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
(No Transcript)
10
(No Transcript)
11
(No Transcript)
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
(No Transcript)