Equation 13 · Embeddings and the Geometry of Similarity

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L_1

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preferable to $L_2$ in high dimensions, $L_2$ to $L_3$ , and that fractional norms preserve contrast better still [ 12 ]. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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L_1

Symbol L_1

preferable to $L_2$ in high dimensions, $L_2$ to $L_3$ , and that fractional norms preserve contrast better still [ 12 ].

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subscript

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with C constant, while typical distances themselves grow like $d^{1/k}$ . Relative contrast therefore decays with dimension, and the constant shrinks as k rises — which is why they conclude that $L_1$ is preferable to $L_2$ in high dimensions, $L_2$ to $L_3$ , and that fractional norms preserve contrast better still [ 12 ] .

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Sources cited in the surrounding passage

[12] On the Surprising Behavior of Distance Metrics in High Dimensional Space ↗

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