# Joint SAR Image Time Series and PSInSAR Data Analytics: An LDA Based Approach
## 5 Results and Discussion
### 3 rd Experiment--An Analytical Approach to Highlight the PS's Temporal Character  
For this analysis, we vary only the parameter representing the number of classes (from 3 to 61) and preserve the same values for all the rest when running the LDA algorithm. A low perplexity indicates that the probability distribution is good for the corresponding number of classes. We computed the perplexity curve for both SL and ML approaches. Figure 14 shows the perplexity evolution for the case of ERS dataset. The inflection point gives us the optimum number of classes for which the LDA model can best predict the temporal behavior of the scene content with minimum loss. For the SL approach, the perplexity recommends 27 classes, while for the ML approach, 26 classes. However, for the sake of the comparison, we choose to work with \(z=27\) classes. On the other hand, Figure 15 presents how the number of classes influences  
Figure 12: Multi-look ERS image amplitude, Buzau (**A**); Scene classification map presenting categories of evolution (**B**); spatial distribution of detected Persistent Scatterers (**C**). Figure 13: Multi-look Sentinel-1 image amplitude, Constanta (**A**); Scene classification map presenting categories of evolution (**B**); spatial distribution of detected Persistent Scatterers (**C**). the perplexity for the Sentinel-1 SITS analytics, in both SL and ML cases. The results of the curves recommend an optimum number of 34 classes for the LDA analysis for both SL and ML approaches. We expect that the urban area, as a land use class, to suffer various transformations. We propose to transfer the categories of evolution from the SITS classification results to the PS points. We use the PS map as a mask and we overlap it on the classification map. The comparison will show to what extent the PS can be grouped according to their temporal behavior. Figure 16 illustrates to which categories of evolution the PS belongs and what percentage of their number is included in each class. The upper part of Figure 16 presents the PSs distribution for the Buzau area. For the SL approach (Figure 16A), the most frequent category off evolution includes approximately 35% of the PS, while for the ML approach (Figure 16B) almost 62% of the PS share the same temporal behavior. The PS distribution corresponding to the Constanta area is illustrated in the bottom side of Figure 16 The SL approach highlights that the detected PS are distributed over almost 16 categories of evolution. The most frequent category of evolution comprises 30.6% of the total number of PSs (Figure 16C). In the case of the ML approach, the PSs are almost completely concentrated in two categories of evolution, with 44.5% and 33.9% (Figure 16D). The PSs are better located within one or two categories of evolution for the ML approach. The speckle noise in the SL data upholds the separation of PS in several categories of evolution. These analytics show that the increased spatial resolution of SL data over the ML data generates a higher information content, supporting the target separation in the SL data, including the corresponding PS. Figure 14: Perplexity curves for ERS dataset. The inflection point—27 (for Single-Look) and 26 (for Multi-Look). Figure 15: Perplexity curves for Sentinel-1 dataset. The inflection point is 34 for both Single-Look and Multi-Look. The highest percentages of PS belonging to the same evolution class, from all the conducted experiments, are synthetized in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Reduced Number of Classes (3–8)**} & **Perplexity Based Algorithm (3–61 Classes)** \\ \hline ERS & SL & 99.68\% & 35\% \\ ERS & ML & 94.45\% & 62\% \\ Sentinel-1 & SL & 93.3\% & 30.6\% \\ Sentinel-1 & ML & 96.21\% & 44.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Percentage of identified Persistent Scatterers classified in the same category of evolution. Figure 16: Persistent Scatterer classification based on the LDA categories of evolution.