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# Functional Data Analysis

Functional Data Analysis. CORONA FRANCESCO, Lendasse Amaury , Liitiäinen Elia. What is a Functional Variable?. From different fields of sciences! Environmetrics, Chemometrics, Biometrics, Medicine, Econometrics, Time series prediction, ... Collected data are curves Definition

## Functional Data Analysis

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1. Functional Data Analysis CORONA FRANCESCO, Lendasse Amaury, Liitiäinen Elia Lendasse A., Corona F., Liitiäinen E.

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. Lendasse A., Corona F., Liitiäinen E.

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 Lendasse A., Corona F., Liitiäinen E.

4. Infinite dimensional space? Yes, but discretized! Lendasse A., Corona F., Liitiäinen E.

5. Infinite dimensional space? Or interpolated! Lendasse A., Corona F., Liitiäinen E.

6. EXAMPLES Lendasse A., Corona F., Liitiäinen E.

7. Long-term prediction of Time Series • Functional Neural Networks • Amaury Lendasse, Tuomas Kärnä and Francesco Corona • Inputs and outputs are functions Lendasse A., Corona F., Liitiäinen E.

8. Input-output pair Output concentration  Model Estimatedoutput Chemometry? What’s the Problem? • Amaury Lendasse and Francesco Corona Lendasse A., Corona F., Liitiäinen E.

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12. BOOKS Lendasse A., Corona F., Liitiäinen E.

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 Lendasse A., Corona F., Liitiäinen E.

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 Lendasse A., Corona F., Liitiäinen E.

15. Organization Lendasse A., Corona F., Liitiäinen E.

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@cc.hut.fi, fcorona@cis.hut.fi, lendasse@hut.fi Lendasse A., Corona F., Liitiäinen E.

17. T-61.6030 Special Course in Computer and Information Science III L: Functional Data Analysis Lendasse A., Corona F., Liitiäinen E.

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