A Appendix for Details of Deriving HTGM A.1 The lower-bound of the likelihood function posterior q (v

In this section, we provide the details of the lower-bound in Eq. (3). This completes the derivation of Eq. (3). In other words, there is no overlap between any pair of balls. Therefore, we have the following derivation from Eq. (9). The training algorithm of HTGM is summarized in Algorithm 1.