Dendritic Deep Residual Learning for COVID‐19 Prediction

Abstract

Deep residual network (ResNet), one of the mainstream deep learning models, has achieved groundbreaking results in various fields. However, all neurons used in ResNet are based on the McCulloch‐Pitts model which has long been criticized for its oversimplified structure. Accordingly, this paper for the first time proposes a novel dendritic residual network by considering the powerful information processing capacity of dendrites in neurons. Experimental results based on the challenging COVID‐19 prediction problem show the superiority of the proposed method in comparison with other state‐of‐the‐art ones. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

1. Introduction

Coronavirus disease 2019 (COVID‐19) has emerged as one of the greatest challenges to humanity in recent years. The capacity to identify infected individuals accurately is the most important step. Many methods and studies have been proposed to detect COVID‐19 pneumonia. The goal of these studies is to identify and treat COVID‐19 afflicted individuals as soon as possible, and to isolate these patients to stop the disease from spreading. Although the testing strategy for COVID‐19 diagnosis is the reverse transcription polymerase chain reaction (RT‐PCR) test‐kits, medical imaging can play an important complementary role in improving diagnostic accuracy and may even become an alternative method in some countries where RT‐PCR is not readily available.

Nowadays, with the development of deep learning, larger datasets such as medical imaging can be evaluated more efficiently. Therefore, deep learning solves many practical problems, such as protein structure prediction, medical diagnosing assistance, and image/video recognition. Representative deep learning models include the very deep convolutional networks (VGG), ResNet, and Inception V3.

Some studies have rethought the modeling of neurons from scratch rather than building deeper and deeper neural networks [1]. Recently, the dendritic neuron model (DNM), which considers both synaptic and dendritic nonlinear information processing capabilities, has shown great promise for classification problems [2]. The combination of DNM and convolutional neural networks also has promising results in image recognition tasks [3]. In this study, we for the first time incorporate DNM into ResNet and design a new deep learning model, namely dendritic deep residual network (DResNet). Its performance is verified on the early COVID‐19 predication task. Experimental results show that DResNet performs better than its peers.

2. Dendritic Deep Residual Network

DResNet has two components: ResNet18 layers and the dendritic neuron layer. Figure 1 shows its architecture.

Fig. 1.

Architecture of DResNet

The used ResNet18 consists of residual units stacked by convolutional layers and pooling layers. It is worth emphasizing that 18 layers of ResNet are used in DResNet since it performs much better than other settings of this hyper‐parameter. As illustrated in Fig. 1, the ResNet18 component introduces the data output of one of the several preceding layers directly to the input part of the later data layers by skipping multiple layers, which means that the content of the later feature layer is partially contributed linearly by one of its preceding layers. Subsequently, the DNM is innovatively incorporated into DResNet to substitute the full connection layer in ResNet18. DNM consists of the synaptic layer, dendritic layer, membrane layer, and soma layer, which has been demonstrated to possess more powerful information processing capacity with the aid of its dendrites [2, 3].

We have made a simple improvement to DNM so that it can be better incorporated into DResNet. In ResNet, the result obtained from the last convolutional layer can be flattened to obtain a one‐dimensional vector. We use this vector as the input to the DNM synaptic layer. After that, we remove the linear layer in ResNet and use the result obtained from the DNM calculation as the final output.

The DNM used in DResNet is described as follows: the synaptic layer processes $n$ signals on $M$ dendrites. The connecting function expressed by a ReLU function from the input to the receptors is formulated as:

$$Y_{\mathit{ij}}=\max \left(0,k*\left(w_{\mathit{ij}}*x-q_{\mathit{ij}}\right)\right)$$ (1)

Initially, the learnable parameters $k=0.5$, and $w_{\mathit{ij}}$ and $q_{\mathit{ij}}$ $(i=1,\dots ,n,j=1,\dots ,M)$ are randomly generated in $(0,1)$.

In the dendritic layer, dendrites receive all signals from the synaptic layer by a summation function. The function of the jth dendrite branch is formulated as:

$$Z_j=\sum _{i=1}^N{Y}_{\mathit{ij}}$$ (2)

The membrane layer collects signals from all dendritic branches. A summation function is used to implement this layer, expressed as:

$$V=\sum _{j=1}^M{Z}_j$$ (3)

Finally, the output of the membrane layer is processed in the soma layer using another ReLU function. It is used to determine whether the neuron fires, and the final output is shown as:

$$O=\max \left(0,k_s*\left(V-q_s\right)\right)$$ (4)

where both $k_s$ and $q_s$ are learnable parameters, and they are initially set to a random value in $(0,1)$. It is worth pointing out that the number of dendritic neurons in DResNet is equal to the category number of the tackled task. To be specific, there are two dendritic neurons for the COVID‐19 prediction problem. Additionally, Adam is used as the optimizer.

3. Experiments and Result

We use the COVID‐19 Radiography Database from Kaggle [4]. There are 3616 COVID‐19 positive cases and 10 192 normal cases. We split the data into a training set and a validation set with the ratio of 80% and 20%, respectively. The input images are converted to a size of 224 × 224 with 3‐dimensional channels during data processing. We use Pytorch 1.11 with Python 3.8 to implement DResNet, VGG16, Inception V3, and ResNet18. All experiments are run on Windows 10 using an Intel (R) Core (TM) i9‐12 900K CPU at 4.56GHz (20 cores) and an NVIDIA GeForce RTX 3090 GPU with VRAM size of 24 GB. In all compared models, the learning rate, batch size and epoch are set to $0.0001$, $32$, and $200$, respectively. The only hyper‐parameter in DResNet is the number of dendrites in a DNM. After a preliminary experiments, performs better than other settings $(M=\mathrm{1,\; 10,\; 15,\; 20})$.

We train and test DResNet, ResNet18, VGG16, and Inception V3 for 30 times using the same parameters, and the results of these 30 times are averaged and summarized in Table I, where the best values are shown in bold. From it, we can find that DResNet outperforms others in terms of train accuracy, test accuracy, train loss, test loss, classification sensitivity, and classification specificity. We also calculate the $p$‐value by Wilcoxon signed rank test in terms of the test accuracy and find that all are smaller than 0.01, proving that DResNet is significantly better than others. Figure 2 illustrates the loss curve of all compared models. It is clear that DRestNet can be well trained and converges to smaller loss values.

Table I.

Experimental results for different networks

Classification	Train accuracy (%)	Test accuracy (%)	$p$‐value	Train loss	Test loss	Sensitivity	Specificity
DResNet	96.24 ± 1.29	96.34 ± 1.76	—	0.0956 ± 0.03	0.1057 ± 0.05	0.9588 ± 0.04	0.9680 ± 0.02
ResNet18	93.08 ± 0.86	92.26 ± 5.62	1.67e‐6	0.1925 ± 0.03	0.2648 ± 0.23	0.8790 ± 0.13	0.9662 ± 0.03
VGG16	94.53 ± 0.41	93.71 ± 4.04	3.02e‐5	0.1394 ± 0.01	0.2124 ± 0.22	0.9067 ± 0.09	0.9675 ± 0.03
Inception V3	96.17 ± 0.42	94.02 ± 3.02	4.79e‐3	0.0971 ± 0.01	0.1844 ± 0.11	0.9198 ± 0.07	0.9606 ± 0.03

Fig. 2.

Loss of four compared models

4. Conclusion

To solve the diagnostic problem of COVID‐19, we proposes a novel dendritic residual learning model, termed DResNet. With the aid of dendritic calculation, DResNet can possess more powerful information processing capacity in comparison with the original fully connected layers. Experimental results based on the COVID‐19 radiography dataset show that DResNet performs much better than other state‐of‐the‐art models in all used evaluation metrics.