A large amount of remote sensing data can be easily acquired due to the increase in the advances in sensor’s technologies. The sensors can generate high-dimensional data in a lower time producing problems related to big data such as management and organization. Since the acquired data is characterized by a large dimension and lack of structure, the information analysis becomes harder. Therefore, an organization stage should structure the data reducing the dimension while maintaining the main properties to enable further analysis. The feature extraction and selection methods can achieve this task. Consequently, we aim to explore various pixel-wise feature extraction and selection algorithms to manage the organization stage of big data for hyperspectral images. Our work covers the comparison between feature vectors computed using the discrete Fourier transform, discrete cosine transform (DCT), and stationary wavelet transform. Moreover, spectral angle mapper, Jeffries–Matusita distance, spectral information divergence, and linear discriminant analysis (LDA) were implemented as feature selectors. Feature extraction and selection methods were combined and evaluated in terms of algorithm complexity, reduction efficiency, and classification accuracy with the aid of a support vector machine and a maximum likelihood classifier. The analysis shows that some linear transformations can perform better in natural landscapes and others in urban images. Furthermore, the study found that the combination of DCT and LDA, which achieves high classification rates with an efficient dimension reduction, can be suitable for the organization stage of a big data remote sensing application of hyperspectral images.