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Table 2 Two Boundary based tests for Task B

From: Bi-linear matrix-variate analyses, integrative hypothesis tests, and case-control studies

Type Description
(1) on the projected samples of y t =w T x t , we use the one dimensional case of Equation (24) or the Welch’s t-test to test Equation (1) merely along the normal direction of the boundary.
(2) measuring the distances of samples from a separating boundary, we consider \( s_{B}=\frac {\sum _{{\mathbf {x}}\in X^{(1)}_{1}\cup X^{(0)}_{0} } | \frac {{\mathbf {w}}^{T}({\mathbf {x}}-{\mathbf {c}}_0)}{\Vert {\mathbf {w}} \Vert }|{\!~\!}^{q}}{ \sum _{{\mathbf {x}}\in X^{(1)}_{0}\cup X^{(0)}_{1} } | \frac {{\mathbf {w}}^{T}({\mathbf {x}}-{\mathbf {c}}_0) }{\Vert {\mathbf {w}} \Vert }|{\!~\!}^q+\gamma _{B}}, \ q \ge 0. \) with q=2 for the square distance, q=1 for the Euclidean one.