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Kramer (1992) was the first to discuss anomaly detection, both to detect sensor failures and replace the failed or missing values. |
Added much earlier citation on reduction of dimensionality by autoencoders. |
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The simplest way to perform the copying task perfectly would be to duplicate the signal. To suppress this behavior, the code space <math>\mathcal Z</math> usually has fewer dimensions than the message space <math>\mathcal{X}</math>.
Such an autoencoder is called ''undercomplete''. It can be interpreted as [[Data compression|compressing]] the message, or [[Dimensionality reduction|reducing its dimensionality]].<ref name=":12" /><ref name=":7" />
At the limit of an ideal undercomplete autoencoder, every possible code <math>z</math> in the code space is used to encode a message <math>x</math> that really appears in the distribution <math>\mu_{ref}</math>, and the decoder is also perfect: <math>D_\theta(E_\phi(x)) = x</math>. This ideal autoencoder can then be used to generate messages indistinguishable from real messages, by feeding its decoder arbitrary code <math>z</math> and obtaining <math>D_\theta(z)</math>, which is a message that really appears in the distribution <math>\mu_{ref}</math>.
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