2020/05/14 by Hufei Zhu, Zhu, Hufei
Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and ELM #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2005.07045
openalex publication_date 2020/05/14 · openalex created_date 2020/05/21 · openalex updated_date 2026/07/28
Greville's method has been utilized in (Broad Learn-ing System) BLS to propose an effective and efficient incremental learning system without retraining the whole network from the beginning. For a column-partitioned matrix where the second part consists of p columns, Greville's method requires p iterations to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part. The incremental algorithms in BLS extend Greville's method to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part by just 1 iteration, which have neglected some possible cases, and need further improvements in efficiency and numerical stability. In this paper, we propose an efficient and numerical stable algorithm from Greville's method, to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part by just 1 iteration, where all possible cases are considered, and the recently proposed inverse Cholesky factorization can be applied to further reduce the computational complexity. Finally, we give the whole algorithm for column-partitioned matrices in BLS. On the other hand, we also give the proposed algorithm for row-partitioned matrices in BLS.