In this paper, we propose a deep learning framework based on randomized neural network. In particular, inspired by the principles of Random Vector Functional Link (RVFL) network, we present a deep RVFL network (dRVFL) with stacked layers. The parameters of the hidden layers of the dRVFL are randomly generated within a suitable range and kept fixed while the output weights are computed using the closed form solution as in a standard RVFL network. We also propose an ensemble deep network (edRVFL) that can be regarded as a marriage of ensemble learning with deep learning. Unlike traditional ensembling approaches that require training several models independently from scratch, edRVFL is obtained by training a single dRVFL network once. Both dRVFL and edRVFL frameworks are generic and can be used with any RVFL variant. To illustrate this, we integrate the deep learning networks with a recently proposed sparse-pretrained RVFL (SP-RVFL). Extensive experiments on benchmark datasets from diverse domains show the superior performance of our proposed deep RVFL networks.
ELM @cite_13 , developed in 2004, can be viewed as a variant of RVFL without direct links and bias term (see Figure (b)). Thus, Eq. becomes
@cite_13
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This paper first reviews extreme learning machine (ELM) in light of coverpsilas theorem and interpolation for a comparative study with radial-basis function (RBF) networks. To improve generalization performance, a novel method of combining a set of single ELM networks using stacked generalization is proposed. Comparisons and experiment results show that the proposed stacking ELM outperforms a single ELM network for both regression and classification problems.