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Lecture SS 19 Selected Topics in Numerical Methods in Science and Technology

Nonlinear Dimensionality Reduction

Prof. Jochen Garcke
Wednesdays, 10:15 to 12:00 in room 2.035 Endenicher Allee 19b.
Alternative Slot Thursdays, 10:15 to 12:00 in room 2.035 Endenicher Allee 19b.
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The second round of exams will be in the week of the 2nd September. If you have days in that week where you are unavailable, please contact me.

The website to compare faces generates by the StyleGAN algorithm with real images is Which Face is Real?


Mathematics plays a significant role in the analysis and further development of many machine learning and data mining algorithms. This lecture will cover nonlinear dimensionality reduction, a.k.a. manifold learning, for high-dimensional data analysis and data representation. At least the following approaches will be addressed:

  • Principal Component Analysis (as the baseline linear approach)
  • IsoMap
  • Diffusion Maps
  • t-SNE
  • (Variational) Autoencoder

Lecture Notes

Lecture Notes (10. Jul 2019)