I have compared different distance functions by computing the average tf/idf distance between documents. My results show a range between $10-15$ for the Manhattan and a range between $1-1.5$ for the Euclidean distance.

I am asked "what behaviour can we expect about the $L_1$ vs. $L_2$ norms as the dimensionality of the data increases? Is this behaviour observed in our dataset? If not, why not?"

Any one have a clue about what is asked here?

I know that $L_1$ is more robust than $L_2$ and that the $L_k$ norm worsens faster with increasing dimensionality for higher values of $k$ but I don't really know what I am supposed to answer.

  • 1
    $\begingroup$ Wasn't really such question already answered not once here? $\endgroup$ – ttnphns Oct 14 '17 at 16:39

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