Identifying Early Signs of Mental Health Crises Using Social and Economic Data

Quantum Logic Proofs

This exercise explores the linear independence of spectral bands by comparing DVI (Difference Vegetation Index) and NDVI (Normalized Difference Vegetation Index). First, Sentinel-2 raster data for NIR and Red bands is loaded and converted into matrices, which are then flattened into 1D arrays to enable matrix operations. The indices are computed with DVI and NDVI. Covariance matrices for {NIR, Red, DVI} and {NIR, Red, NDVI} are analyzed, where DVI's determinant approaches zero, confirming strong linear dependence, while NDVI’s determinant is notably larger, indicating some independent variability. Eigenvalues and eigenvectors reveal DVI has a near-zero eigenvalue, proving redundancy, whereas NDVI retains non-zero eigenvalues, signifying added dimensionality. This distinction is crucial for regression models sensitive to multicollinearity, as linearly dependent features like DVI can create instability, while NDVI offers a more informative alternative. By eliminating redundant spectral bands and focusing on indices with independent variations, this exercise enhances feature selection for environmental modeling, leading to better analytical insights and predictive accuracy.