# Two Novel Multidimensional Data Analysis Approaches Using InSAR Products for Landslide Prone Areas
## 3 Methodology
### Implementation of the Proposed Approaches MIRA and InCROSS
#### 3.4.2 InCROSS (Crosta Application in InSAR)  
The other novel approach for analyzing InSAR is InCROSS which is based on principal component of input InSAR data sets. In the statistical evaluation of surface deformation velocity images obtained through the LiCSBAS method, principal component analysis (PCA), and the Crosta technique were employed to reveal the structural characteristics of high-dimensional data. A PCA transforms highly correlated multiband data into a set of uncorrelated new components (principal components) based on variance, thereby reducing the dimensionality of the data and enhancing dominant structural patterns [52]. This method emphasizes the systematic variation within the deformation data while suppressing the noise components caused by irradiance effects and observation geometry. The advantage offered by PCA is particularly important in remote sensing-based surface deformation analyses, as it simplifies data statistically and enhances its interpretability. The  
Figure 7: Result of MIRA approach using SVM classification with pyramid layer 0 (**a**) and with pyramid layer 1 (**b**). Crosta technique, developed based on PCA, facilitates the discrimination of anomalies by emphasizing the components that exhibit specific spectral or statistical properties among the principal components [53]. The combined application of both methods, also referred to in the literature as feature-oriented principal component selection (FPCS) or selective principal component analysis, provides effective results in identifying active deformation zones, filtering out non-systematic variations, and classifying different deformation patterns within the study area. The landslide polygons in the existing landslide inventory (from MTA and AFAD) and the four InSAR products (i.e., the ascending and descending LOS velocities, and their decomposition into vertical (U-D) and east-west (E-W) components) were evaluated simultaneously. When the values of the pixels in landslide areas are analyzed for each InSAR product, a trend for the pixel values of InSAR products in landslide areas will be determined. Then, within the four principal components obtained by the PCA analysis using these four InSAR products as input, the principal component in which this trend is captured will correspond to the deformation areas desired (Figure 8). For this reason, the principal component that contains all four InSAR products will cover the desired feature. In our study, it was observed that the first principal component (PC1) indicated a trend opposite to the trend observed in the landslide areas. Therefore, the opposite of this component was determined as our desired solution. Table 2 shows the principal component and eigenvalue of four InSAR product. The trend patterns corresponding to this classification (or its inverse (low (L), very high (VH), high (H), very low (VL)) were captured through principal component analysis (PCA), as presented in Table 2, and used to construct the dataset for this study. Blue and red color show negative and positive values, respectively, in Table 2. Dark colors indicate larger absolute values, while light color indicate smaller absolute values. The main logic of the InCROSS analysis is to use a directly related principal component to represent the desired trend for all combined InSAR products. Therefore, the highest values obtained in the single principal component indicate the highest amount of similarity of the desired trend.