  Stacking-based deep neural network (S-DNN) is aggregated with pluralities of
basic learning modules, one after another, to synthesize a deep neural network
(DNN) alternative for pattern classification. Contrary to the DNNs trained end
to end by backpropagation (BP), each S-DNN layer, i.e., a self-learnable
module, is to be trained decisively and independently without BP intervention.
In this paper, a ridge regression-based S-DNN, dubbed deep analytic network
(DAN), along with its kernelization (K-DAN), are devised for multilayer feature
re-learning from the pre-extracted baseline features and the structured
features. Our theoretical formulation demonstrates that DAN/K-DAN re-learn by
perturbing the intra/inter-class variations, apart from diminishing the
prediction errors. We scrutinize the DAN/K-DAN performance for pattern
classification on datasets of varying domains - faces, handwritten digits,
generic objects, to name a few. Unlike the typical BP-optimized DNNs to be
trained from gigantic datasets by GPU, we disclose that DAN/K-DAN are trainable
using only CPU even for small-scale training sets. Our experimental results
disclose that DAN/K-DAN outperform the present S-DNNs and also the BP-trained
DNNs, including multiplayer perceptron, deep belief network, etc., without data
augmentation applied.
