Subspaces and Machine Learning

Low-dimensional linear subspace approximations to high-dimensional data have provided a powerful tool to many areas of engineering and science: problems of estimation, detection and prediction, with applications such as network monitoring, collaborative filtering, object tracking in computer vision, and environmental sensing. In this talk I will give you a reminder of what are subspaces, the SVD, and PCA. I'll discuss several of the applications that use these for modeling and approximation. Then I'll introduce a little bit of optimization, and talk about why optimization theory and algorithms offer a very nice framework to pose and solve new engineering problems related to subspace identification.