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Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality reduction effective for high-dimensional data embedding nonlinear low-dimensional manifold, it is understood that some sort of geodesic distance metric should be used to discriminate the data samples. Inspired by the success of geodesic distance approximators such as ISOMAP, we propose to use a minimum spanning tree (MST), a graph-based algorithm, to approximate the local neighborhood structure and generate structure-preserving distances among data points. We use this MST-based distance metric to replace the Euclidean distance metric in the embedding function of autoencoders and develop a new graph regularized autoencoder, which outperforms a wide range of alternative methods over 20 benchmark anomaly detection datasets. We further incorporate the MST regularizer into two generative adversarial networks and find that using the MST regularizer improves the performance of anomaly detection substantially for both generative adversarial networks. We also test our MST regularized autoencoder on two datasets in a clustering application and witness its superior performance as well.
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Unsupervised learning can leverage large-scale data sources without the need for annotations. In this context, deep learning-based auto encoders have shown great potential in detecting anomalies in medical images. However, state-of-the-art anomaly scores are still based on the reconstruction error, which lacks in two essential parts: it ignores the model-internal representation employed for reconstruction, and it lacks formal assertions and comparability between samples. We address these shortcomings by proposing the Context-encoding Variational Autoencoder (ceVAE) which combines reconstruction- with density-based anomaly scoring. This improves the sample- as well as pixel-wise results. In our experiments on the BraTS-2017 and ISLES-2015 segmentation benchmarks, the ceVAE achieves unsupervised ROC-AUCs of 0.95 and 0.89, respectively, thus outperforming state-of-the-art methods by a considerable margin.
Dimensionality reduction is considered as an important step for ensuring competitive performance in unsupervised learning such as anomaly detection. Non-negative matrix factorization (NMF) is a popular and widely used method to accomplish this goal. But NMF do not have the provision to include the neighborhood structure information and, as a result, may fail to provide satisfactory performance in presence of nonlinear manifold structure. To address that shortcoming, we propose to consider and incorporate the neighborhood structural similarity information within the NMF framework by modeling the data through a minimum spanning tree. We label the resulting method as the neighborhood structure assisted NMF. We further devise both offline and online algorithm
In data systems, activities or events are continuously collected in the field to trace their proper executions. Logging, which means recording sequences of events, can be used for analyzing system failures and malfunctions, and identifying the causes and locations of such issues. In our research we focus on creating an Anomaly detection models for system logs. The task of anomaly detection is identifying unexpected events in dataset, which differ from the normal behavior. Anomaly detection models also assist in data systems analysis tasks. Modern systems may produce such a large amount of events monitoring every individual event is not feasible. In such cases, the events are often aggregated over a fixed period of time, reporting the number of times every event has occurred in that time period. This aggregation facilitates scaling, but requires a different approach for anomaly detection. In this research, we present a thorough analysis of the aggregated data and the relationships between aggregated events. Based on the initial phase of our research we present graphs representations of our aggregated dataset, which represent the different relationships between aggregated instances in the same context. Using the graph representation, we propose Multiple-graphs autoencoder MGAE, a novel convolutional graphs-autoencoder model which exploits the relationships of the aggregated instances in our unique dataset. MGAE outperforms standard graph-autoencoder models and the different experiments. With our novel MGAE we present 60% decrease in reconstruction error in comparison to standard graph autoencoder, which is expressed in reconstructing high-degree relationships.
Variational autoencoder (VAE) is a widely used generative model for learning latent representations. Burda et al. in their seminal paper showed that learning capacity of VAE is limited by over-pruning. It is a phenomenon where a significant number of latent variables fail to capture any information about the input data and the corresponding hidden units become inactive. This adversely affects learning diverse and interpretable latent representations. As variational graph autoencoder (VGAE) extends VAE for graph-structured data, it inherits the over-pruning problem. In this paper, we adopt a model based approach and propose epitomic VGAE (EVGAE),a generative variational framework for graph datasets which successfully mitigates the over-pruning problem and also boosts the generative ability of VGAE. We consider EVGAE to consist of multiple sparse VGAE models, called epitomes, that are groups of latent variables sharing the latent space. This approach aids in increasing active units as epitomes compete to learn better representation of the graph data. We verify our claims via experiments on three benchmark datasets. Our experiments show that EVGAE has a better generative ability than VGAE. Moreover, EVGAE outperforms VGAE on link prediction task in citation networks.
Graph convolution operator of the GCN model is originally motivated from a localized first-order approximation of spectral graph convolutions. This work stands on a different view; establishing a textit{mathematical connection between graph convolution and graph-regularized PCA} (GPCA). Based on this connection, GCN architecture, shaped by stacking graph convolution layers, shares a close relationship with stacking GPCA. We empirically demonstrate that the textit{unsupervised} embeddings by GPCA paired with a 1- or 2-layer MLP achieves similar or even better performance than GCN on semi-supervised node classification tasks across five datasets including Open Graph Benchmark footnote{url{https://ogb.stanford.edu/}}. This suggests that the prowess of GCN is driven by graph based regularization. In addition, we extend GPCA to the (semi-)supervised setting and show that it is equivalent to GPCA on a graph extended with ghost edges between nodes of the same label. Finally, we capitalize on the discovered relationship to design an effective initialization strategy based on stacking GPCA, enabling GCN to converge faster and achieve robust performance at large number of layers. Notably, the proposed initialization is general-purpose and applies to other GNNs.
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