Robust feature space separation for deep convolutional neural network training

Abstract

Abstract 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 $$\{\text {DCNN}_i\}_{i=1}^{M}$$ { DCNN i } i = 1 M . Each of the networks $$\text {DCNN}_i$$ DCNN i is composed of a convolutional neural network ( $$\text {CNN}_i$$ CNN i ) and a fully connected neural network ( $$\text {FCNN}_i$$ FCNN i ). In training, a set of projection matrices $$\{\mathbf {P}_i\}_{i=1}^M$$ { P i } i = 1 M are created and adaptively updated as representations for feature subspaces $$\{\mathcal {S}_i\}_{i=1}^M$$ { S i } i = 1 M . A rejection value is computed for each training based on its projections on feature subspaces. Each $$\text {FCNN}_i$$ FCNN i acts as a binary classifier with a cost function whose main parameter is rejection values. A threshold value $$t_i$$ t i is determined for $$i^{th}$$ i th network $$\text {DCNN}_i$$ DCNN i . A testing strategy utilizing $$\{t_i\}_{i=1}^M$$ { t i } i = 1 M 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 $$\mathcal {S}_i$$ S i and the sum of all remaining subspaces $$\{\mathcal {S}_j\}_{j=1,j\ne i}^M$$ { S j } j = 1 , j ≠ i M . 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.

Keywords

• Deep Convolutional Neural Networks
• Subspace Separation
• Robust Deep Learning