On Learning Rotations
Raman Arora · 2009
An algorithm is presented for online learning of rotations. The proposed algorithm involves matrix exponentiated gradient updates and is motivated by the von Neu-mann divergence. The multiplicative updates are exponentiated skew-symmetric matrices which comprise the Lie algebra of the rotation group. The orthonormal-ity and unit determinant of the matrix parameter are preserved using matrix log-arithms and exponentials and the algorithm lends itself to intuitive interpretation in terms of the differential geometry of the manifold associated with the rotation group. A complexity reduction result is presented that exploits the eigenstructure of the matrix updates to simplify matrix exponentiation to a quadratic form. 1