Distances grows as dimensionality grows is the curse of dimensionality. Imagine you have a circle with unit radius inscribed in a square whose sides are 2. The

Distances grows as dimensionality grows is the curse of dimensionality. Imagine you have a circle with unit radius inscribed in a square whose sides are 2. The circle's area is pi, so pi/2^2 = 79% of all points in the space [-1,-1]-[1,1] are less than unit distance away from origin. For a sphere inside a cube the fraction is (4*pi/3)/2^3 = 52%, for a hypersphere it is (pi^2/2)/2^4 = 31%, and so on. As the number of dimensions grows the fraction approaches zero. E.g. only 0.25% of all points are inside the 10-dimensional sphere. So the distance between two random points in a high-dimensional space is likely large. Thus, modelling documents as high-dimensional vectors breaks down because they will be distant from each other and therefore dissimilar even though they may be "similar" to a human. One way to get around this is to take the cosine of the angle between the documents' respective vectors. While this often works better than the Euclidean distance, it is also affected by the curse of dimensionality. Afaik, there is no good way to work around the curse of dimensionality and similarity metrics not using vector representations often work better in practice. For example, one can model documents as bag-of-words and divide the size of the intersection with the size of the union.