Cholesky Factorization Based Online Sequential Extreme Learning Machines with Persistent Regularization and Forgetting Factor

Abstract

The online sequential extreme learning machine with persistent regularization and forgetting factor (OSELM-PRFF) can avoid potential singularities or ill-posed problems of online sequential regularized extreme learning machines with forgetting factors (FR-OSELM), and is particularly suitable for modelling in non-stationary environments. However, existing algorithms for OSELM-PRFF are time-consuming or unstable in certain paradigms or parameters setups. This paper presents a novel algorithm for OSELM-PRFF, named “Cholesky factorization based” OSELM-PRFF (CF-OSELM-PRFF), which recurrently constructs an equation for extreme learning machine and efficiently solves the equation via Cholesky factorization during every cycle. CF-OSELM-PRFF deals with timeliness of samples by forgetting factor, and the regularization term in its cost function works persistently. CF-OSELM-PRFF can learn data one-by-one or chunk-by-chunk with a fixed or varying chunk size. Detailed performance comparisons between CF-OSELM-PRFF and relevant approaches are carried out on several regression problems. The numerical simulation results show that CF-OSELM-PRFF demonstrates higher computational efficiency than its counterparts, and can yield stable predictions.