Mathematical Foundations of Data Analysis
Organizer: Dr. Boqiang Huang
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
Thursday 16:00-17:30 (Seminarraum 3)
Thursday 16-17.30 Ground Floor 321 Hoersaal III (190 Sitzpl.) Zuelpicher Str. 77, Physikalische Institute
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.
1. S. Mallat, A wavelet tour of signal processing, third edition: The sparse way, Academic Press,
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-
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