稀疏自编码器符号一览表

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Here is a summary of the symbols used in our derivation of the sparse autoencoder:
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<br>下面是我们在推导sparse autoencoder时使用的符号一览表：
{| class="wikitable"
{| class="wikitable"
|-
|-
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! Symbol
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|符号
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符号
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|含义
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! Meaning
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含义
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|-
|-
| <math>\textstyle x</math>
| <math>\textstyle x</math>
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| Input features for a training example, <math>\textstyle x \in \Re^{n}</math>.
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| 训练样本的输入特征，<math>\textstyle x \in \Re^{n}</math>.
|-
|-
| <math>\textstyle y</math>
| <math>\textstyle y</math>
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| Output/target values. Here, <math>\textstyle y</math> can be vector valued. In the case of an autoencoder, <math>\textstyle y=x</math>.
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| 输出值/目标值. 这里 <math>\textstyle y</math> 可以是向量. 在autoencoder中，<math>\textstyle y=x</math>.
|-
|-
| <math>\textstyle (x^{(i)}, y^{(i)})</math>
| <math>\textstyle (x^{(i)}, y^{(i)})</math>
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| The <math>\textstyle i</math>-th training example
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| 第 <math>\textstyle i</math> 个训练样本
|-
|-
| <math>\textstyle h_{W,b}(x)</math>
| <math>\textstyle h_{W,b}(x)</math>
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| Output of our hypothesis on input <math>\textstyle x</math>, using parameters <math>\textstyle W,b</math>. This should be a vector of
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| 输入为 <math>\textstyle x</math> 时的假设输出，其中包含参数 <math>\textstyle W,b</math>. 该输出应当与目标值 <math>\textstyle y</math> 具有相同的维数.
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the same dimension as the target value <math>\textstyle y</math>.
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|-
|-
| <math>\textstyle W^{(l)}_{ij}</math>
| <math>\textstyle W^{(l)}_{ij}</math>
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| The parameter associated with the connection between unit <math>\textstyle j</math> in layer <math>\textstyle l</math>, and
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| 连接第 <math>\textstyle l</math> 层 <math>\textstyle j</math> 单元和第 <math>\textstyle l+1</math> 层 <math>\textstyle i</math> 单元的参数.
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unit <math>\textstyle i</math> in layer <math>\textstyle l+1</math>.
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|-
|-
| <math>\textstyle b^{(l)}_{i}</math>
| <math>\textstyle b^{(l)}_{i}</math>
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| The bias term associated with unit <math>\textstyle i</math> in layer <math>\textstyle l+1</math>. Can also be thought of as the parameter associated with the connection between the bias unit in layer <math>\textstyle l</math> and unit <math>\textstyle i</math> in layer <math>\textstyle l+1</math>.
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| 第 <math>\textstyle l+1</math> 层 <math>\textstyle i</math> 单元的偏置项. 也可以看作是连接第 <math>\textstyle l</math> 层偏置单元和第 <math>\textstyle l+1</math> 层 <math>\textstyle i</math> 单元的参数.
|-
|-
| <math>\textstyle \theta</math>
| <math>\textstyle \theta</math>
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| Our parameter vector. It is useful to think of this as the result of taking the parameters <math>\textstyle W,b</math> and ``unrolling'' them into a long column vector.
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| 参数向量. 可以认为该向量是通过将参数 <math>\textstyle W,b</math> 组合展开为一个长的列向量而得到.
|-
|-
| <math>\textstyle a^{(l)}_i</math>
| <math>\textstyle a^{(l)}_i</math>
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| Activation (output) of unit <math>\textstyle i</math> in layer <math>\textstyle l</math> of the network.
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| 网络中第 <math>\textstyle l</math> 层 <math>\textstyle i</math> 单元的激活（输出）值.
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In addition, since layer <math>\textstyle L_1</math> is the input layer, we also have <math>\textstyle a^{(1)}_i = x_i</math>.
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另外，由于 <math>\textstyle L_1</math> 层是输入层，所以 <math>\textstyle a^{(1)}_i = x_i</math>.
|-
|-
| <math>\textstyle f(\cdot)</math>
| <math>\textstyle f(\cdot)</math>
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| The activation function. Throughout these notes, we used <math>\textstyle f(z) = \tanh(z)</math>.
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| 激活函数. 本文中我们使用 <math>\textstyle f(z) = \tanh(z)</math>.
|-
|-
| <math>\textstyle z^{(l)}_i</math>
| <math>\textstyle z^{(l)}_i</math>
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| Total weighted sum of inputs to unit <math>\textstyle i</math> in layer <math>\textstyle l</math>. Thus, <math>\textstyle a^{(l)}_i = f(z^{(l)}_i)</math>.
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| 第 <math>\textstyle l</math> 层 <math>\textstyle i</math> 单元所有输入的加权和. 因此有 <math>\textstyle a^{(l)}_i = f(z^{(l)}_i)</math>.
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|-
| <math>\textstyle \alpha</math>
| <math>\textstyle \alpha</math>
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| Learning rate parameter
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| 学习率
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|-
| <math>\textstyle s_l</math>
| <math>\textstyle s_l</math>
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| Number of units in layer <math>\textstyle l</math> (not counting the bias unit).
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| 第 <math>\textstyle l</math> 层的单元数目（不包含偏置单元）.
|-
|-
| <math>\textstyle n_l</math>
| <math>\textstyle n_l</math>
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| Number layers in the network. Layer <math>\textstyle L_1</math> is usually the input layer, and layer <math>\textstyle L_{n_l}</math> the output layer.
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| 网络中的层数. 通常 <math>\textstyle L_1</math> 层是输入层，<math>\textstyle L_{n_l}</math> 层是输出层.
|-
|-
| <math>\textstyle \lambda</math>
| <math>\textstyle \lambda</math>
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| Weight decay parameter.
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| 权重衰减系数.
|-
|-
| <math>\textstyle \hat{x}</math>
| <math>\textstyle \hat{x}</math>
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| For an autoencoder, its output; i.e., its reconstruction of the input <math>\textstyle x</math>.   Same meaning as <math>\textstyle h_{W,b}(x)</math>.
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| 对于一个autoencoder，该符号表示其输出值；亦即输入值 <math>\textstyle x</math> 的重构值. 与 <math>\textstyle h_{W,b}(x)</math> 含义相同.
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|-
| <math>\textstyle \rho</math>
| <math>\textstyle \rho</math>
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| Sparsity parameter, which specifies our desired level of sparsity
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| 稀疏值，可以用它指定我们所需的稀疏程度
|-
|-
| <math>\textstyle \hat\rho_i</math>
| <math>\textstyle \hat\rho_i</math>
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| The average activation of hidden unit <math>\textstyle i</math> (in the sparse autoencoder).
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| （sparse autoencoder中）隐藏单元 <math>\textstyle i</math> 的平均激活值.
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|-
| <math>\textstyle \beta</math>  
| <math>\textstyle \beta</math>  
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| Weight of the sparsity penalty term (in the sparse autoencoder objective).
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| （sparse autoencoder目标函数中）稀疏值惩罚项的权重.
|}
|}
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{{Sparse_Autoencoder}}
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==中文译者==
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邵杰（jiesh@hotmail.com），许利杰（csxulijie@gmail.com），余凯（kai.yu.cool@gmail.com）
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{{稀疏自编码器}}
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{{Languages|Sparse_Autoencoder_Notation_Summary|English}}

Latest revision as of 05:34, 8 April 2013

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