Equation 11 · Embeddings and the Geometry of Similarity
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the while typical distances themselves grow like. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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superscript
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
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with C constant, while typical distances themselves grow like . Relative contrast therefore decays with dimension, and the constant shrinks as k rises — which is why they conclude that is preferable to in high dimensions, to , and that fractional norms preserve contrast better still [ 12 ] .
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