instances with complex variations.

Gaussian Kernel Grouping
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  \
Original Gaussian kernel set $\mathbb{S} = \{G(t_i, \sigma_i)\}^{T-1}_{i=0}$;\
Intersection over Union (IoU) threshold $\varepsilon$;\
  \
Mixed Gaussian kernel set $\mathbb{G}$;\
Choose the beginning grouping position $p = 0$; Initialize mixed Gaussian kernel set $\mathbb{G} = \varnothing$; Initialize base Gaussian kernel $G_{bs} = G(t_p, \sigma_p)$, the ending grouping position $z = p+1$; Compute IoU value $O$ between kernel $G_{bs}$ and $G(t_z, \sigma_z)$; Group $G_{bs}$ and $G(t_z, \sigma_z)$ to $G'$ according to Eq.(\[Eq2:4\]), replace $G_{bs}$ with the new mixed kernel $G'$; Add kernel $G_{bs}$ to mixed kernel set $\mathbb{G}$; $p = z$,   $G_{bs} = G(t_p, \sigma_p)$; $z = z + 1$; $\mathbb{G}$

Through learning temporal Gaussian kernels, the temporal scales of most action instances can be characterized with the predicted standard deviation. However, if the learned Gaussian kernels span and overlap with each other, that may implicitly indicate a long action centered at a flexible position among these Gaussian kernels. In other words, utilizing the center locations of these original Gaussian kernels to represent this long proposal may not be appropriate. To alleviate this issue, we attempt to generate a set of new Gaussian kernels to predict center location and temporal scales of 