The curse of dimensionality is a phenomena that arise when analyzing and organizing data in high-dimensional spaces and do not occur in low dimensional spaces. It is important to take these phenomena into account when using different techniques, since testing on low-dimensional spaces will work with no issues. ## Distance functions Most notably, the [[Euclidean Distance|Euclidean distance]] is highly affected by it. When using many coordinates, the distance increases in absolute scale but not difference in measurements. Usually, this is illustrated using the n-dimensional hypersphere metaphor, but it is easier to express it saying that [[Almost All Points in a High-Dimensional Space are Equally Distant from Each Other|almost all points in a high-dimensional space are equally distant from each other]].