Online Kernel PCA with Entropic Matrix Up dates

Online Kernel PCA with Entropic Matrix Up dates
Dima Kuzmin - University of California - Santa Cruz, USA Manfred K. Warmuth - University of California - Santa Cruz, USA
A number of updates for density matrices have been developed recently that are motivated by relative entropy minimization problems. The updates involve a softmin calculation based on matrix logs and matrix exponentials. We show that these updates can be kernelized. This is important because the bounds provable for these algorithms are logarithmic in the feature dimension (provided that the 2-norm of feature vectors is bounded by a constant). The main problem we focus on is the kernelization of an online PCA algorithm which belongs to this family of updates.

Dima Kuzmin - University of California - Santa Cruz, USA
Manfred K. Warmuth - University of California - Santa Cruz, USA

A number of updates for density matrices have been developed recently that are motivated by relative entropy minimization problems. The updates involve a softmin calculation based on matrix logs and matrix exponentials. We show that these updates can be kernelized. This is important because the bounds provable for these algorithms are logarithmic in the feature dimension (provided that the 2-norm of feature vectors is bounded by a constant). The main problem we focus on is the kernelization of an online PCA algorithm which belongs to this family of updates.