  In this brief, we improve the Broad Learning System (BLS) [7] by reducing the
computational complexity of the incremental learning for added inputs. We
utilize the inverse of a sum of matrices in [8] to improve a step in the
pseudoinverse of a row-partitioned matrix. Accordingly we propose two fast
algorithms 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. Specifically, when q > k, the proposed algorithm computes only a
k * k matrix inverse, instead of a q * q matrix inverse in the existing
algorithm. Accordingly it can reduce the complexity dramatically. Our
simulations, which follow those for Table V in [7], show that the proposed
algorithm and the existing algorithm achieve the same testing accuracy, while
the speedups in BLS training time of the proposed algorithm over the existing
algorithm are 1.24 - 1.30.
