Light on Math ML: Intuitive guide to matrix factorization

That one would make more sense. In a video feed, a static background would contain most data (data, not information) in terms of the volume. The remaining sparse information belongs to foreground -- because foreground is typically taking small space in the video. Therefore, if I try to force M to become a sparse matrix S, I'd probably capture foreground movements in S. Another way to think is that, S captures the outliers in your data! Now adding up L and S should give us the original video, which is what the robust PCA equation is saying. Now easier said than done! How do we actually ensure these properties for these matrices.