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Reconstruction based methods suppose that anomalies are incompressible and thus cannot be effectively reconstructed from low-dimensional projections. In this category, we can cite methods like Principal Component Analysis (PCA) with explicit linear projections, Kernel PCA with implicit non-linear projections induced by specific kernels, Robust PCA, as well as reconstruction error induced by Deep Autoencoders.
Clustering analysis is another unsupervised approach using the density estimation and anomaly detection. We can cite methods like Multivariate Gaussian Model, Gaussian Mixture Models, K-means, etc. The drawbacks of these methods are the curse of dimensionality and the difficulty to apply these methods for high dimensional data. For this reason, several methods conduct dimensionality reduction prior to clustering analysis.
One class classification approaches learn a discriminative boundary surrounding the normal class. We can cite methods like One-class SVM. For high dimensionality problems, such methods suffer from suboptimal performance. For this reason, dimensionality reduction methods might be jointly used with one-class classification approaches.
References
Chalapathy R, Chawla S. Deep learning for anomaly detection: A survey. arXiv preprint arXiv:1901.03407. 2019 Jan 10.
Chandola, Varun, Arindam Banerjee, and Vipin Kumar. "Anomaly detection: A survey." ACM computing surveys (CSUR) 41.3 (2009): 1-58.
Zong, Bo, Qi Song, Martin Renqiang Min, Wei Cheng, Cristian Lumezanu, Daeki Cho, and Haifeng Chen. "Deep autoencoding gaussian mixture model for unsupervised anomaly detection." In International Conference on Learning Representations. 2018.