kl_div_cross

  ↳ distance

kl_div_cross(probs)

Given a Markov matrix, returns a matrix of cross-Kullback-Liebler divergences between the distributions.

The input probs has the form of a square column-stochastic matrix: that is, that is, np.sum(probs,axis=1) == 1. The output is a square matrix D with length and width probs.shape[0].

Mathematically, if probs[i,j] is given by the matrix \(T_{i,j}\), then D[i,j] is given by \(D_{i,j}\):

\[D_{i,j} = T_{i,i} \log\left(\frac{T_{i,i}}{T_{j,j}}\right) +T_{i,j} \log\left(\frac{T_{i,j}}{T_{j,i}}\right) + \sum_{k\neq j,i} T_{i,k} \log\left(\frac{T_{i,k}}{T_{j,k}}\right)\]