Mathematical Foundations of Data Analysis II
Organizer: Dr. Boqiang Huang
Lectures: Tuesday 16-17:30 (Hörsaal 2.03, Raum 203), Thursday 14-15.30 (Cohn-Vossen Raum 313)
Exercises: Thursday 16-17:30 (Cohn-Vossen Raum 313)
This is part II of the lecture serial "Mathematical Foundations of Data Analysis". Part I had been given in WS 2018/2019.
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 statistical data analysis methods (including statistical learning).
In part II, we mainly focus on the mathematical explanation of multi-channel data decomposition/representation in terms of principal component analysis (PCA) and independent component analysis (ICA), typical regression methods based on linear or nonlinear models, typical classification/clustering methods, where the support vector machine (SVM) will be particularly discussed. Moreover, the concept of supervised learning and unsupervised learning will be explained in details. If we have more time, the ideas of those famous machine learning methods, e.g. backpropagation (BP) neural network, convolutional neural network (CNN), recursive neural network (RNN), residual neural network etc, will be also investigated.
The course will be given in English, and it is mainly designed for Master Students.
1. G. James, D. Witten, T. Hastie, R. Tibshirani, An introduction to statistical learning: with applications in R, Springer, 2013.
2. T. Hastie, R. Tibshirani, J. Friedman, The elements of statistical learning: data mining, inference, and prediction, Springer Series in Statistics, 2016.
3. I. Goodfellow, Y. Bengio, A. Courville, Deep Learning, MIT Press, 2016.
4. A. Hyvaerinen, J. Karhunen, E. Oja, Independent Component Analysis, New York: John Wiley & Sons Inc., 2001.
5. A. Antoniou, W.-S. Lu, Practical optimization: algorithms and engineering applications, Springer, 2007.
6. Y. LeCun, Y. Bengio, G. Hinton, Deep learning, Nature, vol. 521, pp. 436-444, 2015.
7. Y. LeCun, Y. Bengio, Convolutional networks for images, speech, and time-series, The Handbook of Brain Theory and Neural Networks, vol. 3361, 1995.
8. C. Goller, A. Kuechler, Learning task-dependent distributed representations by backpropagation through structure. IEEE Int. Conf. on Neural Networks, 1996.
9. K. He, X. Zhang, S. Ren, J. Sun, Deep Residual Learning for Image Recognition, IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), Las Vegas, USA, 2016.
Week01 2019.04.02 Intro
Week02 2019.04.09 Pro&Info 2019.04.11 Num Paper: IMCRA Exercise01
Week03 2019.04.16 StaMod Exercise02
Week04 2019.04.23 Exercise03
Week05 2019.04.30 Exercise04
Week06 2019.05.07 Exercise05 (updated on 2019.05.22)
Week07 2019.05.14 -- 2019.05.16 Canceled
Week08 2019.05.21 Exercise06
Week09 2019.05.30 Project01 DataSet
Week12 2019.06.18 Exercise07
Week15 2019.07.09 - 2019.07.12 OralExamPlan
Week16 2019.07.17 Project02 DataSet