# Joint SAR Image Time Series and PSInSAR Data Analytics: An LDA Based Approach
## 4 Experimental Setup
### Overview of SITS Temporal Analysis
These kinds of evolutions are multiple and hard to perceive for a human eye, but easy to separate for dedicated SITS analytics algorithms. There is no prior information regarding the correct number of potential evolutions distinguishable in a SITS. We count on the perplexity to emphasize the optimum number of categories of evolution to be extracted. Nevertheless, a correlation between the classes observed in the scene and categories of evolution referring to the land cover modifications is not relevant. Appropriate groupings inside the scene were made based on the similarities that individual points share in terms of temporal signature. The process results in a scene classification map where the labels are assigned beyond human perception. We propose though the measure of perplexity to estimate how well the LDA model can predict the scene content based on its temporal behavior [17]:  
\[perplexity(D_{test})=\exp\left(-\sum_{d=1}^{M}\log p(W_{d})/\sum_{d=1}^{M}N_{d }\right) \tag{10}\]  
where \(D_{test}\) is a test set of \(M\) documents \(D=\{W_{1},\ W_{2},\ldots,\ W_{M}\}\) containing \(N=\{N_{1},\ N_{2},\ldots,\ N_{M}\}\) words. The inflexion point of the perplexity curve will determine the optimum number of distinct temporal evolutions. At last, the classification result is compared against the map pf detected PSs. If the number of LDA classes is low (around 5), it is likely that stable structures detected across the scene will belong to the same evolution class. Therefore, a single class will be expected to contain the vast majority of detected stable targets. If the number of classes delimited by the LDA classification is considerably higher, the set of detected stable targets will be distributed into multiple subclasses, thus allowing a supplementary classification of the PS into multiple evolution classes. Stability propriety of the detected PS is a general concept; this additional inclusion in evolution classes has the potential to be exploited in order to obtain further information related to their characteristics. It can be noticed that, in order to study the temporal evolution of the scene, the LDA method requires solely on the amplitude of the dataset's images. As previously mentioned, PS detection  
Figure 9: Categories of objects visually distinguished at the Constanta scene level: (**A**) water, (**B**) roads, (**C**) built-up area, (**D**) forest, and (**E**) agricultural fields. is based on the study of amplitude's statistics and estimation of spectral coherence, therefore both amplitude and phase information being required in the latter case. Like most coherent systems, SAR images can be affected by speckle noise, which is caused by the interference of electromagnetic waves reflected by multiple scatterers within the same resolution cell [26]. The speckle effects can be reduced by noncoherent averaging, known as multi-looking, but this implies loss of spatial resolution. The comparative study of LDA analysis and PS detection was also implemented on multi-looked (ML) images, in case of both datasets. Spatial filtering is solely implemented based on image amplitude, so phase information is lost after application of ML. This aspect does not influence the LDA classification, but in this case PS detection, will be based exclusively on the amplitude's statistics study, as phase information is lost after the ML process.