Learning low-dimensional manifolds under the L0-norm constraint for unsupervised outlier detection

Unsupervised outlier detection without the need for clean data has attracted great attention because it is suitable for real-world problems as a result of its low data collection costs. Reconstruction-based methods are popular approaches for unsupervised outlier detection. These methods decompose a data matrix into low-dimensional manifolds and an error matrix. Then, samples with a large error are detected as outliers. To achieve high outlier detection accuracy, when data are corrupted by large noise, the detection method should have the following two properties: (1) it should be able to decompose the data under the L0-norm constraint on the error matrix and (2) it should be able to reflect the nonlinear features of the data in the manifolds. Despite significant efforts, no method with both of these properties exists. To address this issue, we propose a novel reconstruction-based method: “L0-norm constrained autoencoders (L0-AE).” L0-AE uses autoencoders to learn low-dimensional manifolds that capture the nonlinear features of the data and uses a novel optimization algorithm that can decompose the data under the L0-norm constraints on the error matrix. This novel L0-AE algorithm provably guarantees the convergence of the optimization if the autoencoder is trained appropriately. The experimental results show that L0-AE is more robust, accurate and stable than other unsupervised outlier detection methods not only for artificial datasets with corrupted samples but also artificial datasets with well-known outlier distributions and real datasets. Additionally, the results show that the accuracy of L0-AE is moderately stable to changes in the parameter of the constrained term, and for real datasets, L0-AE achieves higher accuracy than the baseline non-robustified method for most parameter values.