## 1 Introduction
Most existing and available pathological image resources generally only have coarse-grained label information. For instance, only the image level label is given for a WSI with resolution of a million pixels. The benign and malignant tissues may both appear mixed in a complete pathological image labeled as cancerous. Thus, not all patches extracted from pathological images labeled as cancer contain class-specific information. When only a few regions provide the key information related to the cancerous class of the WSI and the remaining regions are more related to the benign class, standard supervised learning will fail due to the usage of a large number of mislabeled patches. Therefore, compared to the supervised method based on patch-wise classification, modeling the pathological image classification task as a weakly supervised problem with inexact supervision can be more appropriate [7]. In our study, the pathological image classification task was viewed as the multiple instance classification (MIC) problem. The MIC methods can be categorized into three paradigms: Instance-Space, Bag-Space and Embedded-Space [8]. In the Embedded-Space paradigm, each bag is mapped to a single feature vector that represents the whole information about the bag. When the bag-level embeddings are obtained, the original MIC problem can be converted into a standard supervised classification problem. Standard classifiers such as SVM, KNN and neural networks can be applied, where each bag-level feature vector has its own label. To facilitate comparison, the fully connected layers were adopted as bag-level classifiers in our work. How to obtain bag-level embeddings that contain the global information is the key step in the Embedded-Space paradigm. Some studies have introduced multiple instance poolinglayers to neural networks to solve the tasks related to pathological image analysis [9; 10]. The MIL pooling layers integrate instance-level representations into bag-level embedding to serve the downstream task, such as histopathology image retrieval and classification. But the drawback of these fixed MIL pooling operators is clearly that they are pre-defined and unable to adapt to various specific tasks. To address this problem, an attention-based MIL pooling operator [11] is proposed, which can introduce trainable parameters to weight different instances and help obtain a more flexible and adaptive global representation. [PERSON] et al. [12] combined MI-FCN and attention-based MIL pooling to perform the cancer survival prediction task. [PERSON] et al. [13] selected representative regions according to their attention scores to train instance-level clustering layers to enhance the interpretability of the model. Inspired by attention-related works [11], the RMDL network proposed by [PERSON] et al. [2] achieved image-level classification task by multi-scale feature fusion and recalibration of instance features according to the importance of each instance to the image label. Nevertheless, most existing MIC algorithms including attention-related methods treat instances in each bag as independent and identically distributed without considering the spatial topological relationships of instances corresponding to the original bag [14]. The spatial topological relationships between local areas in a WSI were actually destroyed when the high resolution WSI was divided into patches. A graph is an important data structure suitable for processing unstructured data. By way of constructing a series of objects and their interrelations as nodes and edges, the graph structure has strong modeling representation for many real scenarios. In this paper, we designed an effective framework for high-resolution gastric pathological image classification tasks. We introduced graphs to model the spatial relationships between instances. With spatial topological structure information retained, the connections between nodes with similar features were constructed according to their distances in the feature space. We designed a graph convolutional network to solve this MIC problem.