Sparse Autoencoder Notation Summary
Here is a summary of the symbols used in our derivation of the sparse autoencoder:
|Input features for a training example, .|
|Output/target values. Here, can be vector valued. In the case of an autoencoder, .|
|The -th training example|
| Output of our hypothesis on input , using parameters . This should be a vector of
the same dimension as the target value .
| The parameter associated with the connection between unit in layer , and
unit in layer .
|The bias term associated with unit in layer . Can also be thought of as the parameter associated with the connection between the bias unit in layer and unit in layer .|
|Our parameter vector. It is useful to think of this as the result of taking the parameters and ``unrolling them into a long column vector.|
| Activation (output) of unit in layer of the network.
In addition, since layer is the input layer, we also have .
|The activation function. Throughout these notes, we used .|
|Total weighted sum of inputs to unit in layer . Thus, .|
|Learning rate parameter|
|Number of units in layer (not counting the bias unit).|
|Number layers in the network. Layer is usually the input layer, and layer the output layer.|
|Weight decay parameter.|
|For an autoencoder, its output; i.e., its reconstruction of the input . Same meaning as .|
|Sparsity parameter, which specifies our desired level of sparsity|
|The average activation of hidden unit (in the sparse autoencoder).|
|Weight of the sparsity penalty term (in the sparse autoencoder objective).|