High-dimensional visualisation for novelty detection

A key step in the application of novelty detection techniques to high-dimensional data is the exploration of relationships that are typically not obvious when dimensions are examined independently. Visualisation techniques allow such exploration of the structure of the data set by mapping high-dimensional data into lower dimensionality for inspection. This paper discusses the application of the NeuroScale visualisation method for construction of this mapping, which is commonly employed due to its ability to interpolate between training examples into areas of data space not previously encountered. 1) We show that there are disadvantages to using this visualisation method for extrapolation, as is commonly performed when visualising previouslyunseen test data which are “abnormal”. 2) We describe a method for ensuring consistent projection of such previously-unseen “abnormal” examples. 3) We show how the proposed technique can also be used to provide a visualisation of highdimensional decision boundaries, as are typically applied to models of normality in high-dimensional novelty detection cases. An example from a probabilistic model of normality is presented, in which a decision boundary is computed using Extreme Value Statistics and then visualised in two dimensions, showing how the method can be used to communicate the results of novelty detection and allow analysis of high-dimensional “abnormal” data.