Convergence Analysis Of Online Binary Classification Learning Algorithm Based On Reproducing Kernel Banach Spac

The massive amount of data generated by the development of science,technology,and the internet cannot be processed using traditional batch data processing off-line learning classification algorithms.Online learning algorithms have emerged as a solution.The feature space that online classification algorithms are based on is usually a Hilbert space,whose simple geometric structure limits its application and theoretical development.As a result,online learning algorithms based on the Reproducing Kernel Banach Space(RKBS)framework have become a hot research topic.The diversity of distance in the RKBS space greatly expands the scope of data research and enables the establishment of a function space representation theory for a larger range of data types.Effective methods for data classification can be developed based on this,such as considering regularized learning in the RKBS space.The article first defines a kernel regularization online binary classification learning algori thm based on RKBS,which uses a norm with subdifferential and a logistic loss function to def ine an iterative algorithm in RKBS on the based of existing online binary classification algorit hms in RKHS,completing the extension of online classification algorithms from RKHS space to RKBS space.Secondly,we found that the online learning algorithm converges when RKBS satisfies 2-uniform convexity in the convergence process,it is shown that the defined iterative algorithm is feasible to be generalized to RKBS.Finally,for the estimation of learning speed,an upper bound estimation of the error rate is given using the convexity inequality in Banach space,which is also the first application of Banach geometric theory to the study of kernel regularized online learning.This study proposes an effective method for data classification in a larger range of data,breaking the limitations of RKHS and applying the concept of norm sub-differentials to the design of online iterative algorithms in the RKBS.This effectively solves the bottleneck problem of promoting online learning from RKHS to RKBS.We can see that the same convergence rate as in the RKHS can be achieved in the RKBS,which is the latest achievement in online learning.