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

2. 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.

3. Lendasse A., Corona F., Liitiäinen E.3 What is a Functional Dataset?  Several functional samples: x 1, x 2,..., x n  Definition A functional dataset x 1, x 2,..., x n is the observation of n functional variable X 1, X 2,..., X n identically distributed as X.  It covers many things.... For example a curve dataset

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

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

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

7. 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

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

9. Lendasse A., Corona F., Liitiäinen E.9

10. 10

11. Lendasse A., Corona F., Liitiäinen E.11

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

13. Lendasse A., Corona F., Liitiäinen E.13 Functional Data Analysis by J. O. Ramsay and B. W. Silverman 1.Introduction 2.Notation and techniques 3.Representing functional data as smooth functions 4.The roughness penalty approach 5.The registration and display of functional data 6.Principal components analysis for functional data 7.Regularized principal components analysis 8.Principal components analysis of mixed data 9.Functional linear models 10.Functional linear models for scalar responses 11.Functional linear models for functional responses 12.Canonical correlation and discriminant analysis 13.Differential operators in functional data analysis 14.Principal differential analysis 15.More general roughness penalties 16.Some perspectives on FDA

14. Lendasse A., Corona F., Liitiäinen E.14 Nonparametric Functional Data Analysis Ferraty Frédéric, Vieu Philippe 1.Introduction to functional nonparametric statistics 2.Some functional datasets and associated statistical problematics 3.What is a well adapted space for functional data? 4.Local weighting of functional variables 5.Functional nonparametric prediction methodologies 6.Some selected asymptotics 7.Computational issues 8.Nonparametric supervised classification for functional data 9.Nonparametric unsupervised classification for functional data 10.Mixing, nonparametric and functional statistics 11.Some selected asymptotics 12.Application to continuous time processes prediction 13.Small ball probabilities, semi-metric spaces and nonparametric statistics 14.Conclusion and perspectives

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

16. 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

17. Lendasse A., Corona F., Liitiäinen E.17 Each student gives a presentation in the seminar. In addition, requirements include a project work and active participation in the lectures (one absence is allowed). No homeworks! T-61.6030 Special Course in Computer and Information Science III L: Functional Data Analysis

18. Lendasse A., Corona F., Liitiäinen E.18 TimeLecturerSubject 23.02Amaury LendassePresentation of the course 30.02Ramsay: Chapers 1 2 3 06.02Ramsay: Chapers 4 5 6 13.02Ramsay: Chapers 7 8 9 20.02Ramsay: Chapers 10 11 12 27.02Ramsay: Chapers 13 14 15 06.03 Exam week 13.03Ramsay: Chapers 16 17 18 20.03Ramsay: Chapers 19 20 21 22 27.03Ferraty: Chapers 1 2 3 4 03.04 EASTER VACATION 10.04Ferraty: Chapers 5 6 7 17.04Ferraty: Chapers 8 9 12 24.04 Project