## 1 Introduction  
Lung cancer is one of the deadliest diseases with one of the highest mortality rates in the world [1]. Early asymptomatic manifestations of lung cancer may lead patients to miss the optimal treatment time; thus, early detection and treatments are essential to reduce the risk of death. Pulmonary nodules are considered key indicators of primary lung cancer [2]. The National Lung Screening Trial (NLST) [3] test shows that using low-dose chest computed tomography (CT) to examine pulmonary nodules in high-risk populations can reduce lung cancer mortality by 20%. Therefore, the detection of pulmonary nodules is very important for the early detection of lung cancer. Pulmonary nodules have many clinical manifestations, but one of the most prevalent is when nodules are irregular circles with a diameter of 3 mm to 30 mm [4]. According to pathological knowledge, a computer-aided diagnosis system for pulmonary nodule detection can be developed to reduce the workload of doctors, reduce misdiagnosis rate, and improve the efficiency of diagnosis. Typically, a computer-aided diagnosis system (CAD) for pulmonary nodule detection consists of two parts: (1) candidate nodule detection, and (2) false-positive (FP) reduction of candidate nodules. In the candidate nodule detection step, the system detects as many candidates as possible to ensure high sensitivity without considering specificity. This is accompanied by a large number of false-positive nodules detected [5]. To reduce false positives, the system classifies the real nodules and non-nodules in the set of candidates detected in the previous step to reduce the number of false positives. False-positive reduction of candidate nodules is the most important part of a computer-aided diagnosis system for pulmonary nodule detection [6]. As far as we know, the current computer-aided diagnosis system (CAD) for pulmonary nodule detection is still in the development stage. Although the CAD system can improve the reading efficiency of radiologists, it is still not well used in clinical applications. Therefore, it is important to develop an advanced algorithm with high performance. Pathologically, there are many types of nodules (e.g., ground glass nodules, solitary nodules, etc.) [7]. Various nodules have complex morphologies and multiple structures, and they often adhere to the trachea, blood vessels, and other organs. The morphological features of the candidate nodules are often similar to organs in the thoracic cavity (e.g., lymph nodes, blood vessels, etc.). This greatly increases the difficulty of reducing false positives in candidate nodules. Figure 1 shows an example of different types of nodules. This is why many researchers devoted their time to developing stable and effective algorithms to distinguish between nodules and non-nodules, thereby reducing false positives [8; 9; 10]. Recently, with the rapid development of deep learning techniques for medical image analysis [11; 12; 13; 14; 15], more and more researchers successfully applied convolutional neural networks (CNNs) to the detection of pulmonary nodules based on chest CT images [5; 8; 10; 16; 17; 18], and achieved desirable results. By studying these methods, we can list three findings. Firstly, the system that uses volumetric information has fewer false positives than methods that use two-dimensional (2D) slice information alone [5; 16; 17]. For example, [PERSON] et al. [5] proposed a 2D multi-view CNN, which classified nodules based on slices from nine different views. Although the method utilized multiple views of the pulmonary nodules, to some extent, the three-dimensional (3D) information of the nodules was still not fully utilized. Therefore, [PERSON] et al. [17] proposed to use a 3D nodule block as input for 3D-CNN, which was effective in reducing false positives. Secondly, using multi-scale information of nodules can improve the performance of the algorithm [8; 10; 18]. For example, [PERSON] et al.