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I'm looking for a way to convert a set of lines in R^3 into points in R^n so that distance between any pair of points points is a good approximation of the distance between corresponding pair of lines. Can anyone see a practical way of doing this?

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    Maybe you could try transform this set in a manifold. For example, the set of all lines in $\mathbb{R}^{2}$ is a mobius band.2012-10-06

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