## 6 Discussions  
In this study, a new hybrid approach is proposed to the problem of unsupervised anomaly detection in multivariate spatio-temporal data. In unsupervised scenarios, the type of anomalies and the ratio of anomalous events within the given dataset are generally not known. Training data might be contaminated by anomalous data which is the case in most of the real word scenarios. For the proposed unsupervised setting, no labeled dataset is required to train the framework for the anomaly detection problem. The proposed hybrid deep learning framework is designed to be trained in a truly unsupervised fashion with the full absence of labels, for either normal or abnormal data. It is composed of a multi-channel convolutional neural network (CNN) and Long Short-Term Memory (LSTM) network. The architecture of the framework is based on an autoencoder scheme: the multi-channel CNN network is deployed on the encoder side for learning spatial structures of each spatio-temporal multivariate data frame, and LSTM network is deployed on the decoder side for learning temporal patterns from the encoded spatial structures. The architecture is robust enough to learn the important structure of the data even if the training dataset contains noise and anomalous data \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model Variants** & **T = 12, s = 1** & **T = 12, s = 2** & **T = 12, s = 3** & **T = 12, s = 4** & **T = 12, s = 6** & **T = 12, s = 12** \\ \hline CNN(1)-LSTM(1) & 0.815 & 0.833 & 0.864 & 0.857 & 0.863 & 0.862 \\ \hline CNN(1)-LSTM(2) & 0.864 & 0.841 & 0.834 & 0.866 & 0.853 & 0.841 \\ \hline CNN(1)-LSTM(3) & 0.841 & 0.847 & 0.851 & 0.857 & 0.797 & 0.826 \\ \hline CNN(2)-LSTM(1) & 0.815 & 0.828 & 0.818 & 0.817 & 0.849 & 0.871 \\ \hline CNN(2)-LSTM(2) & 0.862 & 0.811 & 0.829 & 0.842 & 0.817 & 0.842 \\ \hline CNN(2)-LSTM(3) & 0.851 & 0.860 & 0.832 & 0.803 & 0.841 & 0.839 \\ \hline CNN(3)-LSTM(1) & 0.806 & 0.799 & 0.805 & 0.807 & 0.816 & 0.869 \\ \hline CNN(3)-LSTM(2) & 0.830 & 0.819 & 0.841 & 0.821 & 0.839 & 0.846 \\ \hline CNN(3)-LSTM(3) & 0.841 & 0.848 & 0.848 & 0.818 & 0.816 & 0.822 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _OAHII_1 measures of the framework variants with window size \(T=12\) and different sliding step sizes \(s=1\), \(2\), \(3\), \(4\), \(6\), \(12\). Figure 9: Boxplot of OAHIII measures of framework variants. Blue line represents mean scores. points. To the best of our knowledge, this is the first deep learning-based approach for unsupervised anomaly detection problem in non-image multivariate spatio-temporal dataset. A set of experiments was carried out using the buoy dataset from National Data Buoy Center which is contaminated with noise and anomalies such as tropical storms and hurricanes. We demonstrated that the proposed encoder-decoder-based architecture achieves better results against state-of-the-art spatio-temporal anomaly detection methods providing at least 10% improvement in quantitative scores. The proposed hybrid model stands out from other traditional and deep learning-based models as it is capable of handling noise and missing values better. Quantitative evaluation tests of framework variants show that the core architecture of the network and the way we use the spatial and temporal context prove to be a powerful and robust approach in the spatio-temporal anomaly detection problem. The major contributions of this study can be summarized as follows:  
* In the proposed hybrid model, we handle spatial and temporal contexts by different deep learning components as these contextual variables refer to different types of dependencies. * Unlike proximity-based methods, the proposed model can be easily implemented on datasets with mixed-type behavioral attributes and it scales well to multivariate datasets with high number of features. * The crafting of multivariate spatio-temporal dataset for unsupervised anomaly detection is also novel.