Figure 2.

Illustration of the Alpha-Beta log-det divergence (AB-LD) divergence $D_{LD}^{(\alpha ,\beta )}({\mathbf{\Sigma }}_1\parallel {\mathbf{\Sigma }}_2)$ in the $(\alpha ,\beta )$-plane. Note that the position of each divergence is specified by the value of the hyperparameters $(\alpha ,\beta )$. This parameterization smoothly connects several positive definite matrix divergences, such as the squared Riemannian metric ($\alpha =0,\beta =0$), the KL matrix divergence or Stein’s loss ($\alpha =1,\beta =0$), the dual KL matrix divergence ($\alpha =0,\beta =1$) and the S-divergence ($\alpha =\frac{1}{2},\beta =\frac{1}{2}$), among others.