Common problems in functional data analysis some issues arise regularly in fda data display and summarization smoothing and interpolation patterns in variability. There is by now a fully developed statistical toolbox allowing for the principled application of the functional data. The tecator data is a benchmark data set in the functional data analysis fda, and many fda methods are applied to analyze this data set lian and li, 2014. If you work through all the case studies you will have covered a broad sweep of existing methods in functional data analysis and, in some cases, you will study new methodology developed for the particular problem in hand. Functional data analysis encyclopedia of mathematics. Functional data analysis is a collection of techniques to model data from dynamic systems possibly governed by differential equations in terms of some set of basis functions the fda package. The journal of functional analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role.
It complements functional data analysis, second edition and applied functional data analysis. Theexisting literature focuses on two antithetical data. Functional data analysis ablet of contents 1 introduction 2 representing functional data 3 exploratory data analysis 4 the fda package 5 functional linear models 6 functional linear models in r 7 registration 8 dynamics 9 future problems. Robust methods for functional data analysis pallavi sawant master of science, august 10, 2009 m. In a typical functional data setting, a sample of n curves are observed at a set of discrete points.
Automated methods for functional genomics andreas rechtsteiner 29th april 2005. These lists can represent differentiallyexpressed genes between two tissues, genes with similar methylation patterns, genes that are close to relevant mutations, etc. Functional data analysis fda models data using functions or functional parameters. Introduction to functional data analysis provides a concise textbook introduction to the field. Functional data analysis ramsay and silverman 2005 is an important special case of objectoriented data analysis, where the atoms are functions. An area of statistics where it is of key interest to analyze data providing information about curves, surfaces, images, and any. In its most general form, under an fda framework each sample element is considered to be a function. The techniques presented in functional data analysis are potentially very useful to people working in a variety of fields. Functional data analysis fda refers to the statistical analysis of data samples consisting of random functions or surfaces, where each function is viewed as one sample element.
The atom of functional data is a function, where for each subject in a random sample, one or several functions are recorded. Functional data analysis is typically conducted within the l2hilbert space framework. Broadly interpreted, fda deals with the analysis and theory of data that are in the form of functions. Functional data that are nonnegative and have a constrained integral can be considered as samples of onedimensional density functions. The atom of functional data is a function, where for each subject in a random sample one or several functions are recorded. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. Antecedent behaviorconsequence form abca a good direct observation data collection tool. We assume that the repeated measurements are randomly located with a random number of rep etitions. Typically, the random functions contained in the sample are considered to be independent and to correspond to smooth realizations of an underlying stochastic process.
The data sets exemplify the wide scope of functional data analysis. Stp 598 functional data analysis functional data analysis fda is the area of statistics concerned with data which consists of continuous, smooth functions. It treats each function as a series of data points that are likely to relate, rather than as series of independent data points. Functional data analysis ramsay major reference works. The book presents novel statistical technology while keeping the mathematical level widely accessible.
Functional data analysis for sparse longitudinal data. Find materials for this course in the pages linked along the left. It explains how to analyze functional data, both at exploratory and inferential levels. Any technique for functional data should take into account the structure of the data results from multivariate data analyses are generally permutationinvariant, but results.
The goals of functional data analysis first steps in a functional data analysis using derivatives in functional data analysis this talk follows closely the. Key aspects of fda include the choice of smoothing technique, data. Oct 15, 2005 functional data analysis fda models data using functions or functional parameters. Our goal is to develop and use statistically sound methods to address public health and scientific questions that depend on complex data sources. The atom of functional data is a function, where for each. Combines algebraic topology and other tools from pure mathematics to give mathematically rigorous and quantitative study of shape functional data analysis fda. Functional data analysis fda encompasses the statistical methodology for such data.
Functional data analysis in the banach space of continuous. Textbook ramsay and silverman 2005, functional data analysis, 2nd edition, springer. While the term \ functional data analysis was coined by ramsay 1982 and. Functional analysis examines the causes and consequences of behaviorit is a powerful method of empirically identifying the variables that maintain a problem behavior rummel, garrisondiehn, catlin. Articles by scientists in a variety of interdisciplinary.
Next, these genes are being annotated functionally, by searching for functional terms that. Typically, the random functions contained in the sample are considered to be independent and smooth. The prototype for the title of this project was functional data analysis, and a goal of the project was to connect others working on new emerging classes or types of complex and high dimensional data. Introduction to functional data analysis 1st edition. The 2011 samsi project on objectoriented data played a big role. Key aspects of fda include the choice of smoothing technique, data reduction, adjustment for clustering, functional linear. But more importantly, we hope that the readers will gain an insight into functional ways of. Introduction sinceramsay and dalzell1991 rst coined the term. Functional data analysis functional data analysis is a method of statistics that doing data analysis in order to provide information about curves over time. Aug 15, 2006 the second section describes functional versions of traditional methods such principal components analysis and linear modelling, and also mentions purely functional approaches that involve working with and estimating differential equations in the functional data analysis process.
Based on the horner, oneal format, offers lots of great information. They are functional in the sense that they are evaluated at any time in the domain, instead of the discrete way, in which they were originally measured or observed ramsay and silverman, 2005. This area of mathematics has both an intrinsic beauty, which we hope to convey to the reader, and a vast number of applications in many elds of mathematics. Methods and case studies by providing computer code in both the r and matlab languages for a set of data analyses that showcase functional data analysis techniques. Program staff are urged to view this handbook as a beginning resource, and to supplement their. Functional data analysis fda is a branch of statistics that analyzes data providing information about curves, surfaces or anything else varying over a continuum. A functional variable is one whose values depend on a. Introduction sinceramsay and dalzell1991 rst coined the term \ functional data analysis fda for analyzing data that are realizations of a continuous function, many statistical methods and tools have been. Though the individual methods and techniques are important, functional data analysis is alsoageneralwayofthinking,wherethebasicunitof. Silverman, 2005functionaldataanalysis, second edition.
Functional data analysis is a statistical methodology in which the input information used to obtain the output results, is a set of curves mathematical functions. Why not just apply multivariate techniques manova, clustering, multiple regression, etc. Multivariate analysis of gene expression data and functional information. Functional data analysis ramsay 2005 major reference. They are functional in the sense that they are evaluated at any time in the domain.
The complexity of the functions is not assumed to be known in advance, so that methods are used for approximating these with as much flexibility as the data require. Pdf principal components analysis for functional data. The book presents novel statistical technology, much of it based on the authors own research work, while keeping the mathematical level widely accessible. Functional data analysis, which lots of us like to call fda, is about the analysis of information on curves or functions. Functional data analysis a functional variable is one whose values depend on a continuous magnitude such as time.
Functional data analysis fda or data analysis with curves is a popular subject in statistics with a wide range of applications. Due to the inherent constraints, densities do not live in a vector space and, therefore, commonly used hilbert space based methods of functional data analysis are not applicable. Program staff are urged to view this handbook as a beginning resource, and to supplement their knowledge of data analysis procedures and methods over time as part of their ongoing professional development. A lot has been happening around the topic of curve registration. Functional data analysis revealed that cantonese and american speakers apply the two rules similarly on both real words and wug words, suggesting that the sandhi forms are stored as part of the. Smoothness has no meaning for multivariate data analysis, which in contrast to fda is permutation invariant. Jun 08, 2005 the data sets exemplify the wide scope of functional data analysis. Although scientific interest is in the underlying stochastic process and. A matlab toolbox for bayesian functional data analysis.
Functional data analysis with r and matlab james o. Functional analysis and assignment of government consolidated report final draft date course title project to prepare public administration for state reforms prepare government of nepal ministry. Functional data analysis fda is a fairly recent research field in statistics concerned with the analysis of data providing information about curves, shapes and images which vary over a continuum. Functional data analysis fda deals with the analysis and theory of data that are in the form of functions, images and shapes, or more general objects. Pdf introduction to functional data analysis researchgate. Even sparsely and irregularly observed longitudinal data can be analyzed with fda methodology. Zhang, 20, \ analysis of variance for functional data. Functional data analysis is a collection of techniques to model data from dynamic systems possibly governed by differential equations in terms of some set of basis functions the fda package supports the use of 8 different types of basis functions. Special topics in genetic epidemiology november 10, 2015. The authors make it easy to get up and running in new applications by adapting the code. Uniform convergence rates for nonparametric regression and. Special issue on functional data analysis and related topics. Pdf functional data analysis for sparse longitudinal data. Review of functional data analysis uc davis department of statistics.
We describe a set of quantitative methods, functional data analysis fda, which can answer a number of questions that traditional statistical approaches. Analog experimental functional analysis data sheet. Ecologists building dynamical models, engineers trying to classify sensor readings, and statisticians trying to understand how traditional multivariate techniques generalize to functional data can all benefit from this book. This is a classic text, also much more sophisticated than the course. The functional data analysis approach retains the structure of the data. Representing functional data representing functional data 14181 representing functional data fromdiscretetofunctionaldata represent data recorded at discrete times as a continuous function in order to med. Some lecture notes include homework assignments plus solutions. Functional data analysis springer series in statistics pdf free. Pdf functional data analysis for sparse longitudinal. Functional data analysis fda is increasingly being used to better analyze, model and predict time series data.
Imaging, for example, a variable whose values depend continously on time, it would be better to use the information of such a variable at any time point than using it only at a. Functional data analysis using topological summary statistics. Robust methods for multivariate functional data analysis. Key concepts and terms topological data analysis tda.