## 1 Introduction  
As an interdisciplinary area, medical image classification is the foundation of automatic disease diagnosis. With the development of deep learning technology, convolutional neural networks (CNNs) [1, 2, 3, 4, 5, 6, 7] have been widely applied in computer vision tasks, such as image classification [8, 9], object detection [10], semantic segmentation [11], etc. The performance of these tasks was greatly improved with the application of CNNs. However, CNNs have limitations. Firstly, the pooling operation provides some transition invariance and results in the loss of important location information. Secondly, CNNs struggle to learn the part-whole relationship. To address these weaknesses, CapsNet [12] is proposed to replace the scalar output with vector output for representing different properties, such as the orientation and viewpoints of objects. Different from the translation invariance from the pooling operation, CapsNet can provide translation equivariance. Equivariance is the detection of objects that can transform into each other. Different from CNNs, the knowledge about part-whole relationships is kept in the capsule network, as discussed in [12, 13]. Capsule networks recognize objects through both local features and part-whole knowledge. For example, a bird, as an object, has several parts, including a head, a trunk, wings, claws, and a tail. When these parts are disturbed, CNNs would still recognize the disturbed object as a bird, while CapsNet can determine that it is not a bird through the part-wholerelationship. In the original CapsNet [12], information is represented in vectorized format, leading to costly calculation of the routing between capsules of different layers. In the matrix CapsNet [13], vectorized information is replaced by matrix capsules, and routing weights are updated by the expectation-maximization (EM) algorithm. However, early CapsNets have their drawbacks. First, the low-level features that consist of the capsule are extracted only by shallow convolutional operations. This results in capsules containing very little semantic high-level information. Secondly, low-level convolutional operations lack an attention mechanism, which may import meaningless and redundant information into the capsules. One of the effective ways for performance boosting is to employ a better feature extractor, which can capture richer and more semantic contextual patterns to build capsules. Recent efforts focusing on the improvement of feature extraction for CapsNets were extensively investigated, such as Multi-Scale CapsNet (MS-CapsNet) [14] and RS-CapsNet [15]. In this paper, we propose a novel capsule network, named the attentive octave convolutional capsule network (AOC-CapsNet) for medical image classification. In AOC-CapsNet, the traditional convolution operation is replaced by an octave convolution operation. In [16], the octave convolution operation is proposed to process both higher and lower frequencies in the inputs at the same time. In natural images, higher frequencies correspond to the detailed information that varies greatly in the images, and lower frequencies correspond to the smoothly changing structure in the images. These two types of information are also very important for medical image classification. It is critical to select which kind of information is more important in medical image classification. However, the traditional octave convolutional operation cannot enhance useful information and suppress useless information. In AOC-CapsNet, we adopt a convolutional block attention module (CBAM) to identify and select useful information. The CBAM allows AOC-CapsNet to highlight critical local regions with rich semantic details utilized as distinguishable patterns, leading to a performance gain in the medical image classification task. Studies on capsule networks [17; 18] have focused on medical image analysis. A recent benchmark, named MedMNIST [19], was proposed and used to validate the performance of different models for medical image analysis.