更改

:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math>

:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math>

Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence

Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence

Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence

Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence

或者，你可能会有兴趣知道 p (x，y) / math 的因式分解会带来多少信息。在这种情况下，完整的分布数学 p (x，y) / 数学传递给矩阵分解的剩余信息是由 Kullback-Leibler 分歧给出的

另一方面，人们可能有兴趣知道在因子分解过程中，有多少信息（𝑝（𝑥，𝑦））携带了多少信息。在这种情况下，全分布𝑝（𝑥，𝑦）通过矩阵因子分解所携带的多余信息由Kullback-Leibler散度给出

:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}

:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}

     {p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}

     {p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}

       \right) }},

       \right) }},

</math>

</math>

The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.

The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.