## 2 Materials and Methods  
### Sample Acquisition and Labeling  
To build a classifier for the pathological subtypes of GGNs, a set of follow-up CTIs with GGNs must be collected. The CTIs used in this study were retrospectively collected from the department of pulmonary tumor surgery, Tianjin Medical University General Hospital, corresponding to 146 patients with early lung adenocarcinoma from January 2020 to June 2021. All GGNs were retrospectively labeled by their surgical pathology. Figure 1 shows the four pathological subtypes of GGNs. All patients had one-time follow-up CTIs at least in which these lesions manifested as GGNs. These GGNs were pathologically analyzed after surgical resection. Hence, their pathological subtypes were confirmed by histopathology analysis. In this paper, the confirmed subtypes were used to label the GGNs for subsequent classification when constructing a classifier. 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 (IRB2020-YX-145-01). The requirement to obtain informed consent from the participants was waived by the ethics committee. Table 1 shows the number subtypes of 146 patients, their number of follow-ups along these subtypes, and the GGNs subtypes in CTIs, respectively. In this paper, we implemented the segmentation and feature extraction of GGNs using 3D Slicer [23]. 3D Slicer is a free and open-source multi-platform software package that is widely used for medical, biomedical, and related imaging research. Each GGN corresponded to a group of CTIs with different sizes and shapes, but we fixed the CTI with the largest area for sequential classification purposes. According to the pathological and the CT detection reports, each patient's GGN location and subtype can be found and labeled. The segmentation and labeling steps of GGN are as follows:  
1. Import a set of CTIs for each patient into 3D Slicer and locate the GGNs. 2. Select CTIs that contain GGNs and then find the CTI with the largest area among these selected CTIs. 3. Segment the GGN with the largest area and save it as sequential classification. 4. Label the GGNs subtype with pathology reports. According to 3D Slicer, 1041 features can be extracted from each GGN from the 146 patients' 386 follow-up CTIs. Algorithmically, let \(Date\) (\(k\), \(i\)) be the \(i\)th follow-up date of \(k\)th patient, \(\Delta t_{k,i}\) be the time interval from \(i\)th to (\(i+1\)) paired follow-up dates, \(f_{k}\) (\(i\), \(j\)) be the \(j\)th extracted feature from GGN in the \(i\)th follow-up CTI, and \(T_{k}\) is the total number of follow-up times of \(k\)-th patient, \(k\) = 1, 2, \(\ldots\), 146, \(i\) = 1, 2, \(\ldots\), 383, \(j\) = 1, 2, \(\ldots\), 1041. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Pathological Subtypes** & **Number of Patients** & **Number of Follow-Ups** \\ \hline \multirow{3}{*}{**Malignant**} & IA & 96 & 249 \\  & MA & 21 & 50 \\  & AIS & 8 & 37 \\
**Benign** & AAH & 21 & 47 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The GGNs subtypes of 146 patients. Figure 1: Examples of the four pathological subtypes of GGNs. (**a**) Benign; (**b**) AIS; (**c**) MIA; (**d**) IA. Consequently, their feature differences along the paired follow-ups is computed as  
\[\Delta f_{k}(i,j)=\left(f_{2}(i,j)-f_{1}(i,j)\right)/\Delta t_{ij},\;k=1,2,\ldots,146;\;i=1,2,\ldots,T_{k};\;j=1,2,\ldots,1041 \tag{1}\]  
where the denominator of \(\Delta t_{\bar{\eta}}\) aims to normalize the feature change in two different follow-up time intervals. Hence, the GGN feature changes of different patients at different dates are comparable. Let \(S_{FFDC}\) be the set of all feature-difference samples from Equation (1) in FFDC, and \(S_{OFDC}\) be the set of samples in OFDC in which the \(T_{k}\)th time CTI for each patient is used to capture the latest features of GGN.