Lung nodule false positive reduction using a central attention convolutional neural network on imbalanced data

2.1. Imbalanced data processing

The lung nodule false positive reduction is a two-class imbalanced classification problem, where the non-nodules outnumber the nodules. We balance the training data by both under-sampling the majority class (or the negative class) and augmenting the minority class (or positive class).

First, the density distribution of lung nodules on the CT images is designed for removing obvious false positives. We divide the center slice of a nodule into thirty-six blocks bounded by six-by-six grids. We calculate the CT value histogram to obtain the grayscale density distribution of nodules. Then some non-nodules can be discarded due to the difference in the density distribution. Second, data augmentation is employed to generate the nodules and help the classification model become invariant to the orientations and positions of the nodule. The horizontal, vertical, and depth flip is performed for each cube containing the nodule, which can produce some nodule samples. Next, confident learning [16] is used to select certain non-nodules for reducing the influence of noise. We collect the parts of non-nodule images and whole nodule images for the model training. According to the training results, we calculate the confident joint and the estimate of the joint, provide a confusion matrix for the assumption of a class-conditional noise process, and use the rank and prune approach to produce clean data of non-nodules for training. Confident joint $C_{\tilde{y},y^{*}}$ is defined as follows:

where $\tilde{y}$ is the label of sample $x,y^{*}$ is the predicted label by model $\theta$, and the threshold $t_j$ is the average self-confidence for the $j$-th class. ${\widehat{X}}_{\tilde{y}=i,y^{*}=j}$ is the estimate of subset of examples in $X$ with given label $i$ and predicted label $j$. Finally, a sampling technique, Balanced-MixUp [17], is used to balance the training data, which can simultaneously perform regular and balanced sampling and mix up the two sets of samples to create more balanced training data. Specifically, regular sampling means random sampling while balanced sampling means purposeful sampling by considering the category of samples. Let $D$ be the training dataset, S_R and S_B be the regular sampling, and balanced sampling, respectively. Balanced-MixUp can be described as follows:

where $\left(x_{\text{R}},y_{\text{R}}\right)\in \left(D,{\text{S}}_{\text{R}}\right),\left(x_{\text{B}},y_{\text{B}}\right)\in \left(D,{\text{S}}_{\text{B}}\right)$. We will get a more balanced distribution of training data by mixing the fewer nodules with the more non-nodules to alleviate the overfitting problem, as illustrated in Figure. 2, where the blue boxes and yellow circles represent the samples with the majority class and minority classes, respectively. Figure. 2 (a) means the regular sampling, which obtains the many samples with the majority class and the few samples with the minority classes because of imbalanced class distribution. Figure. 2 (b) means balanced sampling, which obtains the same number of samples with the two classes. Figure. 2 (c) combines the two above to create more evenly distributed training data. In our experiments, the mixing coefficient $\lambda$ ~ Beta(0.1,1) for a balanced combination.

2.2. Central attention convolutional neural network

For the detected candidate cubes, it is intuitive that the voxels close to the center of the cubes contain more information and less noise caused by the environment. Therefore, we propose a central attention convolutional neural network, to distinguish the nodules from the non-nodules. Based on the ResNet with the cross entropy as the loss function, we focus the attention on the center of the detected candidate cubes by adding the central pooling layer [18] and center residual block.

Different from the traditional max pooling whose pooling kernels are of the same size and uniformly distributed, the central pooling kernels are non-uniformly distributed on the whole cubes. The small pooling kernels are used around the center while the large pooling kernels are used near the edge.

The center residual block is a skip-connection block that learns residual functions with reference to the layer inputs (attention on center), as shown in Figure. 3. Formally, the center residual unit obtains $F(x)$ by processing $x$ with two weight layers. Then it adds the $x$ and its center region, center $(x)$ to $F(x)$ for calculating $H(x)$. $H(x)$ is obtained as follows.

Consequently, our proposed central attention convolutional neural network can reserve many center features and eliminate redundant edge features for allowing the network to easily learn class-related features.

3.1. Dataset

We applied our CACNNID model to the Lung Nodule Analysis 16 (LUNA16) [19]. LUNA16 dataset contains the CT scans whose thickness varies from 0.6 mm to 2.5 mm and the nodules whose sizes are between 3mm and 30mm. The dataset is divided into 10 subsets that can be used for the 10-fold cross-validation. Each of the ten subsets is taken as the test set in turn, and the nine subsets in the remaining data are the training set. The numbers of the ten subsets are shown in Table 1.

3.2. Implementation details and evaluation criteria

Because of the different slice thicknesses of CT scans, we first normalized the candidate cubes to 1mm, and then take the nodule as the center to intercept 48*48*48 3D cubes. The proposed CACNNID method was implemented using Python 3.8 in the PyTorch framework. The experimental platform was equipped with an NVIDIA GeForce RTX 3080 Ti GPU with 12 GB of memory. On the algorithm level, the Adam algorithm with a batch size of 8 was adopted as the optimizer and the maximum iteration number was set to 40. The training was started with an initial learning rate of 0.1 and was periodically adjusted by the CosineAnnealingLR method with a period of 8 epochs. The code will be publicly available at https://github.com/MIAinCS/CACNNID.

Four indicators, sensitivity, specificity, accuracy, and area under the receiver operator curve (AUC) were used for the presentation of performance.

3.3. Performance on the lung nodule false positive reduction

Table 2 shows the quantitative classification results of the proposed CACNNID model in 10-fold cross-validation experiments. We can obtain a mean sensitivity of 92.64%, specificity of 98.71%, accuracy of 98.69%, and AUC of 95.67%. Those results prove that our method can achieve good false positive reduction performance.

The qualitative recognition results are shown in Figure. 4. We randomly take 24 samples classified correctly, where 12 samples are nodules and 12 samples are non-nodules, which are shown in the first two rows and the last two rows. In Figure. 4, we can see that the proposed model can recognize nodules with different sizes and shapes, and distinguish non-nodules from nodules that share visual similarities. It is illustrated that our model can accurately differentiate between nodules and non-nodules for reducing false positives during the automatic detection of pulmonary nodules.