w_{d}=\log \left(\frac{\sum_{d{\prime}=1}{\mathcal{D}} \sum_{h=1}^{\mathcal{H}} d_{i s t}\left(x_{h}{d{\prime}}, x_{h}{*}\right)}{\sum_{h=1}{\mathcal{H}} d_{i s t}\left(x_{h}^{d}, x_{h}^{*}\right)}\right)