Math 309 Course Notes
Contents |
Motivation
Link to the netflix prize story
- the web page for the prize http://www.netflixprize.com/
- New York Times Coverage http://bits.blogs.nytimes.com/2009/09/21/netflix-awards-1-million-prize-and-starts-a-new-contest/
Notes from week One
- part one of Ch1 Media:Ch1.pdf
- part two of Ch1 Media:Ch1p2.pdf
Notes from week two and three
- Ch2 Media:Ch2.pdf
Notes from Week three
- Appendix: See sections B.4 and B.5 for the gradient and Hessian of a Quadratic Function. Media:AppendixGriga.pdf
Week Four and Five
We finished Ch 3. This ends the material which will be covered on the midterm. Some additional Media:NotesonLinearAlg.pdf
Week Six and Seven
Here are the examples from class. You first need to
- download CVX http://www.stanford.edu/~boyd/cvx/
- install it in you matlab directory, by running cvx_setup (in the script below).
- use Matlab Code for Week 6
- and Matlab Code for Week 7 (the code has been updated)
We also refer to section 6.3 of Boyd's textbook, which you can download at http://www.stanford.edu/~boyd/cvxbook/ or just download Ch 6 File:BoydCh6.pdf
We discussed:
- norms which measure Fidelity (the two norm) and norms which measure "noisyness" the one norm of the derivative of the signal.
- we illustrated with examples why the "noisyness" norm is large for noisy signals, but not large for piecewise constant signals.
- we set up a table with the two norms, illustrating how the sum of the fidelity norm and noisyness norm should denoise a signal.
- we all talked about the differences between the one norm and the two norm, as well as the norm of the second derivative of the signal.
- HW problems pursue these topics further.
Week Eight
More theory. The deniosing examples involved projections onto convex sets. The support vector machines (recall Griva 1.7.2) involve separating convex sets. This week we will explore geometric, computational, and analytic approaches to these problems. References are:
- Class notes
- Griva Sec 1.7.2 (Motivation)
- Griva Ch 14.
- Boyd Sec 8.2.
Week Nine
Monday was a research talk by Jack Xin which used optimization to solve problems in signal processing. The applications were: finding chemical spetra using peaks and separating two stereo sound signals for hearing aids.
Thursday: we will discuss general conditions for minima for constrained optimization problems following Griva.
Week Ten
Check out a contest, with 2000 Euros in prizes. This looks like it could be solved using methods from our class.