Dimensionality Reduction and Manifold Estimation

Prof. Mladen Victor Wickerhauser

NEWS

  • hw.pdf, list of homework problems extracted from the lectures.
  • projects.txt, list of suggested projects for the end-of-course presentation.

LINKS

EXAMPLES

  • 01codes.txt, Part 1 (Manifolds) software for Octave.
  • 02codes.txt, Part 2 (Regression) software for Octave.
  • 03codes.txt, Part 3 (Compression) software for Octave.
  • 04datav.txt (Multivariate visualization) R codes.
  • 04stepr.txt (Stepwise regression) R codes.
  • 04trees.txt (Classification trees) R codes.
  • 04malda.txt (Iris data and LDA) R codes.
  • 04clust.txt (Clustering R codes)
  • 04isomap.txt (Multidimensional scaling with Isomap) R codes.
  • 06difmap.txt Octave commands to build diffusion maps, with an example.
  • 06swiss.txt Octave commands for Swiss Roll diffusion map.
  • sr2000x3.dat Plain text file of Swiss Roll points in 3D.
  • dmgk.m Octave function to return first 6 diffusion map coordinates. (Save this file in your Octave home folder.)
  • 07multi.txt, R commands to plot multinomial probabilities on 3 parameters.
  • 07diric.txt, R commands to plot Dirichlet densities on 3 parameters.
  • 07metro.txt, R commands to estimate Beta posteriors with MCMC.

Syllabus

Topics. This course will be a survey of the theory and practice of constructing locally p-dimensional parameterizations of subsets in R^d where p is much smaller than d. Topics will include linear regression, singular value decomposition and CUR factorization, principal component analysis in linear subspaces, smooth manifolds and the implicit function theorem, nonlinear manifold estimation and machine learning with multidimensional scaling and diffusion maps. There will be an emphasis on applications and algorithms.

Prerequisites. Prerequisites are linear algebra and basic Fourier analysis. It will be useful to have some knowledge of statistics and some experience in computer programming.

Time. Class will meet 2-4pm beginning Jan.18th, in Room A.201 at PMF. In-person attendance should be possible and is encouraged. Lectures will be livestreamed and I will request that they be videorecorded for later viewing.

Texts. The lectures will follow a series of book chapters and survey papers on this tentative list of topics:

Homework. Homework will be assigned from time to time. Collaboration on homework is permitted and encouraged, but each student must submit individually written solutions. [List of homework problems (hw.pdf), extracted from the lectures.]

Tests. There will be no examinations. Near the end of the course, each student will be required to present a lecture on one of the topics covered during the course. [List of suggested projects (projects.txt), for the end-of-course presentation.]

Grading. One grade will be assigned for all homework and one for the class presentation. These grades will contribute equally to the course grade.

Office Hours. See the instructor after class or by appointment.


Questions? Return to Mladen Victor Wickerhauser's home page for contact information.