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Planetary atmospheres are inherently 3D objects that can have strong gradients in latitude, longitude, and altitude. Secondary eclipse mapping is a powerful way to map the 3D distribution of the atmosphere, but the data can have large correlations and errors in the presence of photon and instrument noise. We develop a technique to mitigate the large uncertainties of eclipse maps by identifying a small number of dominant spectra to make them more tractable for individual analysis via atmospheric retrieval. We use the eigencurves method to infer a multi-wavelength map of a planet from spectroscopic secondary eclipse light curves. We then apply a clustering algorithm to the planet map to identify several regions with similar emergent spectra. We combine the similar spectra together to construct an "eigenspectrum" for each distinct region on the planetary map. We demonstrate how this approach could be used to isolate hot from cold regions and/or regions with different chemical compositions in observations of hot Jupiters with the James Webb Space Telescope (JWST). We find that our method struggles to identify sharp edges in maps with sudden discontinuities, but generally can be used as a first step before a more physically motivated modeling approach to determine the primary features observed on the planet.