{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:25:37Z","timestamp":1753881937096,"version":"3.41.2"},"reference-count":35,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["92267203"],"award-info":[{"award-number":["92267203"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Key-Area Research and Development Program of Guangdong Province","award":["2023B0303030001"],"award-info":[{"award-number":["2023B0303030001"]}]},{"name":"Guangdong Introducing Innovative and Entrepreneurial Teams","award":["2019ZT08X214"],"award-info":[{"award-number":["2019ZT08X214"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> 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\u20131.57 when [Formula: see text] and 1.09\u20131.13 when [Formula: see text], while on the NYU object recognition benchmark dataset, the speedups are 1.10\u20131.35 when [Formula: see text] and 1.07\u20131.09 when [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219691324500267","type":"journal-article","created":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T14:18:46Z","timestamp":1715955526000},"source":"Crossref","is-referenced-by-count":0,"title":["An efficient implementation to compute the pseudoinverse for the incremental broad learning system on added inputs"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1629-6227","authenticated-orcid":false,"given":"Hufei","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Wuyi University, Jiangmen, 529020, Guangdong, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4145-823X","authenticated-orcid":false,"given":"Zhulin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, South China University of Technology, Guangzhou, Guangdong, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5451-7230","authenticated-orcid":false,"given":"C. L. Philip","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, South China University of Technology, Guangzhou, Guangdong, P. R. China"},{"name":"Pazhou Lab, Guangdong, Guangzhou, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6795-1925","authenticated-orcid":false,"given":"Yanyang","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Wuyi University, Jiangmen, 529020, Guangdong, P. R. 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