## 1 Introduction
### Literature Review and Research Gaps
The CapsNet has successfully shown state-of-the-art performance in image classification tasks as demonstrated in Ref. [26] for brain tumour classification using MRI images and [27] for Hyperspectral Image Classification, and moreover variants of the network have been proposed to utilise gradient descent, as opposed to the dynamic routing algorithm [15]. Combining CapsNet models with LSTM models was also found to be effective for use cases such as transportation network forecasting [28]. However, not much work has been done utilising the CapsNet for use on time series data, and a minimal number of approaches are applied on time series data in its raw format [29]; most approaches use an image representation of the data as the CapsNet has been proven to improve performance in this context. For example, one proposed approach [30] aimed to utilise capsule networks to address an issue with the detection of short circuit faults in a power network transmission line, using a Gramian Angular Field (GAF) representation [31]. An increasing number of modern approaches to anomaly detection have started to tend towards using Autoencoders, to be able to take advantage of the flexibility of a NN whilst maintaining the simplicity of application and simultaneously minimising the need for large volumes of labelled data. One such approach [32] proposes a recurrent autoencoder with multi-resolution ensemble decoding, to overcome overfitting during training, as well as increase patterns captured using different resolutions. Tested on EEG data as well as other time series data from different domains such as power consumption, website traffic and hand gesture data, the model is able to outperform the compared approaches consistently, and the proposed multi-resolution decoding proves to be effective empirically. However, the performance of the model can be improved, since on one EEG dataset the best \(F_{1}\) score is 0.2, and there is no explanation as to how the false positive and false negative rates have affected the results, which could indicate model sensitivity issues. Another approach [33] proposes a variational quasi-recurrent autoencoder, and a bi-directional variant of the latter which aims to improve computational efficiency through convolutions and pooling, and improve the generalisation ability through enhanced latent space learning. The bi-directional model outperforms all other tested methods on five datasets from different domains. However, the authors note that they did not consider the detection of non-statistically separate anomalies. One proposed approach [34] utilises a hybrid LSTM and Convolutional Autoencoder to detect anomalies in advance from a high voltage converter modulator, achieving a precision score of up to 91% and a recall up to 88%. However, with the well-publicised issues with Convolutional NNs, Capsules could significantly improve this score. Concluding the findings from the literature review, it is clear that soft sensing methods of anomaly detection are more efficient and effective methods than hardware redundancy. However, with traditional methods it is difficult to accurately model systems without in depth knowledge of their dynamics and parameters, creating a barrier to flexible and accurate system modelling, which is the basis of many anomaly detection systems. However, NNs provide a solution for this issue, providing a method of easily modelling system behaviour based on previously encountered data. Using NNs such as LSTM NNs for time series data learning, researchers have been able to accurately account for long term dependency in temporal data and create robust anomaly detection systems. However, this creates another issue with requiring access to large amounts of labelled data, which is expensive and time consuming to produce. To avoid labelling data, some literatures have proposed unsupervised learning techniques such as the autoencoder, which is able to learn data features by transforming it into a latent space representation.