You are analyzing a behavioral-telemetry data set in which each user session is encoded as a 25,000-dimensional TF-IDF vector. After sampling 1,000 sessions, you compute the Euclidean distance from every vector to its nearest neighbor and to its farthest neighbor. The mean ratio of (distance to nearest neighbor) / (distance to farthest neighbor) is 0.98, indicating that the two distances are almost identical. Which phenomenon in high-dimensional geometry most directly explains why the nearest and farthest neighbors have nearly the same distance?
A heavy-tailed variance distribution created hub points that pulled average distances toward the mean.
All features were scaled improperly, adding the same constant to every distance calculation.
Only linear growth in sample size versus dimensionality obscured the neighborhood structure.
Distance concentration caused by the curse of dimensionality makes all pairs of points appear almost equidistant.
In very high-dimensional spaces, pairwise distances tend to "concentrate": the minimum and maximum distances from a point differ only by a tiny fraction, so their ratio approaches 1. This distance concentration is a classic manifestation of the curse of dimensionality and undermines distance-based algorithms such as k-NN or k-means. The other options describe issues that can occur in data analysis, but none of them inherently force the nearest and farthest neighbor distances to converge when dimensionality alone is increased.
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What is the 'curse of dimensionality' in data analysis?
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Why do distances 'concentrate' in high-dimensional spaces?
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How does high-dimensionality impact algorithms like k-NN or k-means?