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# Mathematical Foundations of Data Analysis

## Lecture:

Tuesday 10-11.30, Thursday 10-11.30 (Seminarraum 3)
Tuesday      10-11.30    Ground Floor 304 Hoersaal 0.024 (88 Sitzpl.)                Zuelpicher Str. 47b, Biozentrum Koeln (2.BA)
Hoersaal 0.024 will be occupied on 16th Oct., 13th Nov. and 27th Nov.!!!
On 27th Nov., the lecture will be given in 326 Seminarraum 0.03, Ground Floor, Zülpicher Straße 77a
Thursday    10-11.30    Ground Floor 136 Kleiner Hoersaal XXXI (67 Sitzpl.)    Gyrhofstr. 15, Alte Botanik

## Tutorial:

Thursday 16:00-17:30 (Seminarraum 3)
Thursday    16-17.30   Ground Floor 321 Hoersaal III (190 Sitzpl.)                     Zuelpicher Str. 77, Physikalische Institute

## Contents:

This is part I of the lecture serial \Mathematical Foundations of Data Analysis\. Part II will
be given in SS 2019.
The whole serial aims to give a comprehensive introduction of state-of-the-art data analysis
methods together with their mathematical motivations, theories, and algorithm realizations in
MATLAB. In part I, we study deterministic data analysis methods. In part II, we study stati-
stical data analysis methods (including statistical learning).
In part I, we mainly focus on the mathematical explanation of Fourier Analysis, Wavelet Trans-
forms, Empirical Mode Decompositions (EMD) and their di erent modi cations, e.g. Fast Fou-
rier Transform (FFT), Discrete Cosine Transform (DCT), Synchrosqueezed Wavelet Trans-
form (SWT), Optimization-based EMD (OEMD), High-Dimensional Model Representation
(HDMR), not only for one-dimensional (1-D) data but also for multi-variate data or multi-
dimensional (Multi-D) data.
The course will be given in English, and it is mainly designed for Master Students. It is possible
to generate a topic of your Master Thesis based on your work in some designed projects.

## Literature:

1. S. Mallat, A wavelet tour of signal processing, third edition: The sparse way, Academic Press,
2008.
2. C.K. Chui, Q. Jiang, Applied mathematics: Data compression, spectral methods, Fourier
analysis, wavelets, and applications, Atlantis Press, 2013.
3. I. Daubechies, J. Lu, H.-T. Wu, Synchrosqueezed wavelet transforms: An empirical mo-
de decomposition-like tool, Applied and Computational Harmonic Analysis, vol. 30, pp. 243-
261,2011.
4. N.E. Huang, S.S.P. Shen, Hilbert-Huang transform and its applications, World Scienti c Pu-
blishing, Singapore, 2005.

Week 01        2018.10.09    Course Introduction        2018.10.11    MatlabExamples

Announcement: We have applied larger lecture and tutorial rooms. All room details will be clarified on 18.10.2018.

Week 02        2018.10.16    Lecture Notes    Problem Set 01        2018.10.18    Lecture Notes    Matching Pursuits

Week 03        2018.10.23    Problem Set 02

Week 04        2018.10.30    Problem Set 03

Week 06        2018.11.13    Lecture Notes    Problem Set 04        2018.11.15    Lecture Notes    Problem4Matlab

Week 07        2018.11.20    Problem Set 05

Announcement: On Tue. 27.11.2018, the lecture will be given in 326 Seminarraum 0.03, Ground Floor, Zülpicher Straße 77a.

Week 08        2018.11.27    Problem Set 06        2018.11.29    Project 01

Week 09        2018.12.04    Problem Set 07

Week 10        2018.12.11    Lecture Notes          2018.12.13    Synchrosqueezed Wavelet Transforms

Week 12        2019.01.08    Problem Set 08

Week 13        2019.01.15    Problem Set 09

Week 14        2019.01.24    Project 02

Week 15        2019.01.29 - 2019.01.31        Plan of the Oral Exam

Best Report Sample from Submitted Project - 1:    Sample-1    Sample-2