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In the context of deep learning with kernel machines, the deep RestrictedKernel Machine (DRKM) framework allows multiple levels of kernel PCA (KPCA) andLeast-Squares Support Vector Machines (LSSVM) to be combined into a deeparchitecture using visible and hidden units. We propose a new method for DRKMclassification coupling the objectives of KPCA and classification levels, withthe hidden feature matrix lying on the Stiefel manifold. The classificationlevel can be formulated as an LSSVM or as an MLP feature map, combining depthin terms of levels and layers. The classification level is expressed in itsprimal formulation, as the deep KPCA levels, in their dual formulation, canembed the most informative components of the data in a much lower dimensionalspace. The dual setting is independent of the dimension of the inputs and theprimal setting is parametric, which makes the proposed method computationallyefficient for both high-dimensional inputs and large datasets. In theexperiments, we show that our developed algorithm can effectively learn fromsmall datasets, while using less memory than the convolutional neural network(CNN) with high-dimensional data. and that models with multiple KPCA levels canoutperform models with a single level. On the tested larger-scale datasets,DRKM is more energy efficient than CNN while maintaining comparableperformance.

Combining Primal and Dual Representations in Deep Restricted Kernel Machines Classifiers