Online Sequential Extreme Learning of Sparse Ridgelet Kernel Regressor for Nonlinear Time-Series Prediction

In this paper, inspired by Multiscale Geometric Analysis (MGA), a Sparse Ridgelet Kernel Regressor (SRKR) is constructed by combing ridgelet theory with kernel trick. Considering the preferable future of sequential learning over batch learning, we exploit the kernel method in an online setting using the sequential extreme learning scheme to predict nonlinear time-series successively. By using the dimensionality non-separable ridgelet kernels, SRKR is capable of processing the high-dimensional data more efficiently. The online learning algorithm of the examples, named Online Sequential Extreme Learning Algorithm (OS-ELA) is employed to rapidly produce a sequence of estimations. OS-ELA learn the training data one-by-one or chunk by chunk (with fixed or varying size), and discard them as long as the training procedure for those data is completed to keep the memory bounded in online learning. Evolution scheme is also incorporated to obtain a 'good' sparse regressor. Experiments are taken on some nonlinear time-series prediction problems, in which the examples are available one by one. Some comparisons are made and the experimental results show its efficiency and superiority to its counterparts.