Explore a cutting-edge approach to learning unions of subspaces from data corrupted by outliers in this 51-minute lecture by René Vidal from Johns Hopkins University. Delve into Dual Principal Component Pursuit (DPCP), a non-convex method that outperforms state-of-the-art techniques in handling high-dimensional subspaces and large numbers of outliers. Examine the geometric and probabilistic conditions for DPCP's success, and discover how it can tolerate as many outliers as the square of the number of inliers. Learn about various optimization algorithms for solving the DPCP problem, including a Projected Sub-Gradient Method with linear convergence to the global minimum. Gain insights into experimental results demonstrating DPCP's superior performance in handling outliers and higher relative dimensions compared to existing methods.