1. A method for reducing dimensionality of hyperspectral image data having a number of spatial pixels, each associated with a number of spectral dimensions, the method comprising: receiving sets of coefficients associated with each pixel of the hyperspectral image data, a set of basis vectors utilized to generate the sets of coefficients, and a maximum error value; calculating, using a processor, a first set of errors for each pixel associated with the set of basis vectors, and one or more additional sets of errors for each pixel associated with one or more subsets of the set of basis vectors; calculating, using the processor, a percent of the number of spatial pixels having an error greater than the maximum error value, for each of the first set of errors and the one or more additional sets of errors; calculating, using the processor, a plurality of reduction factors associated with each of the first set of errors and the one or more additional sets of errors, the plurality of reduction factors being calculated based on both the percent of the number of spatial pixels having the error greater than the maximum error value and the number of spectral dimensions associated with the hyperspectral image data; and selecting, using the processor, a maximum reduction factor from the plurality of reduction factors, and an optimum size of the set of basis vectors or the subset of basis vectors associated therewith.