Equation 13 · Part 1 · Embeddings and the Geometry of Similarity

Symbol L_1

L_1

L_1

What this part means

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

Its job in the formula

$L_1$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol L_1Article meaning

Where the article explains it

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 ] .

The passage around this formula

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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