# Entity Embeddings in Remote Sensing: Application to Deformation Monitoring for Infrastructure
## 1 Introduction
This motivated the focus of this study, which is on the detection of anomalous deformation measurements using a data-driven approach. Recently, there has been a significant interest in the application of machine learning, especially deep learning (DL) approaches, to InSAR monitoring. DL models have been tasked with identifying the presence of deformation over volcanoes [21], tunnels or gas/water extraction [22], airports [23; 24; 25]. and geological faults [26; 27]. Both sequential-data-based Recurrent (RNN) and image-based Convolutional Neural Net (CNN) approaches have been considered in the literature. The InSAR deformation through time was treated as purely sequential data within RNNs in [PERSON] et al. (2021) [25]. Those authors treated each InSAR deformation measurement separately and based their prediction of the trend and magnitude purely on the 2D temporal history. However, such approaches completely neglect the inherent spatial relationship between deformation measurements and require the generation of synthetic data. In image-based models, synthetic data were also used to train the CNNs in [22; 24]. In [PERSON] et al. (2020) [22], the synthetic data were used for classifying deformation patterns from point- or line-based geometries, representing underground gas/water extraction or tunnelling, respectively. In [PERSON] et al. (2020) [24], the synthetic data were used to learn the non-linear relationship between clean and noisy interferograms for improving deformation data quality. Moreover, various tweaks to traditional CNN approaches have explored combining the spatio-temporal components together. For example, a modified U-Net architecture was used to ingest a sequence of 12 temporal InSAR deformation maps to predict the following 12 time steps in [23]. Similarly, auto-encoders have been trained on synthetic data to extract deformation signals directly from a sequence of nine interferograms to predict the next nine in [27]. [PERSON] et al. (2020) [23] was able to predict both linear settlement and non-linear seasonal deformation from InSAR data over an airport. However, the InSAR data are not spatially continuous, and measurement gaps are common. The use of interpolation techniques on InSAR likely impacts the performance of CNN-type approaches, as they are known to struggle with data gaps [28]. In this paper, a novel methodology based on the use of Entity Embeddings within a Deep Learning framework (EE-DL) is proposed for detecting anomalous InSAR deformation. Embeddings are similar to the \"word vectors\" used in natural language processing, providing a rich numerical representation of categorical variables. A variety of EE-DL applications have recently emerged, from predicting the final destinations using embeddings of taxi rides [29] to projecting sales using embeddings from stores [30; 31] and the fusing of data from different modalities based on shared embeddings [32]. In this study, embeddings were created to represent the categorical variables of the InSAR metadata. The use of entity embeddings captures both the spatial and temporal components of the InSAR measurements, without requiring the generation of image data. This makes the model more flexible and overcomes typical DL challenges around the handling of the inherent spatial data gaps present in InSAR. Due to the time-dependent settlement processes (i.e., consolidation) inherent to tailings, a level of deformation needs to be presumed for TSFs. Therefore, the EE-DL model is tasked with identifying whether that deformation is as expected, i.e., \"normal\". The EE-DL model was benchmarked using the results of a common probabilistic forecasting approach, namely Gaussian Process Regression (GPR) and a simple baseline Random Forest (RF) model. These models were chosen due to their highly interpretable nature and the fact that they represent a spectrum of model complexity. RF is a widely adopted benchmark and is a highly flexible shallow machine learning algorithm.