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A neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer) that seeks to extract the underlying subspace from a latent representation of the given data and removes outliers that lie away from this subspace.
The foundational assumption of machine learning is that the data under consideration is separable into classes; while intuitively reasonable, separability constraints have proven remarkably difficult to formulate mathematically. We believe this problem is rooted in the mismatch between existing statistical techniques and commonly encountered data; object representations are typically high dimensional but statistical techniques tend to treat high dimensions a degenerate case. To address this problem, we develop a dedicated statistical framework for machine learning in high dimensions. The framework derives from the observation that object relations form a natural hierarchy; this leads us to model objects as instances of a high dimensional, hierarchal generative processes. Using a distance based statistical technique, also developed in this paper, we show that in such generative processes, instances of each process in the hierarchy, are almost-always encapsulated by a distinctive-shell that excludes almost-all other instances. The result is shell theory, a statistical machine learning framework in which separability constraints (distinctive-shells) are formally derived from the assumed generative process.
A new embedding is proposed using a set of locally varying data projections, with each projection responsible for persever-ing the variations that distinguish a local cluster of instances from all other instances, while simultaneously allowing the probability that an instance belongs to a cluster to be statistically inferred from the one-dimensional, local projection associated with the cluster.
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