Unsupervised feature selection (UFS) is a standard approach to reduce the dimensionality of hyperspectral images (HSIs). The main idea in UFS is to define a similarity metric, and select the features minimizing the metric to reduce the data redundancy. In this paper, we proposed a novel criterion for unsupervised dimensionality reduction based on the representation of spectral reflectance to capture dominant reflectance variations. Since capturing all the spectral information from an entire hyperspectral dataset is a time-consuming process, we proposed a heuristic algorithm named Greedy Search for Spectral Representation (GSSR). This algorithm divides the spectrum into spectral regions with less spectral variations and merges them. GSSR, similar to feature selection techniques, preserves the original data from being distorted or compromised by a transformation. We compared the GSSR algorithm with well-known existing algorithms in different experiments using various datasets. Comparison with the best approximation to represent single spectra as well as entire hyperspectral scene revealed that spectral representation is almost the same. The difference between the best spectral representation and the ones provided by GSSR is less than 0.01%; while on average, GSSR is about 660 times faster to represent single spectra and 37 times faster for a complete hyperspectral scene. Five well-known unsupervised dimensionality reduction methods were also implemented and used for comparison analysis. Based on the image classification accuracy over two hyperspectral datasets, the spectral features identified by the proposed criterion improved the classification accuracy as well.