Spectral clustering has become a standard method for data analysis used in a broad range of
applications.  I will describe a new class of algorithms for multiway spectral clustering based on
optimization of a certain class of functions after the spectral embedding.   
These algorithms can be interpreted geometrically as recovering a discrete weighted simplex.
They have some resemblance to Independent Component Analysis and involve optimization of  ``contrast functions" over a sphere.
However, in our case  theoretical guarantees can be provided for a much broader class of  functions satisfying a ``hidden convexity" condition.
 
The algorithms are straightforward to implement, efficient and are not initialization-dependent.

Joint work with Luis Rademacher and James Voss.