er than mean squared error (MSE) function only. As an additional merit, it is also revealed that rigorous Mercer kernel condition is not required in FKNN networks. When the proposed architecture of FKNN networks is constructed in a layer-by-layer way, i.e., the number of the hidden nodes of every hidden layer may be determined only in terms of the extracted principal com- ponents after the explicit execution of a KPCA, we can develop FKNN’s deep architecture such that its deep learning framework (DLF) has strong theoretical guarantee. Our experimental results about image classification manifest that the proposed FKNN’s deep architecture and its DLF based learning indeed enhance the classification performance

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