LSA

word-document matrix

\[X \in \mathbb{R}^{m*n}\]

word-topic matrix

\[T\in \mathbb{R}^{m*k}\]

topic-document matrix

\[Y\in \mathbb{R}^{k*n}\]

已知X，希望求得T，Y，使 公式$\ref{mul}$成立。

\[\begin{equation} \label{mul} X \approx TY \end{equation}\]

• 截断奇异值分解

\[X \approx U_k\Sigma_k V_{k}^{\top} = U_k\left(\Sigma_k V_{k}^{\top}\right)\]

• 非负矩阵分解

\[X \approx WH\]

• 平方损失

  \[\|A-B\|^{2}=\sum_{i, j}\left(a_{i j}-b_{i j}\right)^{2}\]

• 散度

  \[D(A \| B)=\sum_{i, j}\left(a_{i j} \log \frac{a_{i j}}{b_{i j}}-a_{i j}+b_{i j}\right)\]

PLSA

pass

[1]

“https://www.deeplearningbook.org/contents/ml.html.” https://www.deeplearningbook.org/contents/ml.html (accessed Oct. 11, 2021).