MLSP Fall 2016: Homework 1
SUBMISSION FORMAT INSTRUCTIONS

The template for assignment 1 is available here: hw1_template.tar

Problem 1: Linear Algebra

Please submit all results for this part in “Report_YourAndrewID.pdf” in you submission.

Problem 2: Projections

The “Problem2” subdirectory has a template file called Run_problem2.m. Write your code into this script. There are instructions within the script on how to save your outputs. We repeat the instructions below.

The scripts must be written so that we can simply run Run_problem2.m from matlab within the directory, without any additional commands. If we cannot run the program, we cannot score you.

1. Analysis by individual note
   1. Your solution will give you one “score” $W_i$ per note. Place all the scores in a single matrix ${\mathbf W}$ and save this as a single file named “problam1a.dat“
   2. For this part, the synthesized music must be saved as “problem1b_synthesis.wav” within the “results” directory.
2. Joint analysis using all notes
   1. Your solution will give you singe “score” matrix ${\mathbf W}$. Save this as a single file named “problam2a.dat“
   2. For this part, the synthesized music must be saved as “problem2b_synthesis.wav” within the “results” directory.

Problem 3: Optimization and non-negative decompositions

1. For this part, return the solution in “Report_YourAndrewID.pdf” in you submission.
2. for this part, store the final ${\mathbf W}$ for each $\eta$ value in a text file called “problem3b_eta_xxx.dat” where xxx is the actual $\eta$ value. E.g. for $\eta = 0.01$, xxx will be “0.01”. Plot the plot of $E$ (total error) vs. iterations for each $\eta$ in a file called “problem3b_eta_xxx_errorplot.png”, where xxx is the $\eta$ value. Also plot the $\eta$ vs. $E$ as a bar plot and save it in “problem3b_eta_vs_E.png“.
3. For this part, save the synthesized music in the “results” directory in a file called “polyushka_syn.wav”.