Hyperspectral images collect hundreds of co-registered images of the earth surface with different wavelengths in visible and short-wave inferred region. With such high spectral resolution, many adjacent bands are highly correlated, i.e., they contain a lot redundant information. How to remove unnecessary information from this huge amount of data and preserve all the information is a challenging problem. Principal component analysis (PCA) is one of the widely used algorithms for this problem. It assumes the larger variance contains the most information, so it projects the data into the direction to maximize the variance. Most of the signals will be kept in the first several principal components, and the rest will be considered to be noise and neglected. To further reduce the redundancy, segment PCA is proposed, which first separate the whole spectral bands into blocks and then perform the original PCA in each block individually. Both these two approaches perform well for data compression, but for image classification in its feature space, they did not achieve comparable results. In this study, we adopt the greedy modular subspaces transformation (GMST) to find the optimal feature subspace for the segment PCA. It is expected to provide a comparable classification results with high compression performance.