1. Progress Report
Alvaro Velasquez

2. Topic: “Subspace Clustering via Graph Regularized Sparse Coding”
Currently using the SegTreck_ dataset to track objects of interest using sparse representations.
Next step is to add a graph regularizer and Laplacian matrix and apply this framework to video segmentation.

3. I started by choosing an object of interest and splitting into six patches. I calculated the sparse representation of these patches by representing them as a linear combination of coefficients and a dictionary.
The equation is presented as a minimization problem to minimize the L1-norm of the coefficients matrix, thereby guaranteeing sparsity.
The equation is solved using the SPAMS library for Matlab. More specifically, the function mexLasso is used (the dictionary and the column-wise vector representation of the patches are unit normalized first).

4. To track the patches in sequential frames in the video, we find the patches with the minimal Euclidean distance from the patches in the previous frame.
The candidate matches are selected as all the possible patches in a subset of the image where the object of interest is likely to be (using the whole image proved to be too expensive).
Six patches were tracked per frame for 20 frames. Only two of the 120 total patches were outliers.

5. Each patch is 18x18. They are represented as 324x1 vectors, of which all elements are initially nonzero.
After finding the sparse representation of each patch, the new 324x1 vectors contained between 10 and 20 nonzero elements, but there was less than 0.1% difference in the euclidean distance from the sparse representation and the original representation.