In recommendation systems and decision support systems it is of vital importance to detect anomalies and outliers as they have a high relevance. For example, in case of fraudulent claims, which usually differ considerably from default claims, shall be detected. In clinical / medical decision support systems unusual cases which need special treatment should be filtered out.
Anomaly detection is concerned with identifying observations in new incoming test data, which diverge in a certain sense from the previously seen “normal” data. During recent years, practical importance and difficulty of this task spurred a vast volume of research which resulted in a large number of heterogeneous approaches and methods to its solution. For example:
- Probabilistic approaches that rely on approximating the generative distribution of the observed data [2,3]
- Metric-based anomaly detection 
- Anomaly detection with predictive models is based on regression and classification methods which model the observed dataset 
- Domain-based anomaly detection model the boundary of the relevant “normal” region 
The aim of this topic is to approach problems of detecting anomalous nodes in large-scale networks and detecting anomalous graphs, as well as sequences.
Tasks for first 2-4 months
- Literature review (related works, state-of-the-art, evaluation approaches)
- Implement node2vec algorithm  and apply a density-based anomaly detection method (e.g. ) on a set of toy graphs
- Compare with one-class-SVM  for graph laplacian kernel.
- Propose a design of the method for detecting anomalies on graphs.
- Implement any algorithm from seq2vec family (see  as an example) and construct anomaly detection rule on basis of the obtained embeddings.
- Ivanov, S. and Burnaev, E., 2018. Anonymous Walk Embeddings. arXiv preprint arXiv:1805.11921.
- V. Barnett and T. Lewis. Outliers in Statistical Data, volume 286. Wiley and Sons, 1994
- D.W. Scott. Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons, 2008.
- A. Srivastava and B. Zane-Ulman. Discovering recurring anomalies in text reports regarding complex space systems. In Proceedings of the IEEE Aerospace Conference, pages 3853– 3862, 2005.
- G. Williams, R. Baxter, H. He, S. Hawkins, and L. Gu. A comparative study of RNN for outlier detection in data mining. In the International Conference on Data Mining, pages 709–712, 2002.
- B. Scholkopf, R. Williamson, A. Smola, J. Shawe-Taylor, J. Platt, et al. Support vector method for novelty detection. In NIPS, volume 12, pages 582–588. Citeseer, 1999.
- M. Breunig, H. Kriegel, R. Ng, and J. Sander. LOF: identifying density-based local outliers. In ACM SIGMOD, volume 29, pages 93–104. ACM, 2000.
- Grover, Aditya, and Jure Leskovec. “node2vec: Scalable feature learning for networks.” In ACM SIGKDD, 2016.
- Piotr Bojanowski, Edouard Grave, Armand Joulin, and Tomas Mikolov. Enriching word vectors with subword information. arXiv preprint arXiv:1607.04606, 2016.