Singular Value Decomposition update and its application to (Inc)-OP-ELM

In this paper, we consider the theory and the practical implementation of Singular Value Decomposition (SVD) update algorithm. By updating, we mean using previously computed SVD to compute the SVD of a matrix augmented by one column (or row). We compare it with the standard SVD algorithm in terms of computational complexity and accuracy. We show that SVD update algorithm scales better and works faster than SVD computed from scratch. In addition, we analyze errors in singular values after many consecutive updates and verify that they are within reasonable bounds. Finally, we apply SVD update to speed up OP-ELM algorithm and propose new algorithm (Inc)-OP-LEM. In conclusion, we believe that SVD update can be applied to other computational intelligence methods to improve their computational time and scaling.