# Two Novel Multidimensional Data Analysis Approaches Using InSAR Products for Landslide Prone Areas
## 3 Methodology
### Implementation of the Proposed Approaches MIRA and InCROSS
#### 3.4.1 MIRA (Multi-Dimensional InSAR Research and Analysis)  
The main logic of this approach is based on the visualization of multi-dimensional data and the delineation of anomalies on multi-dimensional distribution. In this study, the descending and ascending orbit surface deformation velocity maps obtained using the LiCSBAS method, along with their decomposition into east-west (E-W) and vertical (U-D) components, and resulting in a total of four datasets, were analyzed using the n-D Visualizer module available in the ENVI 5.0 software for multidimensional visual and numerical interpretation. The n-D Visualizer is commonly used in hyperspectral and multispectral remote sensing studies, especially for identifying mineral resources and lithological units. Its interactive visualization capability allows the distribution of high-dimensional data to be explored, making it possible to distinguish between spectrally similar or distinct regions [43; 44]. These clouds represent spectrally distinct pixel clusters within the multi-dimensional feature space created by the deformation velocity components. This approach demonstrates that different classes in n-dimensional space are grouped into clusters with different pixel values. The n-D Visualizer tool makes it easier to visualize classes that are separated from each other within the space having more than 3D axes. Clusters identified as outliers in this approach represent different classes. Although the extent to which classes cover an area seems a subjective decision, the regions in the 1/4 to 1/3 range at the outer ends of the general distribution axis (longest axis) of the point cloud with the greatest variation always indicate two separate clusters. The size of the point cloud determined  
Figure 5: Decomposition of the cumulative LOS velocity maps: (**a**) vertical (up–down) deformation component, and (**b**) east–west horizontal deformation component derived from the combination of ascending and descending orbit data. for each class changes the sample size in the training class, but does not significantly change the classification result. The reason for this is that the SVM algorithm used for classification in this study has the ability to perform successful classification independently of the sample size [45; 46]. During the analysis, 3769 points for red and 624 points for green were collected from the n-D Visualizer. The n-D visualization approach is analogous to endmember identification in hyperspectral imagery, where pixels belonging to different classes are assumed to cluster at the edges of the feature space. As illustrated in Figure 6a, each sample pixel can be described by its digital number (DN) values across multiple bands (e.g., B1, B2, B3), and these values determine the pixel's location in the three-dimensional feature space. In this study, a visual analysis revealed areas with different deformation characteristics, which appeared as red and green pixel clouds in the n-dimensional scatter plot (Figure 6b). During the n-D visualization process, there is not any threshold applied to avoid any missed values. The classification process was carried out using the ENVI-IDL-based ImageSVM tool, which allows for supervised classification based on support vector machines (SVM). The radial basis function (RBF) was selected as the kernel function due to its robust performance in nonlinear classification problems [47; 48; 49; 50]. The RBF kernel computes the similarity between input samples using the mathematical expression shown in Equation (1). \[\mathrm{K(x_{i},x_{j})=exp(-g\|x_{i}-x_{j}\|^{2}),g>0} \tag{1}\]  
In this formulation, the parameter g defines the width of the kernel and controls the influence of individual training samples. In this study, the gamma value (g) was set to 0.25. A higher g value can lead to overfitting, while a lower value may result in underfitting. The penalty parameter (C) was set to 100.0, which governs the trade-off between maximizing the margin and minimizing the classification error.