Choose one of the following 4 projects or challenges (click for details).
(A) Google's Pagerank algorithm. As we saw in class Pagerank is nothing else but the problem of finding an eigenvalue and eigenvector of a matrix. We used LU decomposition before, but for huge matrices (like Google has) it is impossible to solve them like this. One uses iterative methods.
The challenge is to explain and illustrate how they work how the Google search algorithm works. One way to see this project is structure it solving Problems 2.26 and 2.27 of Chapter 2 of Moler and organize them for presentation. But you can be creative in other ways If you prefer you can read a great description of how it works . But there are many other sources online.
(C) Dolby Sound and Noise removal algorithm. We saw that signals are inside a vector space of trigonometric functions. When dealing with sound there is static noise. The challenge is given a noisy sound (e.g., AM radio station) you clean it by decomposition into Fourier components. Chapter 8 of Moler's book shows you how to deal with sounds in MATLAB. You should at least present solutions to problems 8.8 and 8.9 of that Chapter.
(B) Curve fitting formulas. In this project the objective is you take an interesting data set (your sources can be anything, one place to start is OpenData ) and try to use Least Squares to find a good fitting model describing the behavior of data. At minimum you are expected to solve (or be inspired by) problem 5.11 or 5.12 in Chapter 5 of Moler's book.
(D) Image Processing and Eigenvalues. The challenge is to illustrate in a meaningful way how linear algebra can be used to analyze simple picture images. Every black and white image can be thought of as a vector in a vector space. How can you recognize a face within a gallery of pictures, say that of Barack Obama?
The principles of how to recognize images are explained in here . At the very least you should solve problems 10.12 and 10.13
GUIDELINES: Every team (of 1 or two people) needs to be set by Nov 12 (write in midterm). The team will deliver by the deadline of Dec 19th the following:
(a) A short power point presentation (up to 30 minutes long, no more than 30 slides) explaining the idea of the solution and the key linear algebra in solving the applied problem. Explanation should be to the level of a math 167 student (someone that knows the basics of linear algebra terminology, etc). Think of preparing a class about the project.
(b) Write MATLAB code that solves the problem in simple instances.
GRADING CRITERIA: Points will be decomposed as follows:
Content (10 pts) - the mathematics in the presentation should be correct. Your should explain what the questions are that you are answering. The code should run without bugs.
Clarity, Quality of presentation, Organization (10 pts). The reader can follow and understand the mathematics being described. The order of slides makes sense, correct spelling of terms. You should use pictures and diagrams when possible.
Creativity and Originality: ( 5 pts). You will get these last points for giving new spins to the challenge. E.g., if you create a youtube video instead of slides, or your MATLAB code can do more than just the minimum expected or can do it in many more cases. Another example is if you use LaTEX to create your transparencies instead of power point. But these are only suggestions to invite you to innovate!
NOTE on outside help: You may only discuss the project with your classmates and with Prof. De Loera or the TA. You are allowed to use any book available in the UC Davis library or online. Sources must be cited!!