# Joint SAR Image Time Series and PSInSAR Data Analytics: An LDA Based Approach
## 6 Conclusions  
The paper presents a compound temporal analysis for SAR imagery, considering the persistent characteristics as well as the evolving Earth land cover behavior. The authors address the issue of irregular time sampling SITS and adapt a well-known generative model to deal with the particularities of SAR image content. Once the analogies for word, document, and corpus required by the LDA model were defined, the main advantage of the study presented here for SAR SITS is the possibility of eliminating the sparsity effect, which is characteristic to optical temporal series. Another advantage of the SAR temporal series exploited in this work is the ability to conduct the detection of points with stable temporal characteristics--persistent scatterers. The results of PS detection have been combined with the outputs of LDA classification in order to characterize the temporal behavior of the evolution classes. The evolving character extracted could be further used to determine the temporal behavior of persistent scatterers, included in built up areas. The analytical approach of this manuscript highlights the evolutionary character of persistent structures in SAR data based on image time series analysis. For a complete analysis, two implementations for LDA classification have been conducted, differing in the number of classes and types of transformations envisaged. In the first implementation, the number of evolution categories was determined based on the visual examination of the scene. The second implementation determined the number of classes by perplexity curve analysis, thus exceeding human perception. In the case of visual analysis, a class of stable structures, belonging mainly to built-up areas, was defined. The stable character of this class was confirmed by the PS detection results--over 90% of PS candidates are contained by this evolution class, in case of both single-look and multi-look analysis conducted on two test areas (Table 4). Therefore, this analysis highlights the fact that, although LDA classification and PS detection methods are based on different principles, common features exist between their results. The defining of evolution categories based on perplexity analysis leads to a significant increase of the classes number, compared to the visual based classification (from five to around 30 evolution categories in case of all analyzed scenarios). As expected, this increase leads to a supplementary classification of the detected PS into multiple evolution categories, providing a reduction in the percentages of PSs belonging to the same class, as synthesized in Table 5. Two approaches can be defined to exploit this result. The set of PS candidates can be used to derive further information related to the temporal character of the LDA classes: evolution categories which contain high percentages of stable points can be characterized by high temporal correlation. Alternatively, this analysis can be used to derive a supplementary classification of the evolutionary character of the detected PS. The statistical analysis of the amplitude's mean temporal correlation coefficient leads to a supplementary validation of the conducted analysis. It confirms the stable character of the detected PS candidates (in comparison with other pixels of the test scenes). As expected, when visual-based LDA classification is conducted, the class which contains the vast majority of the stable targets presents the highest temporal correlation. Furthermore, this analysis provides supplementary information for understanding the evolutional categories: the mean temporal correlation index of each class can be exploited alongside the visual interpretation for identification of its physical structure. This process is facilitated by the diversity of the index's mean values across the evolution classes, which vary from 0.19 in water covered areas to 0.42 in the stable points class (built-up areas).