Cosine distance

Euclidean and Manhattan distance measures do not perform well in high-dimensional space. In a high-dimensional problem space, cosine distance more accurately reflects the closeness between two data points in a multidimensional problem space. The cosine distance measure is calculated by measuring the cosine angle created by two points connected to a reference point. If the data points are close, then the angle will be narrow, irrespective of the dimensions they have. On the other hand, if they are far away, then the angle will be large:

Textual data can almost be considered a highly dimensional space. As the cosine distance measure works very well with h-dimensional spaces, it is a good choice when dealing with textual data.Note that in the preceding figure, the cosine of the angle between A(2,5) and B(4.4) is the cosine distance. The reference between these points is the origin—that is, X(0,0). But in reality, any point in the problem space...