We propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and remove outliers that lie away from this subspace. It is used together with an encoder and a decoder. The encoder maps the data into the latent space, from which the RSR layer extracts the subspace. The decoder then smoothly maps back the underlying subspace to a manifold" close to the original data. We illustrate algorithmic choices and performance for artificial data with corrupted manifold structure. We also demonstrate competitive precision and recall for image datasets.
The above works are designed for datasets with a small fraction of outliers. However, when this fraction increases, outliers are often not distinguished by high reconstruction errors or low similarity scores. In order to identify them, additional assumptions on the structure of the normal data need to be incorporated. For example, Zhou and Paffenroth @cite_18 decompose the input data into two parts: low-rank and sparse (or column-sparse). The low-rank part is fed into an autoencoder and the sparse part is imposed as a penalty term with the @math -norm (or @math -norm for column-sparsity).
@cite_18
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Deep autoencoders, and other deep neural networks, have demonstrated their effectiveness in discovering non-linear features across many problem domains. However, in many real-world problems, large outliers and pervasive noise are commonplace, and one may not have access to clean training data as required by standard deep denoising autoencoders. Herein, we demonstrate novel extensions to deep autoencoders which not only maintain a deep autoencoders' ability to discover high quality, non-linear features but can also eliminate outliers and noise without access to any clean training data. Our model is inspired by Robust Principal Component Analysis, and we split the input data X into two parts, @math , where @math can be effectively reconstructed by a deep autoencoder and @math contains the outliers and noise in the original data X. Since such splitting increases the robustness of standard deep autoencoders, we name our model a "Robust Deep Autoencoder (RDA)". Further, we present generalizations of our results to grouped sparsity norms which allow one to distinguish random anomalies from other types of structured corruptions, such as a collection of features being corrupted across many instances or a collection of instances having more corruptions than their fellows. Such "Group Robust Deep Autoencoders (GRDA)" give rise to novel anomaly detection approaches whose superior performance we demonstrate on a selection of benchmark problems.