University AI - Normal Uses of an Autoencoder

Normal Uses of an Autoencoder

1. Let ${\mathbb{R}}^d$ be the original feature space, $\tau =\{(\underline{x},\underline{\hat{y}})|\underline{x}\in {\mathbb{R}}^d,\underline{\hat{y}}\in {\mathbb{R}}^m\}$, so our goal is to train an ANN to realize the function $\varphi :{\mathbb{R}}^d\to {\mathbb{R}}^m$.
2. From $\tau$ we define $\tau ’$ the training set for our Autoencoder: $\tau =\{(\underline{x},\underline{x})\}$ and then train our Autoencoder.
3. We remove just the output layer from our Autoencoder and obtain a new function $\psi :{\mathbb{R}}^d\to {\mathbb{R}}^k$ such that $k<d$ , using this function on the input $\underline{x}$ we obtain a new set ${\tau }^{\prime \prime }=\{(\underline{x},\underline{z})|\underline{z}\in {\mathbb{R}}^k\}$
4. We train a new MLP via backpropagation on ${\tau }^{\prime \prime \prime }=\{(\underline{z},\underline{\hat{y}})\}$ and we obtain the function $\hat{\varphi }:{\mathbb{R}}^k\to {\mathbb{R}}^m$ .
5. We mount the two MLP (Autoencoder and new MLP) on top of each other and obtain the function $\varphi :{\mathbb{R}}^d\to {\mathbb{R}}^m$
6. We can tune the completed MLP via backpropagation on the original data set $\tau$, if necessary
7. We can iterate this process stacking even more Autoencoder at the beginning of the whole MLP

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