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第326行：
第326行： − − <math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math> 第333行：
第331行： − + − 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+ − − <math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}} − − 数学运算符名称{ i }{ LRMA } sum { y } in 数学{ y } sum { 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 {( frac { p (x，y)}{和 w ^ prime (x，w) p ^ prime }(w，y)} − − \right) }}, − − 开始，开始, − − </math> − − 数学
→独立性假设 Independence assumptions
:<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
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>.