An efficient implementation to compute the pseudoinverse for the incremental broad learning system on added inputs
Abstract
In this paper, we improve the broad learning system (BLS) by speeding up the incremental learning for added inputs. We propose an efficient implementation for a step that is in the pseudoinverse computation of a partitioned matrix, to reduce the computational complexity. The proposed efficient implementation has two different forms for the cases of q>k and q≤k, respectively, where q and k denote the number of additional training samples and the total number of nodes, respectively. The proposed implementation for q>k utilizes the inverse of a sum of matrices to compute only a k×k matrix inverse, instead of a q×q matrix inverse in the original implementation, and the corresponding speedup for the matrix inversion operation in the number of floating-point operations is 12(q/k)3. Moreover, it also speeds up two relevant matrix multiplication operations in the original implementation. On the other hand, the proposed implementation for q≤k speeds up one matrix multiplication operation in the original implementation. The numerical simulations show that both the proposed and original implementations always achieve the same testing accuracy. On the Modified National Institute of Standards and Technology dataset, the speedups of the proposed efficient BLS implementation over the original BLS implementation in total training time are 1.35–1.57 when q>k and 1.09–1.13 when q<k, while on the NYU object recognition benchmark dataset, the speedups are 1.10–1.35 when q>k and 1.07–1.09 when q<k.
