Feature Purity: A Quantitative Evaluation Metric for Feature Extraction in Convolutional Neural Networks

The quantitative analysis of specific convolutional layer feature information in Convolutional Neural Networks (CNN) has received considerable critical attention in the field of deep learning. In this paper, we proposed an innovative measuring method based on the principle of information entropy to quantitatively analyze the performance of feature extraction in CNN. In the method, the feature purity was defined as the normalized entropy of activation histogram, which was calculated from all kernels in feature layer of CNN. Feature purities were evaluated respectively in different layers of CNN as the inspection for internal structure in specific classification models. At the same time, general degrees of purities among different models were compared with classification performances. The experiments were performed in models of AlexNet, VGG, ResNet, and SENet with different epochs trained by cifar10 and ImageNet1000 datasets. Additionally, a visualization evaluation was performed by grad-CAM method in the manners of the intra-model and inter-model purities. Experimental results showed a strong relationship between feature purity and the classification accuracy in each model. Additionally, the visualized feature map also demonstrated that salient region extracted in specified feature layer had good consistency with purity value. As a result, the proposed feature purity can serve as a quantitative metric representing the degree of feature extraction in CNN without the dependency of label or specific network structure; and has significant interpretability and versatility across models.