Learning low-dimensional representation of images is a fundamental task in computer vision. Deep learning techniques, especially the convolutional neural network (CNN) architectures have achieved remarkable breakthroughs in learning image representation for classification[22, 14, 15]. However, most of the existing approaches for image representation only considered each input image independently while ignored the relations between images. In reality, multiple relations can exist between images, especially in clinical setting, medical images from the same person can show pathophysiologic progressions. Intuitively, related images can give certain insights to better understand the current image. For example, images present in the same web page can help to understand each other; knowing a patient’s other medical images can help to analyze the current image.
We model the images and the relations between them as a graph, named ImageGraph, where a node corresponds to an image and an edge between two nodes represents a relation between the two corresponding images. An ImageGraph incorporating multiple types of relations is a multigraph where multiple edges exist between two nodes. The neighborhood of an image in the ImageGraph represents the images that have close relations with it. Fig. 1(a) shows an example of ImageGraph of CXR images incorporating 3 types of relations between 5 nodes.
Learning an image representation incorporating both neighborhood information and the original pixel information is difficult, because the neighborhood information is unstructured and varies for different nodes. Inspired by the emerging research on graph convolutional networks (GCN) [21, 13, 4, 40] that can model graph data to learn informative representations for nodes based on the original node features and the structure information, we propose ImageGCN, an end-to-end GCN framework on ImageGraph, to learn the image representations. In ImageGCN, each image updates the information based on its own features and the images related to it. Fig. 1 shows an overview of ImageGCN, where each node in an ImageGraph is transformed into an informative representation by a number of ImageGCN layers.
There are several issues when applying the original GCN 
to an ImageGraph. (1) The original GCN is inductive and requires all node features present during training, which does not scale out to large ImageGraphs. (2) The original GCN is for simple graphs and can not support the multi-relational ImageGraphs. (3) The original GCN is effective for low-dimensional feature vectors in nodes, and can not be effectively extended to nodes with high-dimensional or unstructured features in ImageGraphs. Thanks to GraphSAGE, the inductive learning issue was addressed for GCN; the multi-relational issue was also addressed by relational GCN . However, the third issue, applying GCN to high-dimensional or unstructured features still remains unaddressed. The ImageGCN is proposed to address this issue and further to incorporate the idea of GraphSAGE and relational GCN for batch propagation on multi-relational ImageGraphs.
In this paper, for graphs with high-dimensional or unstructured features in the nodes, we propose to design flexible message passing units (MPU) to do message passing between two adjacent nodes, instead of a linear transformation in the original GCN. In the proposed ImageGCN, we use a number of MPUs equipped with a multi-layer CNN architecture for message passing between images in a multi-relational ImageGraph. We introduce partial parameter sharing between different MPUs corresponding to different relations to reduce model complexity. We also incorporate the idea of GraphSAGE and relational GCN to our ImageGCN model for inductive batch propagation on multi-relational ImageGraphs.
We evaluate ImageGCN on the ChestX-ray14 dataset  where rich relations are available between the Chest X-ray (CXR) images. The experimental results demonstrate that ImageGCN can outperform respective baselines in both disease identification and localization.
Besides the improved performance, the main contributions are as follows. (1) To our best knowledge, this is the first study to model natural image-level relations for image representation. (2) We propose ImageGCN to extend original GCN to high-dimensional or unstructured data in an ImageGraph. (3) We incorporate the idea of relational GCN and GraphSAGE into ImageGCN for inductive batch propagation on multi-relational ImageGraphs. (4) We introduce the partial parameter sharing scheme to reduce the model complexity of ImageGCN.
2 Related work.
Deep learning for disease identification with CXR. Since the ChestX-ray14 dataset  was released, an increasing amount of research on CXR image analysis have used deep neural networks for disease identification [46, 51, 23, 31, 12]. The general idea of previous work is to generate a low-dimensional representation by a deep neural network architecture, independently. In our work, we consider the relation between the CXR images, and learn a representation based on the image itself and the its neighbor images.
Relational Modeling. The previous research on relational model in computer vision mainly focused on pixel-level relations [30, 33], object-level relations [49, 32, 6, 56, 52] and label-level relations [25, 45]. image-level similarity relation were also studied in literature [10, 45]. However, Few studies are found to model the natural image-level relations for image representation.
Graph Neural Networks. Recently, inspired by the huge success of CNN on regular Euclidean data like images (2D grid) and text (1D sequence), a large number of research tried to generalize the operation of convolution to non-Euclidean data such as graph [36, 7, 33, 3, 21]. In the pioneering studies, Kipf and Welling 
resolved the computational bottleneck by learning polynomials of the graph Laplacian and provided fast approximate convolutions on graphs, Graph Convolutional Networks (GCN), which improved scalability and classification performance in large-scale graphs. GCN had a wide range of applications across different tasks and domains, such as nature language processing[50, 1, 54, 27], recommender systems [2, 33, 53], life science and health care [18, 57, 9, 5]19, 28], . GCN was also explored in several computer vision tasks, such as image classification [47, 10], scene graph generation [48, 17], semantic segmentation [24, 44], visual reasoning [37, 35, 52]
. In most of previous studies, the graphs were built based on the knowledge graph[47, 37, 35] or the object relations [48, 17] or the point clouds [24, 44]. In this paper, we take into account the natural image-level relations to construct a multi-relational ImageGraph, and use GCN to model the relations to learn informative representations for the nodes images.
3.1 Graph Convolutional Networks
Graph convolutional network (GCN)  can incorporate the node feature information and the structure information to learn informative representations for nodes in the graph. GCN learns node representations with the following propagation rule derived from spectral graph convolutions for an undirected graph :
where is the adjacency matrix with added self-connection, is a diagonal matrix with , can be seen as a symmetrically normalized adjacency matrix, and are the node representation matrix and the trainable linear transformation matrix in the th layer, is the original feature matrix of nodes,
The propagation rule of GCN in Eq. 1 can be interpreted as the Laplacian smoothing for a graph , the new feature of a node is computed as the weighted average of itself and its neighbors, followed by a linear transformation before activation function, Eq. 2,
where is the representation of node in the th layer, is the set of all nodes that have a connection with (self included), is a problem-specific normalization coefficient. It can be proven that Eq. 2 is equivalent to the original GCN Eq. 1 when is the entry of the symmetrically normalized graph Laplacian . Eq. 2 can be easily interpreted as that a node accepts messages from its neighbors , by adding self-connection, a node is also considered a neighbor of itself.
The relational GCN formulated by Eq. 3 is interpreted as that a node accepts messages from the nodes that have any relations with it. The message passing weights vary with different relations and different layers. In Eq. 3, note that there is a special relation in that deserves more attention, the self-connection (denoted by ). We have , if we consider each node equally accepts the self-contribution as is during information updating. Different from the original GCN Eqs. 1 and 2, where all connections, including the self-connection, are considered equally, the relational GCN designs different message passing methods for different relations, including the self-connection.
is an identity matrix. By Eq.4, the computation efficiency can be improved using sparse matrix multiplications.
Note that Eq. 3 and 4 can be generalized to the situation of multi-relations between two nodes and the directed graphs. For multi-relations between two nodes, two CXR images share the same patient and the same view position, the message passing should be conducted multiple times, one for each relation. For directed graphs, the directed edges can be regarded as two relations, the in relation and the out relation, thus there should be two different message passing methods corresponding to the message passing from the head node to tail node and from the tail to the head, respectively.
(a), where the original feature for each image is a 3-dimensional tensor (). If we flatten the tensor and use the linear transformation matrix for message passing, the transformation matrix will be extremely large, low efficiency and even low non-linear expressive capacity. To tackle this issue, in our ImageGCN, we propose to design flexible message passing methods between images as
where is the kernel Message Passing Unit (MPU) corresponding to relation in layer , can be a 4-dimensional tensor () that is the representations of the all images in the th layer, is the original pixel-level input tensor of images. In the last layer, should be a matrix where each row corresponds to a distributed representation of an image. The multiplication between a matrix and a tensor in Eq. 5 is expanded correspondingly.
The propagation rule of ImageGCN can be illustrated in Fig. 2, where each node of the input ImageGraph gets a representation through a GCN layer, by stacking multiple GCN layers, each node could get an informative representation eventually.
ImageGCN Layer. A ImageGCN layer contains a number of MPUs to do message passing between layers. An MPU corresponds to the message passing of a type of relation. A ImageGCN layer also has an aggregator for each node to aggregate the received messages from its neighbors. An activation function (ReLU) is applied to the aggregation to enhance the non-linear expressive capacity. Though many aggregators are available for this task [13, 34], we use the mean aggregator for simplicity as the original GCN did. In ImageGCN, MPUs can be designed as a multi-layer CNN architecture in the middle ImageGCN layers to extract high-level features, and linear MPUs can be used in the last layers to generate vector representations for images.
Propagation. For each image (Image 4 in Fig. 2), each of its neighbors are input to the corresponding MPU, the outputs are aggregated and then activated to generate the new representation of this image in the next layer. For each image, the propagation rule is
Partial Parameter Sharing. Because each relation has an MPU, an issue with applying Eq. 5 to a ImageGraph with many relation types is that the number of parameters would grow rapidly with the number of relations. This will lead to a very large model that is not easy to train with limited computing and storage resources, especially for MPUs with multi-layer neural networks.
To address this issue, we introduce the partial parameter sharing (PPS) scheme between MPUs. With PPS, The MPUs share most of the parameters to reduce the total number of parameters. In our design, the same CNN architecture is applied to all MPUs in the same layer, all the parameters are shared between these MPUs except for the last parameter layer where the parameters are used to make the message passing rule different for different relations, see Fig. (a)a for an ImageGCN layer with PPS. Thus, the message passing rule Eq. 5 can be further refined as:
where is shared by all relations, only that has only a few parameters determines the different message passing methods for different relations. Also, we can further share all the parameters between all MPUs, that is, assigning the same message passing rule to different relations, all parameter sharing (APS) in Fig. (b)b. However, APS will reduce the multiple relations to a single relation, thus reduce the model’s expressive capacity, our experimental results in Section 4.5 and 4.6 also demonstrate the less effectiveness of APS than PPS.
3.3 Training Strategies
The loss function relies on the downstream task. Specifically, for a classic node classification task, we can use a softmax activation function in the last layer and minimize the cross-entropy loss on all labeled nodes. For multi-label classifications, the loss function can be design as in our experiments in Section4.4.
Batch propagation. Equation 7 requires all nodes in the graph being present during training, it can not support propagation in batch. This is difficult to scale out to a large graph with high-dimensional node features, which is common in computer vision. One may want to simply construct a subgraph in a batch, this usually causes no edges in a batch if the graph is sparse. GraphSAGE  was designed to address this issue for single relational graphs. Inspired by GraphSAGE, we introduce an inductive batch propagation algorithm for multi-relational ImageGraphs in Algorithm 1. For each sample in a batch, for each relation , we randomly sample neighbors of to pass message to with relation in a layer (Line 8). The union of the sampled neighbors and the samples in the batch are considered as a new batch for the next layer (Line 3 to 11). For a layer ImageGCN, the neighbor sampling should be repeated times to reach the th order neighbors of the initial batch (Line 2 to 12). We construct the subgraph based on the final batch (Line 13 to 16, is the final batch). In each ImageGCN layer, the message passing is conducted inside the subgraph (Line 17). Note that the image features can be in persistent storage, and are loaded when a batch and the neighbors of images in the batch are sampled (Line 13), This is important to reduce memory requirement for large-scale graphs or graphs with high-dimensional features in the nodes.
In test procedure, given a test batch ( can have only one or more samples), the relations between test samples and the training samples are added to the adjacency matrices . The batch propagation algorithm Eq. 1 can be directly applied for test data representation.
4.1 ChestX-ray14 Dataset
We test ImageGCN for disease identification and localization on the ChestX-ray14 dataset  which consists of 112,120 frontal-view CXR images of 30,805 patients related with 14 thoracic disease labels. The labels are mined from the associated radiological reports using natural language processing, and are expected to have accuracy90% . Out of the 112,120 CXR images, 51,708 contains one or more pathologies. The remaining 60,412 images are considered normal. ChestX-ray14 dataset also provides the patients information for a CXR image based on which we construct the ImageGraph. We randomly split the dataset into training, validation and test set by the ratio 7:2:1 (training 78484 images, validation 11212 images, 22424 images). We regard the provided labels as ground truth to train the model on training set and evaluate it on test set. We do not apply any data augmentation techniques.
4.2 Graph Construction
To construct an ImageGraph based on the dataset, besides the self-connection, we consider 4 types of relations between two CXR images that are relevant for disease classification and localization. (1) Person relation, if two images come from the same person, a person relation exists. (2) Age relation, if the two images come from the persons of the same age when the CXR were taken, an age relation exists. (3) Gender relation, if the owners of two images have the same gender, a gender relation exists. (4) View relation, if two CXR images were taken with the same view position (PosteroAnterior or AnteroPosterior ), a view relation exists.
The four relations are all reflexive, symmetric and transitive, thus each relation corresponds to a cluster graph that consists of a number of disjoint complete subgraphs. Person relation usually implies gender relation but can not imply age relation, because a person can take several CXR images at different ages. The adjacency matrix of each relation is a diagonal block matrix. Our ImageGCN is built on this multi-relational graph. The adjacency matrices are normalized in advance. Note that because the self-connection relation is considered separately, The adjacency matrices do not need to add self-connection.
4.3 MPU design
Since the ImageGraph in our experiments is a cluster graph for each relation, each node can reach other reachable nodes by 1 step, one-layer ImageGCN is enough to catch the structure information of an image node. Stacking multiple GCN layers would result in over-smoothing issues . For the one-layer ImageGCN, we design the MPUs in our experiments as a deep CNN architecture to catch high-level visual information. According to partial parameter sharing introduced in Section 3 and Fig. 3, each MPU consists of two parts: the sharing part and the private part .
The sharing part.
The sharing part of the MPUs consists of the feature layers of a pre-trained CNN architecture, a transition layer and a global pooling layer, sequentially. For a pre-trained model, we discard the high-level fully-connected layers and classification layers and only keep the remaining feature layers as the first component of the sharing part. The transition layer consists of a convolutional layer, a batch normalization layer and a ReLu layer sequentially. In the transition layer, we let the convolutional layer have 1024 filters with kernel size to transform the output of previous layers into a uniform number (1024 in our experiment) of feature maps which is used to generate the heatmap for disease localization. The global pooling layer pools the generated 1024 feature maps to a 1024-dimensional vector with a kernel size equal to the feature map’s size. Thus, by the sharing part of MPUs, an image is transformed to a 1024-dimensional vector. We test the feature layers of three different pre-trained CNN architectures independently in our experiments, AlexNet , VGGNet16 with batch normalization (VGGNet16BN) , and ResNet50 .
The private part.
The private part accepts the output of the sharing part and outputs an embedding to the aggregator. For each relation, we use a linear layer (with different parameters) as the private part to transform the 1024-dimensional vector from the sharing part to a 14-dimensional vector. For an image, the 14-dimensional vectors from its neighbors are aggregated and fed to a sigmoid activation function to generate its probabilities corresponding to the 14 diseases. With a similar method in, the weights of the private linear layer of self-connection combined with the activations of the transition layer in the sharing part can generate a heatmap for the disease location task.
All the learnable parameters of the ImageGCN model are contained in these two parts, the sharing part corresponds to the feature layers of a pre-trained architecture, and the private parts corresponds to 5 linear layers corresponding to the 4 relations and self-connection. Though only a part of the pre-trained model, AlexNet, is incorporated in an MPU, we call it an AlexNet MPU for convenience, similarly, VGGNet16BN MPU and ResNet50 MPU. For each MPU type (AlexNet), we use two baselines to evaluate our model, ImageGCN with all parameter sharing (APS) and the basic pre-trained model (AlexNet) fine-tuned in the dataset. In the following statement in this paper, we use A-GCN-PPS to denote the ImageGCN with AlexNet MPUs and partial parameter sharing, similarly V-GCN-PPS for VGGNet16BN MPUs and R-GCN-PPS for ResNet50 MPUs.
The AUC results of various models to classify for the 14 diseases on ChestX-ray14 dataset. For each disease, the best results are bolded. The red text means our ImageGCN can perform better than or equal to the corresponding baseline models. Abbrs: Atel: Atelectasis; Card: Cardiomegaly; Effu: Effusion; Infi: Infiltration; Nodu: Nodule; Pneu1: Pneumonia; Pneu2:Pneumothorax; Cons: Consolidation Edem: Edema; Emph: Emphysema; Fibr: Fibrosis; PT:Pleural Thickening Hern: Hernia.
4.4 Experimental settings
Weakly supervised learning.
The ChestX-ray14 dataset provides pathology bounding box (Bbox) annotations of a small number of CXR images, which can be used as the ground truth of the disease localization task. In our experiments, we adopt the weakly supervised learning scheme, where no annotations are used for training, they are only used to evaluate the performance of disease location of a model trained with only image-level labels.
Loss function. For multi-label classification on ChestX-ray14, the true label of each CXR image is a 14-dimensional binary vector where denotes the corresponding disease is present and for absence. An all zero vector represents “No Findings” in the 14 diseases. Due to the high sparsity of the label matrix, we use the weighted cross entropy loss as Wang  did, where each sample with true labels and output probabilities has the loss
where and are the number of ‘0’s and ‘1’s in a mini-batch respectively. The loss of images in a mini-batch are averaged as the loss of the batch.
. We terminate the training procedure when it reaches 10 epochs. In each epoch, the model with the best classification performance on the validation set is saved for evaluation.
4.5 Disease Identification
For the disease identification task, we use AUC score to evaluate the performance of the models. Table 1 shows the AUC scores of all the models on the 14 diseases. From Table 1, as expected in Section 3, for all the three types of MPUs, PPS outperform APS obviously. For each type of MPU, GCN-PPS outperform GCN-APS and the corresponding basic model overall and in most of the diseases. V-GCN-PPS with can even outperform the corresponding V-GCN-APS and VGGNet16BN for all the 14 diseases.
Table 1 also lists some results reported in the related references. Some studies like  that used a different training-validation-test split ratio or augmented the dataset are not listed. Our V-GCN-PPS achieved the best overall results, compared with the state-of-the-art methods. On 7 out of the 14 disease, ImageGCN achieves the best results among these state-of-the-art methods.
|0.1||Acc||A-GCN-PPS (ours)||[rgb] 1, 0, 00.4889||0.9932||[rgb] 1, 0, 00.6667||[rgb] 1, 0, 00.6667||[rgb] 1, 0, 00.4706||0.0000||[rgb] 1, 0, 00.6417||[rgb] 1, 0, 00.3469|
|AFP||A-GCN-PPS (ours)||[rgb] 1, 0, 00.5111||0.0137||[rgb] 1, 0, 00.3333||[rgb] 1, 0, 00.3333||[rgb] 1, 0, 00.5294||1.0127||[rgb] 1, 0, 00.3583||[rgb] 1, 0, 00.6531|
|0.5||Acc||A-GCN-PPS (ours)||[rgb] 1, 0, 00.0222||[rgb] 1, 0, 00.3836||0.0458||[rgb] 1, 0, 00.1138||0.0471||[rgb] 1, 0, 00.0000||[rgb] 1, 0, 00.0750||[rgb] 1, 0, 00.0408|
|AFP||A-GCN-PPS (ours)||[rgb] 1, 0, 00.9778||[rgb] 1, 0, 00.6233||0.9542||[rgb] 1, 0, 00.8862||0.9529||1.0127||[rgb] 1, 0, 00.9250||[rgb] 1, 0, 00.9592|
In Table 1, GCN-APS is less effective than the corresponding basic model because the graph is a complete graph if all relations are considered equally by APS, an image’s own feature would be heavily dwarfed by the messages of its neighbor images. For example, in Fig. (b)b, the message from the image itself is considered equal to its neighbors’. This makes an image and its neighbors indistinguishable, thus leads to even lower performance than the baseline. On the contrary, by PPS in Fig. (a)a, messages from neighbors with different relations will be considered differently by , the less important messages will have less influence to the results. Thus, ImageGCNs with PPS perform better than those with APS and the baseline model.
4.6 Disease Localization
ChestX-ray14 dataset also contains 984 labelled Bboxes for 880 CXR images by board-certified radiologists. The provided Bboxes correspond to 8 of the 14 diseases, we consider these Bboxes as ground truth to evaluate the disease localization performance of the models.
With class activation mapping , for each image, we generate a heatmap normalized to with the MPU of self-connection in a weakly supervised manner. Following the setting of Wang , we segment the heatmap by a threshold of 180, and generate Bboxes to cover the activated regions in the binary map. We use intersection over union ratio () between the detected region and the annotated ground truth to evaluate the localization performance. We define a correct localization when , where is the self-defined threshold.
Fig. 4 shows example localization qualitative results of A-GCN-PPS compared to the results of the baselines. From 4, it can be seen that our ImageGCN with AlexNet MPU and PPS usually have smaller and more accurate Bboxes than the baselines.
We propose ImageGCN to model relations between images and apply it to CXR images for disease identification and disease localization. To our best knowledge, this is the first study to model natural image-level relations for image representation learning. ImageGCN can extend the original GCN to high-dimensional or unstructured data, and incorporate the idea of relational GCN and GraphSAGE for batch propagation on multi-relational ImageGraphs. We also introduce the PPS scheme to reduce the complexity of ImageGCN. The Experimental results on ChestX-ray14 dataset demonstrate that ImageGCN outperforms respective baselines in both disease identification and localization and can achieve comparable and often better results than the state-of-the-art methods. Future research includes tuning the MPU of ImageGraph for different vision tasks, and test ImageGCN on more general datasets.
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