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Functional Data Analysis

CORONA FRANCESCO, Lendasse Amaury, Liitiäinen Elia

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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.

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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

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Infinite dimensional space? Yes, but discretized!

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Infinite dimensional space? Or interpolated!

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EXAMPLES

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Long-term prediction of Time Series Functional Neural Networks

Amaury Lendasse, Tuomas Kärnä and Francesco Corona Inputs and outputs are functions

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Estimatedoutput

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 50 100 150 200 250

Output concentration

Model

Input-output pair

Chemometry? What’s the Problem?

Amaury Lendasse and Francesco Corona

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BOOKS

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Functional Data Analysisby 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

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Nonparametric Functional Data AnalysisFerraty Frédéric, Vieu Philippe

1. Introduction to functional nonparametric statistics2. Some functional datasets and associated statistical problematics3. What is a well adapted space for functional data?4. Local weighting of functional variables5. Functional nonparametric prediction methodologies6. Some selected asymptotics7. Computational issues8. Nonparametric supervised classification for functional data9. Nonparametric unsupervised classification for functional data10.Mixing, nonparametric and functional statistics11.Some selected asymptotics12.Application to continuous time processes prediction13.Small ball probabilities, semi-metric spaces and nonparametric statistics14.Conclusion and perspectives

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Organization

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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 LiitiäinenCredits (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

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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

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Time Lecturer Subject23.02 Amaury Lendasse Presentation of the course

30.02 Ramsay: Chapers 1 2 3

06.02 Ramsay: Chapers 4 5 6

13.02 Ramsay: Chapers 7 8 9

20.02 Ramsay: Chapers 10 11 12

27.02 Ramsay: Chapers 13 14 15

06.03 Exam week

13.03 Ramsay: Chapers 16 17 18

20.03 Ramsay: Chapers 19 20 21 22

27.03 Ferraty: Chapers 1 2 3 4

03.04 EASTER VACATION

10.04 Ferraty: Chapers 5 6 7

17.04 Ferraty: Chapers 8 9 12

24.04 Project