I'm not sure if its been done before, but neural networks could be used for outlier detection. Autoencoders can also be thought of as a form on nonlinear PCA, a

I'm not sure if its been done before, but neural networks could be used for outlier detection. Autoencoders can also be thought of as a form on nonlinear PCA, and the LISA group in Montreal has actually proved that the reconstruction error from a contractive or denoising autoencoder for a data point serves as an estimator of the probability density under that point.