scholarly journals Spatial and Temporal Variabilities of PM2.5 Concentrations in China Using Functional Data Analysis

2019 ◽  
Vol 11 (6) ◽  
pp. 1620 ◽  
Author(s):  
Deqing Wang ◽  
Zhangqi Zhong ◽  
Kaixu Bai ◽  
Lingyun He
Keyword(s):  
Air Pollution ◽  
Data Analysis ◽  
Environmental Protection ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Pollution Prevention ◽  
Functional Principal Component Analysis ◽  
Environmental Protection Policies ◽  
Concentration Curves ◽  
Pm2.5 Concentration

As air pollution characterized by fine particulate matter has become one of the most serious environmental issues in China, a critical understanding of the behavior of major pollutant is increasingly becoming very important for air pollution prevention and control. The main concern of this study is, within the framework of functional data analysis, to compare the fluctuation patterns of PM2.5 concentration between provinces from 1998 to 2016 in China, both spatially and temporally. By converting these discrete PM2.5 concentration values into a smoothing curve with a roughness penalty, the continuous process of PM2.5 concentration for each province was presented. The variance decomposition via functional principal component analysis indicates that the highest mean and largest variability of PM2.5 concentration occurred during the period from 2003 to 2012, during which national environmental protection policies were intensively issued. However, the beginning and end stages indicate equal variability, which was far less than that of the middle stage. Since the PM2.5 concentration curves showed different fluctuation patterns in each province, the adaptive clustering analysis combined with functional analysis of variance were adopted to explore the categories of PM2.5 concentration curves. The classification result shows that: (1) there existed eight patterns of PM2.5 concentration among 34 provinces, and the difference among different patterns was significant whether from a static perspective or multiple dynamic perspectives; (2) air pollution in China presents a characteristic of high-emission “club” agglomeration. Comparative analysis of PM2.5 profiles showed that the heavy pollution areas could rapidly adjust their emission levels according to the environmental protection policies, whereas low pollution areas characterized by the tourism industry would rationally support the opportunity of developing the economy at the expense of environment and resources. This study not only introduces an advanced technique to extract additional information implied in the functions of PM2.5 concentration, but also provides empirical suggestions for government policies directed to reduce or eliminate the haze pollution fundamentally.

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.

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.

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.

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.

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.

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