Distance functions on subsets of matrices
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#Partitioned Distances

pdist on CRAN

Given a matrix X with m observations and another matrix Y with n observations, Partitioned Distances computes the m by n distance matrix. A rectangular distance matrix can be more appropriate than a square matrix in many applications; for example, in bipartite graphs we might be concerned with the distance between objects in Graph A with objects in Graph B, but we may not care about the distance between objects within Graph A or Graph B. Currently, R only has a dist function which returns square distance matrices.

##Performance pdist is a slightly optimized version of the native dist function; distances are not computed between objects that are both in X or both in Y. Using native functions, we could stack X and Y on top of each other using rbind, and call dist on the result, but this would compute the (m+n) by (m+n) distance matrix, yielding m^2 + mn + n^2 unnecessary distance computations. If the matrices have p columns, and the distance metric is the Euclidean metric, then p(m^2 + mn + n^2) unnecessary flops are made. More complex metrics, such as dynamic time warping, can run in O(p^3), which means a naive dist function would make O(p^3(m^2 + mn + n^2)) unnecessary flops!

##Timing Using a matrix X that is 1000 by 100, it took 0.543 seconds to compute the distance matrix based on the Euclidean metric using dist. Using pdist, the timing was the same. If we are interested in the subset A taken by the first 100 rows of X, and subset B taken by the next 100 rows of X, we can compute a smaller distance matrix in only 0.006 seconds!