Beyond COVID-19 Diagnosis: Prognosis with Hierarchical Graph Representation Learning
Authors: CHEN LIU
Jinze Cui
Dailin Gan
Guosheng Yin
Venue:  (2021)
Keywords: COVID-19 Diagnosis
COVID-19 Prognosis
GCN

Abstract: Coronavirus disease 2019 (COVID-19), the pandemic that is spreading fast globally, has caused over 34 million confirmed cases. Apart from the reverse transcription polymerase chain reaction (RT-PCR), the chest computed tomography (CT) is viewed as a standard and effective tool for disease diagnosis and progression monitoring. We propose a diagnosis and prognosis model based on graph convolutional networks (GCNs). The chest CT scan of a patient, typically involving hundreds of sectional images in sequential order, is formulated as a densely connected weighted graph. A novel distance aware pooling is proposed to abstract the node information hierarchically, which is robust and efficient for such densely connected graphs. Our method, combining GCNs and distance aware pooling, can integrate the information from all slices in the chest CT scans for optimal decision making, which leads to the state-of-the-art accuracy in the COVID-19 diagnosis and prognosis. With less than 1% number of total parameters in the baseline 3D ResNet model, our method achieves 94.8% accuracy for diagnosis. It has a 2.4% improvement compared with the baseline model on the same dataset. In addition, we can localize the most informative slices with disease lesions for COVID-19 within a large sequence of chest CT images. The proposed model can produce visual explanations for the diagnosis and prognosis, making the decision more transparent and explainable, while RT-PCR only leads to the test result with no prognosis information. The prognosis analysis can help hospitals or clinical centers designate medical resources more efficiently and better support clinicians to determine the proper clinical treatment. 

Under review as a conference paper at ICLR 2021
BEYOND COVID-19 DIAGNOSIS: PROGNOSIS wITh HIERARCHICAL GRAPH REPRESENTATION LEARNING
Anonymous authors Paper under double-blind review
ABSTRACT
Coronavirus disease 2019 (COVID-19), the pandemic that is spreading fast glob- ally, has caused over 34 million confirmed cases. Apart from the reverse transcrip- tion polymerase chain reaction (RT-PCR), the chest computed tomography (CT) is viewed as a standard and effective tool for disease diagnosis and progression monitoring. We propose diagnosis and prognosis model based on graph con- volutional networks (GCNs). The chest CT scan of patient, typically involving hundreds of sectional images in sequential order, is formulated as a densely con- nected weighted graph. A novel distance aware pooling is proposed to abstract the node information hierarchically, which robust and efficient for such densely connected graphs. Our method, combining GCNs and distance aware pooling, can integrate the information from all slices in the chest CT scans for optimal decision making, which leads to the state-of-the-art accuracy in the COVID-19 diagnosis and progmosis. With less than 1% number of total parameters in the baseline 3D ResNet model, our method achieves 94.8% accuracy for diagnosis. It has 2.4% improvement compared with the baseline model on the same dataset. In addition. we can localize the most informative slices with disease lesions for COVID-19 within a large sequence of chest CT images. The proposed model can produce visual explanations for the diagnosis and prognosis, making the decision more transparent and explainable, while RT-PCR only leads to the test result with no prognosis information. The prognosis analysis can help hospitals or clinical cen- ters designate medical resources more efficiently and better support clinicians determine the proper clinical treatment.
INTRODUCTION
Coronavirus disease 2019 (COVID-19) has resulted in an ongoing pandemic the world. To control the sources of infection and cut off the channels of transmission, rapid testing and detection are of vital importance. The reverse transcription polymerase chain reaction (RT-PCR) is a widely-used screening technology and viewed as the standard method for suspected cases. However, this method highly relies upon the required lab facilities and the diagnostic kits. In addition, the sensitivity of
RT-PCR is not high enough for early diagnosis (Ai et al.] 2020 Fang al., 2020). To mitigate the limitations of RT-PCR, the computed tomography (CT) has been widely used as an effective complementary method, which can provide medical images of the lung area to reveal the details of
the disease and its prognosis (Huang et al.] 2020 Chung et al. 2020), for which RT-PCR cannot. Additionally, CT has also been proved be useful monitoring the COVID-19 disease progression and the therapeutic efficacy evaluation (Rodriguez-Monl Matrriggzz-Mrales et al. 2020 Liechti et al. 2020).
The chest CT slices of patient have sequential and hierarchical data structure. The relationship between slices possesses more information than the order of the slices. The adjacent ones with the same abnormality could be considered as one lesion. The slices containing the same type of lesions may not be continuous as the lesions are distributed in various lung parts. We propose diagnosis and prognosis system that combines graph convolutional networks (GCNs) and a distance aware pooling, which integrates the information from all slices in the chest CT scans for optimal decision making. Our major contributions are three-fold: (1) Owing to the sequential structure of CT images, this is the first work to utilize GCNs to extract node information hierarchically, and conduct both diagnosis and prognosis for COVID-19. The prognosis can help facilitate medical resources, e.g., ventilators or admission Intensive Care Units (ICUs), more efficiently by triaging

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mild severe patients. (2) A novel pooling method called distance aware pooling, is proposed to aggregate the graph, Le., the patient's CT sean, effectively. The new pooling method integrated with GCNs can aggregate densely connected graph efficiently. (3) The model can localize the most informative slices within a chest CT sean, which significantly reduces the amount of work for radiologists.
RELATED WORK
Al-assisted and CT-based COVID-19 Diagnosis and Prognosis. Although RT-PCR is the stan- dard way for COVID-19 diagnosis, there are many limitations using RT-PCR along, e.g., time delay in receiving an RT-PCR test, occurrence of false negatives, and no prognostic information provided, etc. CT images are often recommended as an alternative for precise lesion detection AAlizadebsani al., 2020). However, as each CT scan includes large number of (up to several hundreds of) image slices, it requires much time and labor of the radiologists (Shoeibi et al., (020)) Furthermore, since the radiological appearances of COVID-19 are similar to other types of pneumonia, radiolo- gists need to go through extensive training before they can achieve high diagnostic accuracy (Shi
ct al. 2020).
Recently, several Al-assisted and CT-based COVID-19 diagnostic systems have been developed. Chen et al. (020) use Unet++ (Zhou et al. 2018) to segment infectious areas the lung. Butt et al. (2020) develop a deep learning model to detect lesions from CT images, and then use 3D ResNet to classify the images into COVID-19, influenza-A viral pneumonia or healthy groups. [Song et al. 2020) use the whole lung for diagnosis instead of only extracting the lesions. [Wang al. (2020) propose an Al system that can diagnose COVID-19 patients as well as conducting the prognostic analysis.
Graph Neural Networks. Various types of graph neural networks (GNNs) have been proposed, which can be divided into spectral or non-spectral domains. In the spectral domain, the Fourier transformation and graph Laplacian define the convolutional filters (Bruna et al., 2013). By utilizing Chebyshev polynomials, Kipf & Welling (2016) simplify the filters of graph convolution, rendering a layer-wise propagation method. However. the generalization of spectral methods may not be ideal due to the variety of graphs (Bronstein al.) 2017). Non-spectral methods focus on the local topology of nodes, directly working on graphs instead of the Fourier domain. Methods proposed by Hamilton et al.) (2017), Monti et al. (2017) and Veličković et al. (017)) aggregate nodes based on adjacent nodes when the next layer is created. This aggregation process, as mentioned by Gilmer process.
ct al. 2017), can be regarded as a message-passinnn
Pooling Methods Pooling methods allow GNNs hierarchically aggregate nodes, obtaining and assembling local information of graphs. The major purpose of the hicrarchical pooling method is to use locally based model to aggregate nodes in each layer, that higher level graph representa- tion can be created (Lee et al. 2019). The self-attention based pooling method (Mao et al., (018)) implemented for video classification, locally obtaining weighted and fused feature sequences. Spectral pooling methods, such as the one proposed by Ma et al.. (2019). focus on the application of eigen-decomposition to capture the graph information. However, since spectral pooling methods are computationally demanding, they may not be accessible to large graphs. Non- Non-spectral pooling methods are scalable to large graphs and pay more attention to the local structures of graphs. Adap- tive Structure Aware Pooling (ASAP) (Ranjan et al.) 2020) and DiffPool (Ying et al., 2018) resort to clustering techniques, aggregating nodes into different clusters, and then choosing top clusters based on cluster ranking scores (Gao & Ji, 2019). However, the ASAP method partially ignores the edge weight information when using hops to aggregate nodes, resulting in unstable convergence.
METHODOLOGY
We propose a GCN- diagnosis and prognosis method that models the sequential slices of CT scans hierarchically. To downsample and learn graph-level representation from the input node fea- tures, a novel distance aware pooling method is proposed. In this paper, the node features refer to the slices in CT scan. The model gradually extracts information from the slice level to the patient level by graph convolution and pooling. Eventually, a ligher-level representation is learned, and further used for diagnosis, prognosis, and lesion localization. The schema of our model is illustrated in
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GCN
GCN
+
Fenture Extractor & Graph Construction
Distance Aware Pooling
Distance Aware Pooling
w
One-drop localization
Output feature matrix
Diagnosis
MLP
Prognosis
Schema of our model structure. The CT scan of one patient is converted to a densely connected graph. The GCN and the Distance Aware Pooling method are integrated to learn graph-level representation. At each of the two layers, the node embedding learned by GCN, and the cluster membership is calculated by the Distance Aware Pooling method. The aggregated graph, which on the top right corner, is passed to MLP. Mcanwhile, the one-drop localization can localize the most informative slices in the CT scan in a weakly supervised manner.
Figure 1:
Figure D which is composed of GCNs, pooling modules, a multilayer perceptron (MLP) classifier, and one-drop localization module. The graph cnvvolution-based method can integrate all slices in the chest CT scans for optimal decision making. Furthermore, we propose the one-drop localiza- tion to localize the most informative slices, so that radiologists may focus on those recommended slices with the most suspected lesion areas. Consequently, the proposed model can produce visual explanations for the diagnosis and prognosis, making the decision more transparent and explainable. We argue that this method could effectively assist radiologists by reducing redundancies the vast amount of CT slices during diagnosis and prognosis in the clinical settings.
3.1 PROBLEM STATEMENT
Let G (V, E) be patient's 's CT scan graph, with | cardinality of a set. For each E V, is the corresponding d'dimensional vector. Let X Nx be the node feature matrix, and Andi E N be the weighted adjacency matrix. Fach entry in odjj
= N nodes and |E] edges, where represents the
A adj is defined based on cosine similarity, which is A.j = < 2, Zy >/[[2,]|| ||=,|])- Define A adه where
the distance matrix A Adis as Ai
the matrix with all entries of I's. The definition of A dis means that the more similar two nodes are, the shorter distance they have. In the construction of A adj the diagonal entries are automatically I's since = j is allowed.
Each graph has a label y. For diagnosis, the label represents its class from normal, common pncumonia, and COVID-19 19. For prognosis, the class indicates whether COVID- positive patient develops into sever/critical illness status. Thus, the diagnosis and prognosis of COVID-19 is task of graph classification under our setting. Given training dataset T {(G1, 31) ..).... (GM- yMr } the goal is to learn mapping f + y, which classifies a graph G into the corresponding class y. Our model is composed of two modules: fi includes node convolution and feature pooling, and fe involves a MLP classifier which determines the class of each graph. At each layer of f1, node embeddings and cluster membership are learnt iteratively. The first module be written fi
+ Gº, where GP the pooled graph with fewer nodes and a hicrarchical feature representation. The second module is f2 g y. which utilizes the graph-level representation learnt for patient
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diagnosis and prognosis. The two modules integrated in an end-to-end fashion. That is to say, the cluster assignment is learnt merely based on the graph classification objective.
3.2
NODE CONVOLUTION AND FEATURE POOLING
3.2. NODE CONVOLUTION
Node convolution applies the graph convolutional network to obtain high-level node feature rep- resentation in the feature matrix X. Although several methods exist to construct the convolutional network, the method recommended by Kipf & Welling (2016) is effective for case, which is given by X (1+1) a(V (()) add(()) V D X (Ow where D is the diagonal degree matrix of A (1) I, and W Ra is learnable weight matrix the 1-th layer. Due to the applica- tion of feature pooling, the topology of the graph changes at each layer, and thus the dimension of matrices involved are reduced accordingly.
3.2.2 DISTANCE AWARE POOLING METHOD
We propose an innovative pooling method, which includes graph-based clustering and feature pool- ing. Below, outline the pooling module and illustrate how it is integrated into end-to-end GCN based model. Empirically, shown to be more robust for densely connected graphs. The overall structure of the pooling method is illustrated in figure
Selecting cluster
Node clustering
1/
b
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Clastering ranking
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Claster score:
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0.79
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= #== 0.49
Distance matrix dls
Center nude feature puoling
W, b,/
B, +
Feature matrix
0.57
Column Sum
#2
0.77
Pooled center feature vector
4
0.67
Figure 2: The structure the Distance Aware Pooling method with numeric example. Four steps mentioned in the above figures are node clustering, clustering ranking. selecting cluster centers, and center node feature pooling, which correspond to those mentioned in Section 3.2.2 In this figure, the proposed center in the node clustering step is node It should be noted that the proposed center may not be the final center for this cluster. The cluster score as each cluster with proposed center v; = can be calculated. decided. In the selecting cluster centers step, b is the average of each row sum, and node v2 is still chosen as the center with the least average distance value. In the center node feature pooling step, wy is the weight of nodes derived from b. In this way, can derive the weighted pooled center feature vector.
2, and the corresponding RF neighborhood within A" = 0.5 nodes 0, 2, and
a; top proportion clusters could be
Improved receptive field. The concept of the receptive field, RF, used in the convolutional neural network (CNN) was extended to GNNs (Ranjan al. 2020). They defined Rooo as the number of hops required cover the neighborhood of a given node, such that given chosen node, cluster can obtained based on a fixed receptive field h. However, this design may not be applicable to densely connected graphs, because Even given a small value of h, for instance, = 1 which the default value (Ranjan et al.] 2020), clusters formed within hop may include most of the nodes of the graph. Hence, the clustering
node may be connected most of the nodes in the graph.
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step may be inefficient. In addition, the value of hops can only be integers, which loses the edge weight information in the clustering process.
Therefore, we define improved receptive field for densely connected graphs RF denoted by h", which can be treated as a radius centered at a given node. The value of htd is not restricted to integers but can be positive real number. Define N(sss) the local neighborhood of the node e, and N (U;) as the RF4 neighborhood of the node o with a radius h", and Vez E E ((a)), v2 and vy are connected by the edge (v%, U;).
Node clustering. Inspired by the clustering and ranking ideas mentioned in Ranjan et al. (2020) and Gao & Ji] 2019), we propose local node clustering, and score ranking method. Each node is considered as a center of a cluster for a given h². Then, we score all the clusters and choose the top & proportion of them to represent the next layer's nodes with pooled feature values, where is hyperparameter.
Clustering ranking. Given a node v and radius h", Naa (D;) ) is the corresponding RF neigh- borhood. Let (2;) be the index set of the nodes in (2;). The cluster score is defined as 0; = Em,nel,(om (wx) die //N (us)l, where m of n. or small, nodes in N (vz) are close to each other. The top & proportion of clusters form the next layer's 's nodes.
Selecting cluster centers. We first introduce some notation: Vu, E (v:), define V, [[y]] Na (vi) as the set of nodes connected to M Na (v:). where N(vx is the closed neighborhood of the node vy. Let 02 (1z) be the index set of the nodes in V,. The node score is defined b,
Eee (v:) A hec /1yl The node with the smallest value of by is chosen the center of the cluster, and is used to represent a new node in the next layer's node representation.
Center node feature pooling. Based on the node scores, we rank the nodes in V/ and assign weight wp to ær, where r E I2(2,)- Let b = 1 b. The weight vector w is defined as w,- = d, + +), where 1 is vector with all 1's, is an extremely small positive value to avoid O's in the denominator, and b is the vector containing all the weights of nodes in V,. The value of the pooled center feature is defined as x" = =x and then x. is used as the center feature representing..o (v:).
Next layer node connectivity. Following the idea in Ying et al. 2018), the connectivity of the nodes in the next layer is preserved as follows. According to the above ranking and pooling methods, pooled graph G with the node set VP is obtained. The next step is to decide the pooled adjacency matrix A ab Define matrix S such that the columns of S are the top k clusters' weight vectors w. Hence, the pooled adjacency matrix defined as A adji = S A S.
3.3 CLASSIFICATION AND LOCALIZATION BASED ON POOLED GRAPHS.
Graph classification. A hierarchical representation for each patient is abstracted by the above GCNs with distance aware pooling. The representation is an N' x D' feature matrix, where N is the number of clusters and D' is the number of features in each cluster. For each feature, the mean and the maximum over the N' clusters are calculated. Subsequently, we obtain a 2D' feature vector. The first D' elements are the mean values of each feature, and the second D' elements are the maximal values. Then, we use an MLP to classify the 2D' feature vector into one of the three classes: COVID-19, common pneumonia, or normal, The MLP classifier is mainly composed of two linear layers. For each input 2D' feature vector, it can output the scores of each class, normalized by the softmax function.
Weakly supervised informative CT slices localization. Besides the classification, localizing the CT slices with lesions is also vital for the diagnosis. To achieve this goal, we propose the one- drop localization to select the most informative CT slices for the model to make a decision. This method does not require mask annotation for lesion, and thus the localization learned in a weakly supervised manner. We are inspired by the stepwise regression that is used for knowledge discovery (Cios et al. 1998), an automatic procedure that integrates the variable selection. One of the ideas is backward elimination. For each patient with the N' D' feature matrix, we first predict the target class using the above MLP classifier. Then, we drop one cluster each time so that we obtain N' new feature matrices in total with an equal size of (N' 1) x D'. For each of the feature matrices,
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the score of the target class is calculated using the same MLP classifier. The lowest score from the N' results and the corresponding dropped cluster are chosen. Since ignoring this cluster leads to the lowest score of the target class, this cluster should contain the most crucial diagnosis information. We can then determine the center of this cluster, and trace back to the corresponding input CT slice. We further localize the top k CT slices with the highest similarity the cluster center. We believe this whole k* + CT slices are most informative for the diagnosis, which can be suggested as reference the radiologists.
EXPERIMENTS AND RESULTS
For diagnosis and prognosis, we compare our model with the baseline, a 3D ResNet- 18 classification network (Zhang et al. 2020), and the state-of-the-art graph classification method, GCNs with ASAP (Ranjan et al. 2020). Moreover, we appraise whether the proposed method can deliver meaningful and interpretable clusters on the input chest CT scans by comparing the localization results with the slices containing lesions.
4.1 DATASET
We utilize the CT dataset from the 2019 Novel Coronavirus Resource (2019nCoVR) (Zhag et al. 2020). The dataset includes the complete chest CT scans of 929 COVID-19 positive patients, 964 common pneumonia patients, and 849 healthy individuals.
The dataset also provides these patients' clinical prognosis, whether the patients developed into severe/critical illness status, referring to the admission to ICU, mechanical ventilation, or death. The prognosis analysis could support the hospitals to designate medical resources more efficiently. In addition, the dataset summarizes the slices with lesions for COVID-19 positive and common pneumonia patients, which can be used to evaluate the one-drop localization method. Each CT slice is normalized into the dimension 256 x 256. For each chest CT scan, we use systematic sampling ensure that an equal number of slices are chosen.
4.2 DATA PREPROCESSING: CHEST CT SCAN IMAGE FEATURE EXTRACTION
CNN feature extraction. Feature extraction is a common strategy in computer vision. In case, we utilize Inception V3 (Szegedy et al. 2016) pretrained on ImageNet (Russakovsky et al. 2015). The feature map of the bottleneck layer, which the last layer before the flatten operation, is regarded as the node representation in the graph. In our case, each node represents a slice in a chest CT scan, and the node representation is vector of dimension 2048.
Wavelet decomposition extraction. Considering each slice in CT scans as a can be viewed function with two variables, which can be reconstructed summation of wavelet functions multiplying their coefficients for a given resolution (Mallai 1989). The formula required to reconstruct the image is
2 2-dimensional signal,
f(x,y)= VMN
Σ MA,
W Wolio m. (.. +
Σ Σ
W Wi W) ( (x.
i.H.V.Di=jo
where f(x, v) is the energy function an image, M and N are the image dimension, Wi and W are the coefficients of scaling function yo and wavelet function v respectively. The coefficient W.p is used in down streaming analysis since it contains the major approximation information of an image. We choose the Haar wavelet function with resolution 3. The flattened approximation matrix of the image signal, which is a vector of dimension 1024, is used as the feature embedding of a slice in CT scan.
4.3 IMPLEMENTATION DETAILS
For dataset 19nCoVR. scan are chosen. CT scans of 60% individual are randomly chosen as the training set, 25% as the test set, and the remaining 15% for the validation. To avoid information leakage, the dataset is split
systematic sampling to ensure that 48 number of slices for each CT

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(a) COVID-19 Diagnosis Confusion Matrix
(b) COVID-19 Prognosis Confusion Matrix.
364
12
12
NCP
300
48
3
Mid
True label
labal
30
5
376
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Figure 3: The confusion matrices for COVID-19 diagnosis and prognosis. 'NCP,, 'CP', and 'Normal' indicate COVID-19 positive patients, common pneumonia patients, and healthy individuals respectively. 'Severe' or 'Mild' indicates whether patient develops into severe/critical illness status. The severe/critical illness status refers to admission the ICU, mechanical ventilation, death.
according to individuals instead of the CT scan. Similar to Zhang et al. (2019) and Ying et al. ()018), repeat the data splitting aforementioned on 20 random seeds. For each random seed, the model is trained from scratch. The maximum, average and standard deviation of test accuracies are reported.
We use five GCN layers, and the MLP classifier is composed of fully connected layers. The pooling proportion & is set as 0.5 for the experiments of diagnosis and prognosis. The Adam op- timizer with an initial learning rate 0.0002, and linear decay schedule used. The negative log- likelihood loss is used for training the diagnosis and prognosis model, For prognosis, the parameters of GCN and pooling are initialized using those pretrained on diagnosis task. All models are trained for 128 epochs with early stopping applied.
4.4 QUANTITATIVE RESULTS
(a) Performance Evaluation of COVID-19 Diagnosis
Method
Feature Extractor
Average Accuracy + SD
Best Accuracy
Time (s/epoch)
GCN-DAP
Inception V3
93.93% + 0.41% %
94.80%
22.70
GCN-DAP
Wavelet
83.65% + 1.01%
85. 16%16%
20.90
GCN-ASAP
Inception V3
75.20% + 18.70%
93.74%
30.00
GCN-ASAP
Wavelet
51.43% 11.90%
81.50%
27.25
GCN-DiffPool
Inception V3
71.22% + 23.73%
94.31%
18.35
GCN-HGP-SL.
Inception V3
93.89 % + 0.39%
94.22%
45.60
(b) Performance Evaluation of COVID-19 Prognosis
Method
Feature Extractor
Average Accuracy + SD
Best Accuracy
Time (s/epoch)
GCN-DAP
Inception V3
82.70% + 3.90%
91.39 %
7.67
GCN-DAP
Wavelet Inception V3
78.98% + 3.38%
84.95%
1.83
GCN-ASAP
67.90% + 11.09%
82.80%
9.67
GCN-ASAP
Wavelet
60.22% + 5.63%
72.04%
2.30
Table 1: Performance evaluation of COVID-19 diagnosis and prognosis, where 'GCN-DA DAP'' indicates the proposed GCN-based method integrated with distance aware pooling. 'ASAP', 'DiffPool', 'HGP- SL' refer to the state-of-the-art hierarchical pooling methods. Besides, we list the average time in seconds to complete one training epoch for cach model using a single NVIDIA V100 GPU in the column "Time (s/epoch)'.
Diagnosis and prognosis performance. According to the ROC Curve for diagnosis in Figure method is comparable to the senior radiologists with 15 to 25 years of clinical experience. In Table I we compared the performance of our model and GCN model with the saate-of-theass art hierarchical pooling methods, including ASAP, DiffPool (Ying et al., 2018), and HGP-SL (Zhang ct al. 2019). The maximum, average, and standard deviation of test accuracies on 20 random seeds reported. We observed that the Inception V3 feature extraction method constantly outperforms

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Diagnosis ROC Curve
1.0
0.8
Positive Rate
0.6
micro-average ROC curve [area = 0.991
macro-average ROC: curve (area 0.99)
RCC curve of NCP (area 0.99)
0.4
ROC curve of Normal (area 0.99)
Senior Radiologist
0.2
Senior Radiologist
Senior Radiologist
Senior Radiologist
0.0
False Positive
Figure 4: The ROC urve and AUC for diagnosis. 'NCP', 'CP', and 'Normal' indicate COVID-19 positive patients, common pneumonia patients, and healthy individuals respectively. The filled dots represent the per- formance on 'NCP' diagnosis senior radiologists with 15 25 years clinical experience (Zhang et al. 2020). It shows that our method is comparable to the senior radiologists.
the wavelet decomposition method under the model configuration. The gradient explosion occurs in around 50% of the runs under the ASAP and DiffPool, resulting in optimization failures. ASAP and DiftPool are very unstable unfortunately, while this issue has been witnessed during the training of our method and HGP-SL. Thus, the standard deviations of ASAP and DiftPool are much higher. Additionally, our method outperforms HGP-SL marginally but the training of our method is about times faster.
The training curves using DAP versus the aforementioned hierarchical pooling methods over 20 runs, with varied random seeds and different train-validation -est split are presented in Figure The figure shows that our model improves the training convergence, and DAP consistently outperforms ASAP and DiffPool across almost all runs.
Training Loss
Validation Accuracy
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Figure 5: Training curves of GCN diagnosis model using DAP versus three hierarchical pooling methods over 20 runs, with varied random seeds and different train-validation-te split. The solid lines represent the mean training loss and validation accuracy, and the shade visualizes the interval of one standard deviation. It shows that DAP consistently outperforms ASAP and DiffPool across almost all runs, and converges much faster.
Weakly supervised lesion localization results. Besides graph classification, we also use our model to localize the most informative CT slices for each CT scan in the test dataset using the procedure in Section 3.33 with k = 10. Since the chosen CT slices are the most decisive ones for the diagnosis, they may contain lesions related to COVID-19 common pneumonia. Then, compare
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selected slices to the CT slices with lesions labeled by the dataset for each CT scan. Considering that the CT slices in the same CT scan are sequential, we choose the slices between the first and last slices localized by our model or labeled with lesions in the dataset. The localization of COVID- patient is visualized in figure [ The results are evaluated by Precision, Recall, and the Intersection over
Union (IoU) for each patient, where IoU # [Localizee Slices Slices Lesioni
# [Localizd SlicesUSSlicss Lesion"" Through hyperparameter searching, the best performance is achieved when the pooling proportion k: is 0.8. We reported the average and standard deviation of precision, recall and IoU among all patients in the test set on 20 random seeds in Table 2 The average IoU is 41.75% with standard deviation 2.59%.
Figure 6: Visualisation of one-drop localization for COVID- 19 positive patient: The index the bottom left corner of each slice refers to the slice index in original CT scan. The slices with green stars the top right corner are the slices containing lesions. The slices within the orange box are localized using the GCN diagnosis model. The recall, precision, and loU of localization for this patient is 80%, 100%, and 80%, respectively.
Average Precision + SD 57.39% + 3.32%
Average Recall + SD 79.89% E 3.94%
Average loU + SD 41.75% 2.59%
Table 2: Performance of one-drop localization. The localization results compared with the CT slices con- taining lesions. We list the average and standard deviation precision, recall, and loU among patients in the test sets over 20 runs.
5 DISCUSSION
In this work, we introduce framework that can provide accurate graph classification based on chest CT seans. Unlike previous diagnosis methods based on CT scans, our model can produce coarse localization highlighting the potential slices with lesions. To build trust in this framework and move towards clinical use, we should ensure that the model can explain the reason for their prediction in- stead of merely outputting the result. We argue that localization can help analyze prediction failure, and help researchers understand the effect of adversarial attacks the medical imaging domain.
As one of the few lesion localization frameworks out there, we argue that the localized slices may help uncover how a given classification method arrives at the conclusion. Specifically, it might help reveal if a method is merely overfitting on the training data by examining the slices it attends to. This will help build more robust and explainable medical AI models. Conversely, may also be used to identify the intrinsic dataset bias, notably the data acquisition bias (Biondetti et al. 2020 thereby guiding the dataset collection process and drive the medical imaging field forward.
6 CONCLUSION
This paper introduces an efficient and robust GCN-based diagnosis and prognosis system with a distance aware pooling method. can cluster nodes and learn the patient-level representation hierar- chically. Apart from accurate diagnosis, a weakly supervised lesion localization method is proposed support prognosis, making the clinical decision more interpretable and reliable.

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Under review as a conference paper at ICLR 2021
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Under review as a conference paper at ICLR 2021
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Reviews:
[{"review_id": "tW3xArvMHZ", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Summary\nThe manuscript proposes  a distance aware pooling method to use in  graph convolutional neural for predicting whether a subject is infected with Covid-19 (diagnosis) and progression of the disease (prognosis). Experiments were conducted on CT images from three groups: Covid-19 group, common pneumonia group, and heathy group with about 900 samples in each group. The proposed model achieved 94.7% accuracy.    \n\nPros:\n\nThe manuscript proposes  a distance aware pooling method which, with the help of features generated through inception v3, could achieve an error rate of a little bit over 5%\n\n\nCons:\n\nIn terms of the potential impact of the work, my concerns are as follows:\n1.\tAlthough the model trained on the dataset achieved a relatively low error rate (~ 5.3% ),  there is no evidence that this error rate is low enough for the model developed to be really useful, e,g. could actions taken based on a diagnosis method of this level of error rate potentially create a local epidemic?\n2.\tThe model is not tested on an independent dataset that consists of other type of lung diseases other than common pneumonia. Is it possible that the model could actually categorize CT from a patient with another type of lung disease as Covid-19?  Thus, this 94.7% accuracy probably needs to be taken with a grain of salt when the model is to be used to test patients clinically.\n\nIn terms of the technical soundness of the work and writing of the manuscript, my concerns are as follows.\n\n1.\tAlthough the manuscript claims the distance aware pooling method as its main contribution, the description of the method is no more than one figure. It is unclear how this pooling function is computed exactly. Nor is it clearly stated how does it fit in overall model of the graph convolutional neural network as well. Even in the figure, some of the terms is used without giving clear definition (e.g. adjacency matrix centered at a specific node ). Further, There is no discussion of strengths and limitations of the proposed pooling method and the method it is trying to compare against ASAP, specifically in the context of CT imagining. \n2.\tAlmost the same can be said about the section of “improved receptive field”.  What is the motivation of improving receptive field? Why is it relevant in the case of graph formed of CT imaging. (incidentally, it seems that how authors do not mention in the manuscript how the edges are added to the graph, but I might have missed this). The impact of the radius “h_d” on the model performance is  not discussed, either.  \n3.\tHow many time have the authors randomly split training and testing set? the variance from different runs are not reported. It is a standard practice to report both the mean of the performance from different runs as well as the variance. \n4.\tSince the problem that the manuscript is trying to solve is a graph classification and main contribution of the manuscript is a pooling method, the authors should consider comparing their pooling methods with different pooling methods and using different graph classification methods as baseline as well. \nSee\nZhang et al   Hierarchical Graph Pooling with Structure Learning      https://arxiv.org/abs/1911.05954  \nLi et al   Graph Matching Networks for Learning the Similarity of Graph Structured Objects      ICML 2019\n\nOverall, the manuscript could be improving by stating more clearly the motivation of their pooling method in the context of CT imaging,  giving a more complete and rigorous definition of the pooling function,   comparing their method against different pooling methods  using different classification methods,  and having a more detailed discussion on the strengths and limitations of different pooling methods. \n", "extra_scores": {}, "extra_text": {}}, {"review_id": "bLlQubr41IV", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Short summary\n---------------------\nThe authors propose a graph convolutional network (GCN) approach to perform the diagnosis and prognosis of COVID-19 from chest CT scans. They propose a novel pooling that takes into account the edges weights compared to recent methods. They validate their method on one dataset and compare the results to one recent baseline.\n\nStrengths\n--------------\nThe paper is very well written and easy to follow. The figures and tables are clear and pleasing. The work is sound.\n\nWeaknesses\n-------------------\nWhile the motivation is clearly depicted, I lacked the clinical relevance or justification to tackle this problem. In addition, case analyses or the usefulness of the proposed prognosis tool are not discussed, and it is difficult to estimate the complexity of the task without this information (e.g. how clinicians evaluate severity, is it obvious from the pulmonary damage?).\nOn the other hand, the technical contribution is underwhelming: the proposed method is only marginally better than its recent counterpart, no confidence intervals are provided and the effect of the preprocessing is much larger. It is also unclear what the motivation was for some choices, how these relate to the literature or how they were practically implemented (see detailed comments).\n\nNovelty\n-------------\nI did not find the technical contribution of significance, especially given the results comparing DAP to ASAP. While the problem of COVID-19 diagnosis and prognosis is timely, it lacked clinical insights.\n\nClarity\n----------- \nVery clear, very well written. A couple of details are missing (see detailed comments), but overall this is an enjoyable read. I wished there was a discussion of the technique, the results and the limitations.\n\nRigor\n--------\nThe methods seemed sound. I wished confidence intervals were provided.\n\nDetailed comments\n---------------------------\n- node clustering: can parts of the graph be “dropped” during this step?\n- If the adjacency is already defined as the cosine distance between nodes, isn’t message passing already doing/reinforcing some kind of clustering? How does the clustering ranking (based on A) relate to comparing nodes in “input” space compared to the layer at stake? Given the proposed next layer connectivity, isn’t the next layer A an exponent version of the first layer A for the terms in top k?\n- How to define h_d and k? What is their effect on model performance?\n- Is there a justification behind the aggregation? Is there a reference for this? Doesn’t that strategy assume that each feature in 1...D’ across nodes N’ represent the same dimension?\n- How would this compare to using a “master node” (Gilmer et al., 2017), where all nodes could write and read from a separate node, to allow for long-distance communication?\n- From my understanding, one-drop localization is similar to occluding a cluster at a time. Is there a reference for this method? \n- How is k_s chosen? Why is a fixed number chosen compared to e.g. a “% of prediction variance explained” type of approach?\n- Any clinical input in this work?\n- Is the number of slices acquired or selected through sampling mentioned in the text? This would help in illustrating the size of each graph.\n- What are the reasons behind the choice of the 2 preprocessing techniques? They seem arbitrary without referencing.\n- On such a low number of patients, confidence intervals are strongly recommended. I am not confident about the significance of DAP compared to ASAP, especially given the large performance gap between feature extractors.\n- Comparison with CNNs would be interesting. This is especially important given the impact of the feature representation. I am wondering whether GNNs are not “too sensitive” to the choice of initial node embedding (which also defines A) and whether this should be investigated in more depth, or maybe CNNs display similar performance without needing this additional step.\n- Won’t IoU on slices heavily depend on the choice of k_s?\n- Selecting slices “included” in the set of slices highlighted by one-drop seems like an arbitrary choice to me. The fact that slices are sequential is specific to this type of data, and this choice seems like an “a posteriori” choice that better aligns with the ground truth.\n- IoU is not reported across all patients, but rather on cherry-picked examples  in Table 2.\n- There is no discussion\n\nMinor\n-------\n- One-drop: I am confused on the wording, where the authors mention the score on the “target class”. Do they refer to the predicted class of the model?\n- The prognosis task is undefined\n\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "4XdDNsgr4G", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper is an application of GCN with good features on chest CT scan images for Covid-19 diagnosis and prognosis. First of all this is a relevant and appreciated effort when the world is fighting the pandemic. Hence some bonus points is directed towards that. As a whole, to the representation learning community, it adds limited research values apart from being an application of GCN which is aligned to the application track of ICLR. The paper claims that with less than 1% number of total parameters in the baseline 3D ResNet model, their method achieves 94.7% accuracy for diagnosis, which is marginally better than state of art - however whether the model was over-fitted is not clear. Prognosis information is an added claim, though automation part is not integrated.\nIt will be better if approach is compared with another concurrent work - \"Covid-19 Classification by FGCNet with Deep Feature Fusion from Graph Convolutional Network and Convolutional Neural Network\" - https://www.sciencedirect.com/science/article/pii/S1566253520303705.\n\nI found too many repeating verbatim and technical descriptions - most can be delegated to references / citations or section numbers.\n\nSections 2.2 and 2.3 is not needed as such - if any special benefit wrt to current problem is given it will be helpful - more text from appendix can be added to paper than spending on explanations of easily searchable material.\n\nFig. 1 is too simple - go deep - can get influenced by similar works in state of art papers - how they present.\n\n\"Empirically, it is shown to be more robust for densely connected graphs\" - this claim needs more substance.\n\n\"may be bootless\" - use inefficient.\n\nIn Node clustering, how is 'k' determined?\n\nAs a general comment, too many to point individually - break the sentences around mathematical terminology into parts and also check the flow of grammar.\n\n\"Haar wavelet function with resolution 3\" - more details on this.\n\nI am not sure about the ablation studies and following of Train-Eval-Test based experiments (refer Andrew Ng ML Yearning).\n\nConclusion - write with quantitative numbers and a few sentences on author's learning / observations from overall experiments / method. And to conclude from my side, the paper is easy to read, needs some polishing and quantitative explained presentation; but overall is a relevant application paper.", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper presents a GCN-based solution with a distance aware pooling method for diagnosis and prognosis of COVID-19 based on CT-scan. It aims to address an important and timely problem. The proposed solution is reasonable. 

The paper receives mixed ratings, and therefore we had extensive discussions. It is agreed by all of us that  

(1) the novel contribution of the proposed method is relatively low compared with standard ICLR papers; 

(2) the evaluation is interesting, but could be improved with state-of-art baselines on CT-scan (not limited to GCN-based method); 

(3) the authors have improved the writing of the paper significantly, which convinces two reviewers to elevate their scores. 

The paper addresses a timely topic, but there is still room for improvement in methodology and evaluation. We hope that the reviews can help the authors prepare a strong publication in the future. 

Decision: Reject