavioral Statistics ◽

10.3102/1076998620911941 ◽

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.

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Study on the Influence of Air Pressure and Temperature on PM2.5 by Multivariate Functional Linear Regression Model

E3S Web of Conferences ◽

10.1051/e3sconf/202019405009 ◽

2020 ◽

Vol 194 ◽

pp. 05009

Author(s):

Jinjing Yang

Keyword(s):

Data Analysis ◽

Linear Regression ◽

Regression Model ◽

Functional Data Analysis ◽

Linear Regression Model ◽

Functional Data ◽

Basis Functions ◽

Air Pressure ◽

The Internet ◽

Functional Linear Regression

In recent years, the Internet has developed rapidly, and we have more and more ways to collect data. We find that many data have the characteristics of functions. We can use the important method of functional data analysis to analyze these data. The basic idea of functional data analysis is to treat data with functional properties as a whole for analysis and corresponding processing. In this paper, the daily air pressure, temperature and PM2.5 data of 49 cities with serious PM2.5 pollution in 2017 are sorted out. We use a multivariate functional linear regression model to discuss the influence of pressure and temperature on PM2.5 when the number of basis functions is different.

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Prevention- Versus Promotion-Focus Regulatory Efforts on the Disease Incidence and Mortality of COVID-19: A Multinational Diffusion Study Using Functional Data Analysis

Journal of International Marketing ◽

10.1177/1069031x20966563 ◽

2020 ◽

pp. 1069031X2096656

Author(s):

V. Kumar ◽

Ashish Sood ◽

Shaphali Gupta ◽

Nitish Sood

Keyword(s):

Data Analysis ◽

Functional Data Analysis ◽

Functional Data ◽

Regulatory Focus ◽

Disease Incidence ◽

Data Set ◽

Moderating Factors ◽

Incidence And Mortality ◽

Novel Coronavirus ◽

Nonpharmaceutical Interventions

International marketing has rarely explored the diffusion patterns of the spread of a disease or analyzed the factors explaining the differences in the disease incidence patterns. The rapid diffusion of the novel coronavirus has engulfed the entire world in a very short time. Many countries experienced different levels of disease incidence and mortality despite implementing similar nonpharmaceutical interventions (NPIs). Drawing on the regulatory focus theory, the authors propose a framework to conceptualize and investigate the comparative efficacy of diverse NPIs that countries could adopt to prevent or curtail the diffusion of the disease incidence and mortality. They categorize these NPIs as prevention focused (containment and closures) or promotion focused (relief measures and public health infrastructure) and discuss the moderating factors that enhance or impede their effectiveness. Employing functional data analysis, the authors examine a comprehensive data set across 70 countries. They find that prevention-focused interventions inhibit disease incidence, while promotion-focused interventions enhance the nation’s ability to respond to medical emergencies and augment people’s ability to isolate themselves and slow the spread. The authors also generate insights on how a reallocation of resources between prevention- and promotion-focused efforts influence the evolution of disease incidence and mortality, with various countries falling in different clusters.

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

Gestão & Produção ◽

10.1590/1806-9649-2021v28e152 ◽

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.

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An Animated Functional Data Analysis Interface to Cluster Rapid Lung Function Decline and Enhance Center-Level Care in Cystic Fibrosis

Journal of Healthcare Engineering ◽

10.1155/2021/6671833 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Jesse Pratt ◽

Weiji Su ◽

Don Hayes ◽

John P. Clancy ◽

Rhonda D. Szczesniak

Keyword(s):

Cystic Fibrosis ◽

Data Analysis ◽

Lung Function ◽

Functional Data Analysis ◽

Principal Components ◽

Functional Data ◽

Rapid Decline ◽

Components Analysis ◽

Functional Principal Components Analysis ◽

Functional Principal Components

Identifying disease progression through enhanced decision support tools is key to chronic management in cystic fibrosis at both the patient and care center level. Rapid decline in lung function relative to patient level and center norms is an important predictor of outcomes. Our objectives were to construct and utilize center-level classification of rapid decliners to develop an animated dashboard for comparisons within patients over time, multiple patients within centers, or between centers. A functional data analysis technique known as functional principal components analysis was applied to lung function trajectories from 18,387 patients across 247 accredited centers followed through the United States Cystic Fibrosis Foundation Patient Registry, in order to cluster patients into rapid decline phenotypes. Smaller centers (<30 patients) had older patients with lower baseline lung function and less severe rates of decline and had maximal decline later, compared to medium (30–150 patients) or large (>150 patients) centers. Small centers also had the lowest prevalence of early rapid decliners (17.7%, versus 24% and 25.7% for medium and large centers, resp.). The animated functional data analysis dashboard illustrated clustering and center-specific summaries of the rapid decline phenotypes. Clinical scenarios and utility of the center-level functional principal components analysis (FPCA) approach are considered and discussed.

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Sparseness and functional data analysis

10.1093/oxfordhb/9780199568444.013.11 ◽

2018 ◽

Author(s):

Gareth James

Keyword(s):

Data Analysis ◽

Functional Data Analysis ◽

Functional Data ◽

Sequential Algorithm ◽

Data Sets ◽

Growth Data ◽

Sparse Functional Data ◽

Set Of Points ◽

Sparse Set ◽

Functional Linear Regression

This article considers two functional data analysis settings where sparsity becomes important: the first involves only measurements at a relatively sparse set of points and the second relates to variable selection in a functional case. It begins with a discussion of two data sets that fall into the ‘sparsely observed’ category, the ‘growth’ data and the ‘nephropathy’ data, both of which are used to illustrate alternative approaches for analysing sparse functional data. It then examines different classes of methods that can be applied to functional data, such as basis functions, mixed-effects models and local smoothing techniques, as well as specific methodologies for dealing with sparse functional data in the principal components, clustering, classification, and regression settings. Finally, it describes two approaches for performing regressions involving a functional predictor and a scalar response: SASDA (sequential algorithm for selecting design automatically) and FLiRTI (Functional Linear Regression That’s Interpretable).

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Research on the Two-Way Time-Varying Relationship between Foreign Direct Investment and Financial Development Based on Functional Data Analysis

Sustainability ◽

10.3390/su13116033 ◽

2021 ◽

Vol 13 (11) ◽

pp. 6033

Author(s):

Deqing Wang ◽

Qian Huang ◽

Tianzhi Ye ◽

Sihua Tian

Keyword(s):

Foreign Direct Investment ◽

Data Analysis ◽

Financial Development ◽

Functional Data Analysis ◽

Functional Data ◽

Direct Investment ◽

Mutual Influence ◽

Time Varying ◽

Promoting Effect ◽

Functional Linear Regression

Studying how to achieve mutual promotion between financial development and foreign direct investment inflow contributes to the Chinese government’s work of formulating rational financial policy and FDI policy from a holistic point of view and promoting the healthy and ordered growth of the entire economy in China. Based on the provincial panel data from 2007 to 2018, this paper constructs comprehensive evaluation indexes for financial development and introduces functional data analysis (FDA) methods, extracts functional β-convergence from functional linear regression to analyze the two-way time-varying relationship and convergence and divergence between financial development and FDI in the country and the eastern, central, and western regions. The empirical results show that the mutual influence of FDI and financial development presents regional differences. In general, FDI has a promoting effect on financial development, while financial development has an inhibitory effect on FDI, and there is basically no convergence effect. Based on these conclusions, if the governments of various regions in China want to reduce the differences in financial development, promote coordinated financial development, and promote sustainable financial development, they should actively implement financial development policies, optimize the financial environment, and implement differentiated foreign investment policies to promote regional financial development.

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