Analysis of Capsule Networks for Image Classification

International Conferences Computer Graphics, Visualization, Computer Vision and Image Processing 2021; Connected Smart Cities 2021; and Big Data Analytics, Data Mining and Computational Intelligence 2021

ANALYSIS OF CAPSULE NETWORKS FOR IMAGE CLASSIFICATION

Evgin Goceri Biomedical Engineering Department, Engineering Faculty Akdeniz University, Dumlupinar Boulevard, 07058, Antalya, Turkey

ABSTRACT Recently, the interest in convolutional neural networks have grown exponentially for image classification. Their success is based on the ability to learn hierarchical and meaningful image representation that results in a feature extraction technique which is general, flexible and can encode complex patterns. However, these networks have some drawbacks. For example, they need a large number of labeled data, lose valuable information (about the internal properties, such as shape, location, pose and orientation in an image and their relationships) in the pooling and are not able to encode deformation information. Therefore, capsule based networks have been introduced as an alternative to convolutional neural networks. Capsules are a group of neurons (logistic units) representing the presence of an entity and the vector indicating the relationship between features by encoding instantiation parameters. Unlike convolutional neural networks, maximum pooling layers are not employed in a capsule network, but a dynamic routing mechanism is applied iteratively in order to decide the coupling of capsules between successive layers. In other words, training between capsule layers is provided with a routing-by-agreement method. However, capsule networks and their properties to provide high accuracy for image classification have not been sufficiently investigated. Therefore, this paper aims (i) to point out drawbacks of convolutional networks, (ii) to examine capsule networks, (iii) to present advantages, weaknesses and strengths of capsule networks proposed for image classification.

KEYWORDS Image Classification, Capsule Network, Dynamic Routing, Deep Network, Convolutional Neural Networks

1. INTRODUCTION

In recent years, the importance of deep neural networks has increased due to their great success in many fields. Particularly, Convolutional Neural Networks (CNNs) have been widely implemented for classification of images because of their learning ability by using convolution filters and non-linearity units (Seeland and Mader, 2021; Guoqing et al., 2021; Abbas et al., 2021). However, their architectures lead to two important issues. One of them is about the robustness of these architectures for affine transformation (e.g., shifting in pose). This problem is usually alleviated by various image augmentations. However, the testing dataset can present some unpredictable shifts. Therefore, CNNs need a huge amount of training dataset. The other problem is about the spatial relationships between features. CNNs have a tendency to memorize data instead of understanding it and they do not have the capability to learn the relationships between required features (Hinton et al., 2018). Several pooling algorithms can provide a little translation invariance. However, pooling methods do not store information about the location of features since they maintain only the presence information and ignore the pose information (Szegedy et al., 2013). To be able to overcome these two drawbacks in CNNs, Capsule Networks (CapsNets) (Sabour et al., 2017), new architectures based on the capsule concept (Hinton et al. 2011; Kosiorek et al.,2019; Wang and Liu, 2018), have been proposed. Unlike CNNs, CapsNets can store information at a vector level not as scalar values. These capsule vectors (groups of neurons) represent richer information in the architecture. Also, to classify objects in an image, CapsNets use routing-by-agreement method. The routing process enables each capsule to maintain information, which is obtained from the parent (previous) capsules, and provides classification agreement by comparing the information. Therefore, CapsNets can store the orientation and location of components in an image. For example, a CapsNet can learn to decide whether a flower does exist in the image, and also whether it is rotated or located to the right/left. This property is called as equivariance. The authors in

(Jimenez-Sanchez et al., 2018) reported that this property reduces the requirement of huge data in the training stage. Therefore, CapsNets are promising for image classification. CapsNets are new architectures and explorations in the literature about capabilities of CapsNets are focused on designing of capsule layers (Hinton et al., 2018; Rajasegaran et al., 2019; Deliege et al, 2018) and containment of extra convolutional layers to feed primary capsules for feature extraction (Nair et al., 2018; Phaye et al., 2018). However, the performance of CapsNets in classification of images have not been sufficiently investigated. Therefore, this paper aims (i) to point out drawbacks of CNNs, (ii) to examine CapsNets, (iii) to present advantages, strengths and weaknesses of the CapsNets proposed for image classification. This paper has been organized as follows: Fundamentals of a CapsNet architecture and comparison with convolutional networks are explained in Section 2. CapsNet based image classification approaches are given in Section 3. Finally, discussion and conclusion are presented in Section 4.

2. FUNDEMANTALS OF A CAPSNET ARCHITECTURE AND ITS DIFFERENTIATIONS FROM A CNN

In the original CapsNet architecture (Sabour et al., 2017), capsule vectors have been used in the convolutional network. Also, instead of conventional down-sampling algorithms (e.g., maximum pooling), a dynamic routing mechanism has been implemented to link units within a capsule. This original CapsNet structure has been extended and its various models have been designed to achieve image classifications with high performance (Section 3). Like CNNs, a CapsNet constructs a hierarchical representation of an image by passing it in layers. On the other hand, unlike deeper CNNs including many layers, the CapsNet in the original form includes merely 2 layers called as primary and secondary capsule layer. The primary layer captures low-level features. The secondary layer has the ability to predict the existence of an object and its pose information in the image (Figure 1). The main properties of a CapsNet and differentiations from a CNN architecture can be summarized as follows: (i) Convolution is solely applied in the primary capsule layer as the first operation. (ii) A series of feature channels are grouped to construct tensors in a CapsNet rather than performing a non-linear operation with scalar values obtained from convolutional filters. A squashing process is applied to increase non-linearity of the capsules. By the squashing process, a longer capsule is shrunk to a length less than 1 and a short capsule is shrunk to a length close to zero. In other words, squashing algorithm uses j th vector sj and bounds its limit to [0.1] interval for probability modelling and preservation of vectoral-orientations. This process produces a vector vj indicating the probability value about the presence of an object. The direction of this vector (that is also the output value of the capsule j) presents information about the pose of the object. (iii) Routing by agreement is applied to optimize the weight values (wij) in a CapsNet rather than a back-propagation as it is usual in a CNN model. In the routing process, a capsule in a low-level transmits its input value into a capsule in the upper level. Therefore, these weights provide connections between the ith primary capsule (low level information) and jth secondary capsule (high level information). In other words, the weights provide affine transformation to learn part-whole relations. (iv) Similar to a CNN model used for classification, the last layer of a CapsNet is a softmax layer, which is usually implemented by cross-entropy loss function, which can be computed for kth class is as (Sabour et al., 2017); (1)

In (2), the term (0.5) is a weight parameter which is used to guarante the final convergence. The term Tk refers to labels and gets 1 when is 0.1, is 0.9 and an object, whose expected probability is greather than 0.9 (i.e., ), does exist in kth class. The distance between positive samples are forced to be short by the marginal loss because 0.5 is not assigned to the threshold. Therefore a robust classifier is generated.

54 International Conferences Computer Graphics, Visualization, Computer Vision and Image Processing 2021; Connected Smart Cities 2021; and Big Data Analytics, Data Mining and Computational Intelligence 2021

After the original CapsNet, discussed matrix capsules have been discussed and expectation maximization based routing have been applied (Hinton et al., 2018). Figure 1 shows connections in a standard convolutional network (Figure 1.a) and a CapsNet (Figure 1.b).

(b)

(a) Figure 1. A CapsNet structure (a) and a covolutional network (b)

3. CAPSNET BASED IMAGE CLASSIFICATION TECHNIQUES

Various modifications of the original CapsNet architecture have been proposed to improve accuracy and to enhance the computational efficiency and representation capacity for image classification. For instance, in (Xi et al., 2017), the capacity of the network has been increased (by increasing both capsules’ size and numbers of layers) according to the changes in the activation function. To generate semantic and structural information, a multi-scale feature extraction has been used in (Xiang et al., 2018). Then features’ hierarchy has been encoded into primary capsule and a dropout has been applied to improve the robustness of the architecture. Another multi-scale CapsNet including five layers (input layer, convolution layer, primary and

secondary capsule layer, output layer) has been proposed by the authors in (Wang et al., 2019) to classify hyper-spectral images. In (Ren 2019), different types of capsules have been grouped to reduce effects of the capsules that are useless or providing less contribution to the classification. The authors in (Mobiny and VanNguyen, 2018), modified the CapsNet architecture to use a consistent dynamic routing method to provide faster convergence. In (Neill 2018), pairwise learning has been integrated into the original CapsNet to provide better learning of relationships with a feature normalized contrastive loss. In another work (Ding et al., 2019), capsules are partitioned into several groups and corresponding high-level capsules are obtained by group reconstruction routing and then maximum pooling is used to avoid overfitting. In (Mandal et al., 2021) a hierarchical learning and two-phase dynamic routing approach has been used in multi-column CapsNet to provide macro and micro-level equivariance. In (Long et al., 2021) feature extraction has been provided by three convolutional layers instead of one in the modified CapsNet model. The authors in (Iesmantas and Alzbutas 2018) used five convolutional layers before the primary capsule layer. They also used margin loss and a multi-dimensional squashing function. In (Afshar et al., 2018) early-stopping algorithm has been used to increase generalization capability of the architecture for tumor types classification from magnetic resonance images. The CapsNet models proposed recently to solve several image classification problems are presented in Table 1 with their properties, data sets and conclusions. Table 1. Data sets, CapsNet models proposed for image classification and their conclusions

Reference Data set Model Property Conclusion FashionMNIST, A hierarchical learning and two-phase dynamic SVHN, routing approach have been used in multi-column The performance of the model is (Mandal et handwritten CapsNet to provide macro and micro-level higher than those performances al., 2021) digit datasets equivariance obtained by other state-of-the-art multi-column networks

Feature extraction has been provided by three 8 categories of The model has a potential to (Long et al., convolutional layers to obtain more specified blood cells assist physicians in classification 2021) feature map in order to feed the primary capsule images of human blood cells layer Training of grouped capsules Public images Different types of capsules have been grouped to makes the model more robust and (Ren 2019) (e.g., MNIST, reduce effects of the capsules with less improves its generalization CIFAR-10) contribution (or useless) in classification. ability A multi-scale feature extraction has been used to The proposed model has generate semantic and structural information. competitive performance for (Xiang et FashionMNIST Then features’ hierarchy has been encoded into classification of images from al., 2018) and CIFAR-10 primary capsule and a dropout has been applied complex data sets with fewer to improve the robustness of the architecture number of parameters The results indicate that The capacity of the network has been increased MNIST and integrating a convolution layer (Xi et al., (by increasing both capsules’ size and numbers of CIFAR-10 into the original CapsNet 2017) layers) according to the changes in the function image data set architecture increases validation providing activation accuracy by 0.41% Capsules are partitioned into several groups and Computational complexity is (Ding et al., CIFAR-10/100 corresponding high-level capsules are obtained reduced and recognition ability is 2019) and SVHN by group reconstruction routing and then increased compared to the the maximum pooling is used to avoid overfitting original model Hyperspectral images from The model can manage spatial The network has been designed with five layers (Wang et Indian pine and and spectral features and extract including a multi- and single-scale convolutional al., 2019) University of more relevant and hyper-spectral layer, a primary and secondary capsule layer Pavia datasets information from images

56 International Conferences Computer Graphics, Visualization, Computer Vision and Image Processing 2021; Connected Smart Cities 2021; and Big Data Analytics, Data Mining and Computational Intelligence 2021

Hyperspectral images from An extra convolutional layer (before the primary The model can provide isolation Kennedy Space capsule layers) has been integrated into the of invalid information and (Lei et al., Center, Salinas architecture to extract features from high-level capture the long-distance 2019) and Pavia layers and to increase the speed of the dynamic dependencies of hyper-spectral University routing-by-agreement process images using. datasets AT&T face recognition and Pairwise learning has been integrated into the The learning ability of the verification original CapsNet to provide better learning of network has been improved and (Neill 2018) dataset, labeled relationships with a feature normalized faster convergence has been faces in the wild contrastive loss observed. dataset (Mobiny Chest images A consistent routing, which enforces primary The model is powerful in and obtained by capsules matching with the same pixels to get the reconstructing the input from the VanNguyen computed same coefficients, has been integrated into the final capsules and increases the , 2018) tomography original CapsNet. network’s efficiency. Magnetic (Afshar et Early-stopping algorithm has been used to resonance The model can outperform CNNs al., 2018) increase generalization capability of the images showing in tumor classification problem architecture brain tumors Breast cancer (Iesmantas The architecture with seven layers has been The model can achieve histological and constructed using five convolutional layers before classification of biopsy images to images (stained Alzbutas, the primary capsule layer, margin loss and multi- distinguish four types of breast with eosin and 2018) dimensional squashing function tissue with high accuracy hematoxylin) Hyperspectral Although promising results can The architecture has been designed with images from be obtained from the proposed adversarial networks and used the information (Wang et Kennedy Space model, it leads to increase the obtained by dual-channel spectral and spatial al., 2021) Center, Salinas computational complexity and fusion to encode more relationships of the and Pavia needs optimization for this features in an image University purpose Two chest X- The original routing algorithm has been modified The model presents satisfying (Afshar et ray datasets and to extract more helpful features and also the performance and needs less al., 2018) external datasets original margin loss has been modified to set number of parameters for training of X-ray images more penalty values for misclassified cases than its counterparts. High accuracy has been obtained. Optical Primary capsules have been fed with the outputs However, the model can classify (Tsuji et al. coherence of five convolutional layers to be able to extract only four types of cases. It should 2020) tomography more features and leaky rectified linear unit has be trained and tested with other images been used types of images A multi-lane CapsNet by using strict-squashing The proposed model provides MNIST, (Chang and function and optimizing dropout implementation better results when they are affNIST and Liu, 2020) to be able to classify images with complex compared to the results obtained CIFAR-10 background from the original CapsNet The secondary capsules in the original CapsNet The model can efficiently have been modified as cancer capsules and (Panigrahi Oral biopsy classify histopathological image parameters have been adapted according to the et al., 2020) images data sets as benign or malignant characteristics of the images to obtain high to help detection of oral cancer accuracy The hierarchical CapsNet model has been The model presents higher (Jia and CIFAR-10, constructed using residual convolutional layers, accuracy than its seven Huang, F-MNIST diverse enhanced primary capsules and adapting ensembles, but its computational 2020) the sigmoid function in the routing algorithm cost should be reduced

A three-dimensional residual-CapsNet (i.e., Res- The proposed approach has the Breast CapsNet) model has been implemented to potential to reduce mis-diagnosis (Xiang et ultrasound diagnose tumors using tumor masks obtained and achieve better accuracy al., 2021) images with U-Net from the images that have been compared with the other CNN cropped and resized. models. Optical Images have been classified using the CapsNet The proposed method can be (Koresh et coherence architecture after removing speckle noises with a applied to provide efficient al., 2021) tomography hybrid noise reduction filter. corneal thickness measurements. images

Dermoscopy After re-sizing of the images to 28x28, the According to the results of images original CapsNet has been used with the Softmax experimental works, the proposed (Cruz et al., (HAM10000 function and the number of epochs, batch size approach is more sensitive than 2020) and BioGPS learning rate, which have been chosen the recent classifiers and presents image datasets) experimentally as 50, 10 and 0.001, respectively. high classification performance.

The proposed conditional Hyperspectral A generative adversarial network architecture has generative adversarial training images from been implemented with three-dimensional algorithm has the potential to (Xue 2020) Indian pine and capsules, batch normalization and the Tanh increase the generalization ability University of function. The routing mechanism does merely for classification of hyperspectral Pavia datasets exist between capsule layers. images. Hyperspectral To integrate spatial and spectral features, training images from The proposed method presents (Paoletti et of the CapsNet architecture has been provided Indian pine and robust results even if the network al., 2020) with active learning by using a small set of Kennedy Space is trained with small data sets. labeled images. Center The proposed CapsNet model containing a The proposed approach produces Indirect immune (Maurya et decoder and encoder section provides results with better performance fluorescence al., 2021) classification with the Sigmoid function in the compared with the results of images final layer CNN based architectures.

Retinal fundus The original CapsNet has been implemented with The proposed network has the (Santos et images in the appropriate parameters that have been potential to classify healthy and al., 2020) healthy and selected experimentally for the images obtained glaucoma cases from images. glaucomatous by histogram equalization.

4. DISCUSSION AND CONCLUSION

CNNs have been considered as efficient feature extractors. However, pooling layers in them lead to loss of spatial relations of pixels. Also, they are not always robust to affine transformations. Therefore, CapsNet have been proposed recently as a novel architecture to overcome those disadvantages of CNNs by encoding not only the presence of features but also their spatial relationships. A CapsNet can learn both desired weights to extract features and pose parameters from the image. Multi-dimensional vectors (with entries indicating spatial changes like skewness, shifting, rotation and thickness) are used for pose modeling. For instance, in a medical case, an image can show different patterns leading to a diagnosis of a disease. To diagnose the disease, while a CNN architecture detects the existence of the features, a CapsNet architecture performs the same detection and also finds information about relationships between the features. The dynamic routing algorithm in the CapsNet provides efficiency in mapping of low- and high-level capsules. Since a capsule contains collections of neurons and the routing process includes all capsules, the CapsNet has an ability for stronger representation when it is compared to conventional networks, which ignore some neurons in the pooling layer. Therefore, CapsNets achieve successful results using less images and provide more robustness to an affine transformation. However, redundant features can be collected with the dynamic routing. Also, if low-level capsules’ information is too much, then the corresponding high-level

58 International Conferences Computer Graphics, Visualization, Computer Vision and Image Processing 2021; Connected Smart Cities 2021; and Big Data Analytics, Data Mining and Computational Intelligence 2021

capsules may lead to interference due to noise or other ir-relevant or redundant information. In addition, computational complexity is an important issue to deal with a large data network. Therefore, a CapsNet architecture should be designed carefully according to the problem handled to have a reasonable generalization capability and further researches are still needed to improve CapsNet based classifiers.

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