Geometric Aspects of Optimization and Applications to Spectral Clustering Mikhail Belkin Ohio State University I will describe a class of algorithms for recovering a certain latent basis and make a connection to geometry of optimization over a sphere. The proposed algorithms are based on what may be called "gradient iteration" that are simple to describe and to implement. They can be viewed as generalizations of both the classical power method for recovering eigenvectors of symmetric matrices as well as the recent work on power methods for tensors. I will discuss theoretical guarantees and new algorithms for multiway spectral clustering and problems such as image segmentation. Joint work with L. Rademacher and J. Voss.