Feature Transformation and Reference hypothesis

Let $ {\bf z}_A = {\bf A}^\prime {\bf x},$ where $ {\bf A}$ is any non-singular $ N\times D$ matrix. This feature does not contain an energy statistic, since no linear function of $ {\bf x}$ can lead to a norm on $ {\cal R}^N$. To add an ES, we augment $ {\bf z}_A$. The feature $ {\bf z}$ is the union of $ {\bf z}_A$ with $ t_2({\bf x}) = \sum_{i=1}^N x_i^2,$ so $ {\bf z}= [ t_2({\bf x}),\; {\bf z}_A].$ The reference PDF $ p({\bf x}\vert H_0)$ is shown in Table 3.1 (``Gaussian"), and $ t_2({\bf x})$ is the ES.

Baggenstoss 2017-05-19