Abstract:

Unsupervised learning is the step stone of machine learning (or artificial intelligence if you like) to the next generation. Several efforts have been made in past decades from both the algorithmic and theoretical viewpoints. We will first discuss a widely applied unsupervised learning algorithm, diffusion map. Then we provide our current theoretical understanding of diffusion map under the differential geometry framework, particularly the spectral embedding theory. If time permits, a comparison with other algorithms, like locally linear embedding or ISOMAP, or some variations, like vector diffusion map and connection Laplacian over the principal bundle structure, will be discussed.