## 2 Materials and Methods  
For this study, we retrospectively collected 436 early GGNs samples from the Tianjin General Hospital, in which the sample rate between IA and non-IA was 216:220. The segmented CT images of GGNs are shown in Figure 1. All subjects gave their informed consent for inclusion before they participated in the study. The study was conducted in accordance with the Declaration of Helsinki, and all experiments were approved by the ethics committee of General Hospital of Tianjin Medical University. After obtaining a sample set of GGNs, we extracted features from each GGN sample for classifying IA and non-IA. Previous studies have demonstrated how the powerful modeling and feature learning capabilities of deep learning lead to remarkable results [17; 18; 19; 20; 21], especially in biomedical image processing applications based on quantitative CT images [22; 23; 24]. Figure 1: Examples of IA and non-IA nodules images. (**a–d**) Segmented IA nodules, (**e–h**) segmented non-IA nodules. (**a,e**) Larger volume; (**b,f**) smaller volume; (**c,g**) more solid components; (**d,h**) less solid components. Transfer learning (TL) is a new research area in deep learning. TL transfer the knowledge obtained by a pre-trained network to other image processing tasks [25]. TL methods, when combined with a convolutional neural network (CNN), have been shown as effective solutions to problems associated with relatively small datasets [26]. Specifically, the deep feature extraction capability of TL methods can activate layers of a CNN model to construct the related feature vectors [27]. In the medical field, use of mainstream networks as feature extractors has become a typical and general method to deal with classification problems [28; 29; 30]. In this work, we use the AlexNet model as the feature extractor to construct a 4096-dimensional feature vector for each GGN sample. The AlexNet model is the first deep CNN model that was trained on the ImageNet competition. It has shown efficacy in image processing [31; 32; 33] and is convenient in terms of implementation and the ability to fine-tune its processes for new tasks. AlexNet has no complex or deep architectures, which means reduced computation time and the need for robust hardware. In addition, our previous research [34] has shown the effectiveness of features extracted by the fully connected (FC) layer of AlexNet for GGNs classification. To find the key features in the sample set, we first use the \(p\)-value calculated by the Analysis of Variance (ANOVA) as a criterion for feature selection [35]. Typically, lower \(p\)-values correspond to larger between-class significant differences. The top ten features with the lowest \(p\)-value are selected to form a feature subset. According to the general principle in SLT, EXP and EMP obey the following relationship with at least (\(1-\eta\)) probability for a limited number of samples \(n\)[36]:  
\[R_{exp}(w)\leq R_{emp}(w)+\sqrt{\frac{\hbar(\ln(2n/h)+1)-\ln(\eta/4)}{n}}, \tag{1}\]  
where the value of EXP is denoted as \(R_{exp}(w)\) and the value of EMP as \(R_{emp}(w)\). Equation (1) can be simplified as  
\[R_{exp}(w)\leq R_{emp}(w)+\Phi(n/h). \tag{2}\]  
where \(\Phi(n/h)\) is the confidence range; \(\eta\) is confidence limits, expressed as the probability that the classifier predicts the outcome to occur; \(n\) is the number of training samples; and \(h\) is VC dimension, indicating the maximum number of samples that a selected type of classifier can distinguish all possible \(2^{h}\) sample combinations [37]. Only few types of classifiers have the known VC dimensions. Essentially, for the most used linear classifiers, the VC dimension is (d + 1), and d is the number of used features. The widely used SVM is just a linear classifier. When dealing with multi-classification problems using the linear classifier, the actual VC dimension in a one-to-rest manner is (d + 1) \(\times\) c, where c is the number of classes [38].