Learning Convolutional Neural Networks using Hybrid Orthogonal Projection and Estimation

Convolutional neural networks (CNNs) have yielded the excellent performance in a variety of computer vision tasks, where CNNs typically adopt a similar structure consisting of convolution layers, pooling layers and fully connected layers. In this paper, we propose to apply a novel method, namely Hybrid Orthogonal Projection and Estimation (HOPE), to CNNs in order to introduce orthogonality into the CNN structure. The HOPE model can be viewed as a hybrid model to combine feature extraction using orthogonal linear projection with mixture models. It is an effective model to extract useful information from the original high-dimension feature vectors and meanwhile filter out irrelevant noises. In this work, we present three different ways to apply the HOPE models to CNNs, i.e., {\em HOPE-Input}, {\em single-HOPE-Block} and {\em multi-HOPE-Blocks}. For {\em HOPE-Input} CNNs, a HOPE layer is directly used right after the input to de-correlate high-dimension input feature vectors. Alternatively, in {\em single-HOPE-Block} and {\em multi-HOPE-Blocks} CNNs, we consider to use HOPE layers to replace one or more blocks in the CNNs, where one block may include several convolutional layers and one pooling layer. The experimental results on both Cifar-10 and Cifar-100 data sets have shown that the orthogonal constraints imposed by the HOPE layers can significantly improve the performance of CNNs in these image classification tasks (we have achieved one of the best performance when image augmentation has not been applied, and top 5 performance with image augmentation).