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.
Several recent works have used autoencoders for anomaly detection. Autoencoders tend to maintain the main structure in the data and often produce large reconstruction errors for outliers, which help identify them. The earliest work on anomaly detection by large reconstruction error of an autoencoder is @cite_12 . It applies an iterative and cyclic scheme, where in each iteration, an inlier set is determined and used for updating the parameters of the autoencoder. @cite_46 apply @math normalization for the latent code of the autoencoder and also consider the case of multiple modes for the normal samples. Instead of using the reconstruction error, they apply @math -means clustering for the latent code, and identify outliers as points whose latent representations are far from all the cluster centers. @cite_11 also use an autoencoder with clustered latent code, but they fit a Gaussian Mixture Model using an additional neural network. Restricted Boltzmann Machines (RBMs) are similar to autoencoders. @cite_5 define energy functions'' for RBMs that are similar to the reconstruction losses for autoencoders. They identify anomalous samples according to large energy values.
@cite_5 @cite_46 @cite_12 @cite_11
2127979711 2889504592 2786088545 2102409316
This paper proposes to use autoencoders with nonlinear dimensionality reduction in the anomaly detection task. The authors apply dimensionality reduction by using an autoencoder onto both artificial data and real data, and compare it with linear PCA and kernel PCA to clarify its property. The artificial data is generated from Lorenz system, and the real data is the spacecrafts' telemetry data. This paper demonstrates that autoencoders are able to detect subtle anomalies which linear PCA fails. Also, autoencoders can increase their accuracy by extending them to denoising autoenconders. Moreover, autoencoders can be useful as nonlinear techniques without complex computation as kernel PCA requires. Finaly, the authors examine the learned features in the hidden layer of autoencoders, and present that autoencoders learn the normal state properly and activate differently with anomalous input. We introduce a potentially powerful new method of searching for new physics at the LHC, using autoencoders and unsupervised deep learning. The key idea of the autoencoder is that it learns to map "normal" events back to themselves, but fails to reconstruct "anomalous" events that it has never encountered before. The reconstruction error can then be used as an anomaly threshold. We demonstrate the effectiveness of this idea using QCD jets as background and boosted top jets and RPV gluino jets as signal. We show that a deep autoencoder can significantly improve signal over background when trained on backgrounds only, or even directly on data which contains a small admixture of signal. Finally we examine the correlation of the autoencoders with jet mass and show how the jet mass distribution can be stable against cuts in reconstruction loss. This may be important for estimating QCD backgrounds from data. As a test case we show how one could plausibly discover 400 GeV RPV gluinos using an autoencoder combined with a bump hunt in jet mass. This opens up the exciting possibility of training directly on actual data to discover new physics with no prior expectations or theory prejudice. Unsupervised anomaly detection on multi- or high-dimensional data is of great importance in both fundamental machine learning research and industrial applications, for which density estimation lies at the core. Although previous approaches based on dimensionality reduction followed by density estimation have made fruitful progress, they mainly suffer from decoupled model learning with inconsistent optimization goals and incapability of preserving essential information in the low-dimensional space. In this paper, we present a Deep Autoencoding Gaussian Mixture Model (DAGMM) for unsupervised anomaly detection. Our model utilizes a deep autoencoder to generate a low-dimensional representation and reconstruction error for each input data point, which is further fed into a Gaussian Mixture Model (GMM). Instead of using decoupled two-stage training and the standard Expectation-Maximization (EM) algorithm, DAGMM jointly optimizes the parameters of the deep autoencoder and the mixture model simultaneously in an end-to-end fashion, leveraging a separate estimation network to facilitate the parameter learning of the mixture model. The joint optimization, which well balances autoencoding reconstruction, density estimation of latent representation, and regularization, helps the autoencoder escape from less attractive local optima and further reduce reconstruction errors, avoiding the need of pre-training. Experimental results on several public benchmark datasets show that, DAGMM significantly outperforms state-of-the-art anomaly detection techniques, and achieves up to 14 improvement based on the standard F1 score. An autoencoder network uses a set of recognition weights to convert an input vector into a code vector. It then uses a set of generative weights to convert the code vector into an approximate reconstruction of the input vector. We derive an objective function for training autoencoders based on the Minimum Description Length (MDL) principle. The aim is to minimize the information required to describe both the code vector and the reconstruction error. We show that this information is minimized by choosing code vectors stochastically according to a Boltzmann distribution, where the generative weights define the energy of each possible code vector given the input vector. Unfortunately, if the code vectors use distributed representations, it is exponentially expensive to compute this Boltzmann distribution because it involves all possible code vectors. We show that the recognition weights of an autoencoder can be used to compute an approximation to the Boltzmann distribution and that this approximation gives an upper bound on the description length. Even when this bound is poor, it can be used as a Lyapunov function for learning both the generative and the recognition weights. We demonstrate that this approach can be used to learn factorial codes.