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Hyperspectral Imaging (HSI) combines microscopy and spectroscopy to assess the spatial distribution of spectroscopically active compounds in objects, and has diverse applications in food quality control, pharmaceutical processes, and waste sorting. However, due to the large size of HSI datasets, it can be challenging to analyze and store them within a reasonable digital infrastructure, especially in waste sorting where speed and data storage resources are limited. Additionally, as with most spectroscopic data, there is significant redundancy, making pixel and variable selection crucial for retaining chemical information. Recent high-tech developments in chemometrics enable automated and evidence-based data reduction, which can substantially enhance the speed and performance of Non-Negative Matrix Factorization (NMF), a widely used algorithm for chemical resolution of HSI data. By recovering the pure contribution maps and spectral profiles of distributed compounds, NMF can provide evidence-based sorting decisions for efficient waste management. To improve the quality and efficiency of data analysis on hyperspectral imaging (HSI) data, we apply a convex-hull method to select essential pixels and wavelengths and remove uninformative and redundant information. This process minimizes computational strain and effectively eliminates highly mixed pixels. By reducing data redundancy, data investigation and analysis become more straightforward, as demonstrated in both simulated and real HSI data for plastic sorting.