From the paper:
"...While these state-of-the-art nonlinear random projection methods have been demonstrated to provide significantly improved accuracy and reduced computational costs on large- scale real-world datasets, they have all primarily focused on embedding nonlinear feature spaces into low dimensional spaces to create nonlinear kernels. As such, alternative strategies for achieving low complexity, nonlinear random projection beyond such kernel methods have not been well-explored, and can have strong potential for improved accuracy and reduced complexity. In this work, we propose a novel method for modelling nonlinear kernels using a Layered Random Projection (LaRP) framework. Contrary to existing kernel methods, LaRP models nonlinear kernels as alternating layers of linear kernel ensembles and nonlinearities. This strategy allows the proposed LaRP framework to overcome the curse of dimensionality while producing more compact and discriminative random features...."
Interesting choice of nonlinearity. As it stands it is the one we also used, great work ! Random Feature Maps via a Layered Random Projection (LaRP) Framework for Object Classification by A. G. Chung, M. J. Shafiee, A. Wong
The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the curse of dimensionality by embedding the nonlinear feature space into a low dimensional Euclidean space to create nonlinear kernels. We introduce a Layered Random Projection (LaRP) framework, where we model the linear kernels and nonlinearity separately for increased training efficiency. The proposed LaRP framework was assessed using the MNIST hand-written digits database and the COIL-100 object database, and showed notable improvement in object classification performance relative to other state-of-the-art random projection methods.
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