# 线性解码器

(Difference between revisions)
 Revision as of 03:25, 29 March 2013 (view source)Kandeng (Talk | contribs)← Older edit Revision as of 05:57, 29 March 2013 (view source)Kandeng (Talk | contribs) Newer edit → Line 1: Line 1: - == 稀疏自编码重述 == == 稀疏自编码重述 == Line 64: Line 63: ==中文译者== ==中文译者== - 严晓东（yan.endless@gmail.com），姚涛（yaothinker@gmail.com），@晓风_机器学习 + 严晓东（yan.endless@gmail.com），姚涛（yaothinker@gmail.com），晓风（xiaofeng.zhb@alibaba-inc.com）

## 稀疏自编码重述

\begin{align} z^{(3)} &= W^{(2)} a^{(2)} + b^{(2)} \\ a^{(3)} &= f(z^{(3)}) \end{align}

S 型激励函数输出范围是 [0,1]，当 f(z(3)) 采用该激励函数时，就要对输入限制或缩放，使其位于 [0,1] 范围中。一些数据集，比如 MNIST，能方便将输出缩放到 [0,1] 中，但是很难满足对输入值的要求。比如， PCA 白化处理的输入并不满足 [0,1] 范围要求，也不清楚是否有最好的办法可以将数据缩放到特定范围中。

## 线性解码器

\begin{align} \delta_i^{(3)} = \frac{\partial}{\partial z_i} \;\; \frac{1}{2} \left\|y - \hat{x}\right\|^2 = - (y_i - \hat{x}_i) \cdot f'(z_i^{(3)}) \end{align}

\begin{align} \delta_i^{(3)} = - (y_i - \hat{x}_i) \end{align}

\begin{align} \delta^{(2)} &= \left( (W^{(2)})^T\delta^{(3)}\right) \bullet f'(z^{(2)}) \end{align}