An Efficient Implementation to Compute the Pseudoinverse for the Incremental Broad Learning System on Added Inputs

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 [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] and [Formula: see text] denote the number of additional training samples and the total number of nodes, respectively. The proposed implementation for [Formula: see text] utilizes the inverse of a sum of matrices to compute only a [Formula: see text] matrix inverse, instead of a [Formula: see text] matrix inverse in the original implementation, and the corresponding speedup for the matrix inversion operation in the number of floating-point operations is [Formula: see text]. Moreover, it also speeds up two relevant matrix multiplication operations in the original implementation. On the other hand, the proposed implementation for [Formula: see text] 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 [Formula: see text] and 1.09–1.13 when [Formula: see text], while on the NYU object recognition benchmark dataset, the speedups are 1.10–1.35 when [Formula: see text] and 1.07–1.09 when [Formula: see text].