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Functional Data Analysis

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Lendasse A., Corona F., Liiti inen E. 1. Functional Data Analysis ... Amaury Lendasse, Tuomas K rn and Francesco Corona. Inputs and outputs are functions ... – PowerPoint PPT presentation

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Title: Functional Data Analysis


1
Functional Data Analysis
  • CORONA FRANCESCO, Lendasse Amaury, Liitiäinen Elia

2
What is a Functional Variable?
  • From different fields of sciences!
  • Environmetrics, Chemometrics, Biometrics,
    Medicine, Econometrics, Time series prediction,
    ...
  • Collected data are curves
  • Definition
  • A random variable X is called a functional
    variable (f.v.) if it takes values in a infinite
    dimensional space (or functional space). An
    observation x of X is called a functional data.

3
What is a Functional Dataset?
  • Several functional samples x1, x2, ..., xn
  • Definition
  • A functional dataset x1, x2, ..., xn is the
    observation of n functional variable X1, X2, ...,
    Xn identically distributed as X.
  • It covers many things.... For example a curve
    dataset

4
Infinite dimensional space? Yes, but
discretized!
5
Infinite dimensional space? Or interpolated!
6
EXAMPLES
7
Long-term prediction of Time Series
  • Functional Neural Networks
  • Amaury Lendasse, Tuomas Kärnä and Francesco
    Corona
  • Inputs and outputs are functions

8
Chemometry? Whats the Problem?
  • Amaury Lendasse and Francesco Corona

9
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12
BOOKS
13
Functional Data Analysisby J. O. Ramsay and B.
W. Silverman
  • Introduction
  • Notation and techniques
  • Representing functional data as smooth functions
  • The roughness penalty approach
  • The registration and display of functional data
  • Principal components analysis for functional data
  • Regularized principal components analysis
  • Principal components analysis of mixed data
  • Functional linear models
  • Functional linear models for scalar responses
  • Functional linear models for functional responses
  • Canonical correlation and discriminant analysis
  • Differential operators in functional data
    analysis
  • Principal differential analysis
  • More general roughness penalties
  • Some perspectives on FDA

14
Nonparametric Functional Data AnalysisFerraty
Frédéric, Vieu Philippe
  • Introduction to functional nonparametric
    statistics
  • Some functional datasets and associated
    statistical problematics
  • What is a well adapted space for functional data?
  • Local weighting of functional variables
  • Functional nonparametric prediction methodologies
  • Some selected asymptotics
  • Computational issues
  • Nonparametric supervised classification for
    functional data
  • Nonparametric unsupervised classification for
    functional data
  • Mixing, nonparametric and functional statistics
  • Some selected asymptotics
  • Application to continuous time processes
    prediction
  • Small ball probabilities, semi-metric spaces and
    nonparametric statistics
  • Conclusion and perspectives

15
Organization
16
T-61.6030 Special Course in Computer and
Information Science III L Functional Data
Analysis
  • Lecturer PhD Francesco Corono and Amaury
    Lendasse
  • Assistants M.Sc. Elia Liitiäinen
  • Credits (ECTS) 7!!!!
  • Semester Spring 2006 (during periods III and
    IV)
  • Seminar sessions On Tuesdays at 14-16 in
    computer science building, Konemiehentie 2,
    Otaniemi, Espoo in hall T4
  • Language English
  • Web http//www.cis.hut.fi/Opinnot/T-61.6030/
  • E-mail eliitiai_at_cc.hut.fi, fcorona_at_cis.hut.fi,
    lendasse_at_hut.fi

17
T-61.6030 Special Course in Computer and
Information Science III L Functional Data
Analysis
18
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