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This paper introduces two deep convolutional neural network training techniques that lead to more robust feature subspace separation in comparison to traditional training. Assume that dataset has M labels. The first method creates M deep convolutional neural networks called {DCNNi}M i=1 . Each of the networks DCNNi is composed of a convolutional neural network ( CNNi ) and a fully connected neural network ( FCNNi ). In training, a set of projection matrices are created and adaptively updated as representations for feature subspaces {S i}M i=1 . A rejection value is computed for each training based on its projections on feature subspaces. Each FCNNi acts as a binary classifier with a cost function whose main parameter is rejection values. A threshold value ti is determined for ith network DCNNi . A testing strategy utilizing {ti}M i=1 is also introduced. The second method creates a single DCNN and it computes a cost function whose parameters depend on subspace separations using the geodesic distance on the Grasmannian manifold of subspaces S i and the sum of all remaining subspaces {S j}M j=1,j≠i . The proposed methods are tested using multiple network topologies. It is shown that while the first method works better for smaller networks, the second method performs better for complex architectures.