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Instead of trying to sparsify the graph of colours, possibly this dimensionality reduction step will work.
This paper uses Laplacian eigenmaps: https://ieeexplore.ieee.org/document/9395231 (GitHub: https://github.com/yuanlinping/deep_colormap_extraction)
They are following the recipe in here: https://onlinelibrary.wiley.com/doi/abs/10.1111/cgf.12567
Some Python resources on the topic:
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researchNeeds researching and testingNeeds researching and testing