We investigate the use of Deep Neural Networks for the classification of image datasets where texture features are important for generating class-conditional discriminative representations. To this end, we first derive the size of the feature space for some standard textural features extracted from the input dataset and then use the theory of Vapnik-Chervonenkis dimension to show that hand-crafted feature extraction creates low-dimensional representations which help in reducing the overall excess error rate. As a corollary to this analysis, we derive for the first time upper bounds on the VC dimension of Convolutional Neural Network as well as Dropout and Dropconnect networks and the relation between excess error rate of Dropout and Dropconnect networks. The concept of intrinsic dimension is used to validate the intuition that texture-based datasets are inherently higher dimensional as compared to handwritten digits or other object recognition datasets and hence more difficult to be shattered by neural networks. We then derive the mean distance from the centroid to the nearest and farthest sampling points in an n-dimensional manifold and show that the Relative Contrast of the sample data vanishes as dimensionality of the underlying vector space tends to infinity.

本文研究了使用深度神经网络对纹理特征重要的图像数据集进行分类的方法，并通过定义手工特征提取的VC维来证明手工特征提取是降低异常误差率的有效工具，同时得出了卷积神经网络、Dropout网络和Dropconnect网络的VC维上限以及它们异常误差率的关系。此外，本文还利用内在维度概念验证了基于纹理的数据集比手写数字或其他目标识别数据集本质上更高维，因此更难以被神经网络粉碎，同时还从n维流形中计算出样本数据的相对对比度随向量空间维度趋于无限大而消失的规律。

深度神经网络在纹理分类中的理论分析