| They don’t have to be. The computation of cosine distance normalizes the distance. In the intuitive explanation I gave, the distance from the origin doesn’t matter at all, unless you are trying to force “cosine disbtance” to mean “metric distance” There are many many ways to quantify closeness. Metric distance i.e taking a ruler and measuring the distance between the 2 points, is one way. Measuring the angles between the 2 lines that join the points to the origin is another way to measure closeness The squared of the measured metric distance is another way The absolute value of the ruler distance is another way The question you asked is only relevant if you’re trying to force cosine distance into ruler distance. You don’t need to. Cosine distance is a sufficient way by itself to measure closeness. But yeah generally speaking, costume distance correlates better with metric distance even the points are relatively more equidistant to the origin |