Progress Report #2 Alvaro Velasquez

Project Selection I chose to work with Nasim Souly on the project titled “Subspace Clustering via Graph Regularized Sparse Coding”. I chose this topic because the mathematical aspect of it interested me and I believe that sparse coding in general is useful to many fields in computer science and possibly graph theory.

Papers Read Sparse Subspace Clustering via Group Sparse Coding.- Saha et al. Graph Regularized Sparse Coding for Image Representation.- Zheng et al. Least Squares Optimization with L1-Norm Regularization. - Mark Schmidt Robust Face Recognition via Sparse Representation.- Wright et al.

Papers Read A Discrete Chain Graph Model for 3d+t Cell Tracking with High Misdetection Robustness. - Kausler et al. Evaluation of Super-Voxel Methods for Early Video Processing.- Xu et al. Spectral Clustering of Linear Subspaces for Motion Segmentation. - Lauer et al. Graph Regularized Nonnegative Matrix Factorization for Data Representation. - Cai et al.

Topics learned L0, L1, L2, Lp norms as constraints. Conjugate and Laplacian matrices. Clustering methods. Sparse coding principles. Basic spectral graph theory (eigenvalues and eigen subspaces of adjacency matrix for image classification). Convex minimization (Gradient descent, subgradient method, etc.).

Work for this week I will be trying to implement the first steps of video segmentation using sparse coding (no graph regularization yet). To achieve this, I will solve the minimization problem ||y – DX|| 2 + lambda||X|| 1. Y is an image patch, D is the dictionary, and X is the coefficient matrix to be made sparse via L1 minimization. I will test my solution on the SegTrack data set.