Recovering the Optimal Solution by Dual Random Projection

26th Conference on Learning Theory

Lijun Zhang [e-mail] ; Rong Jin [e-mail] ; GE Global Research ; San Ramon ; CA 94583 ; USA

PID  :  121246

来源: CEUR

【 摘 要 】

Random projection has been widely used in data classification. It maps highdimensional data into a lowdimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are focused on analyzing the classification performance of using random projection, in this work, we consider the recovery problem, i.e., how to accurately recover the optimal solution to the original optimization problem in the highdimensional space based on the solution learned from the subspace spanned by random projections. We present a simple algorithm, termed Dual Random Projection, that uses the dual solution of the lowdimensional optimization problem to recover the optimal solution to the original problem. Our theoretical analysis shows that with a high probability, the proposed algorithm is able to accurately recover the optimal solution to the original problem, provided that the data matrix is of low rank or can be well approximated by a low rank matrix.