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)