proposals for long action. Inspired by the idea of temporal actionness grouping in [@Xiong:ICCV17], we propose a novel Gaussian Kernel Grouping algorithm for this target.

Figure \[fig2:2\] illustrates the process of temporal Gaussian Kernel Grouping. Given two adjacent Gaussian kernels $G(t_1, \sigma_1)$ and $G(t_2, \sigma_2)$ whose center location and standard deviation are $t$ and $\sigma$, we compute the temporal intersection and union between two kernels by using the width $a_w$ of the default temporal boundary defined in Section \[sec:3.2\]. In upper part of Figure \[fig2:2\], the length of temporal intersection between two kernels is $H$, while the length of union is $L$. If the Intersection over Union (IoU) between the two kernels $H/L$ exceeds a certain threshold $\varepsilon$, we merge them into one Gaussian kernel (bottom part of Figure \[fig2:2\]). The new mixed Gaussian kernel is formulated as follows $$\label{Eq2:4}\small
\begin{split}
&W[i] = \frac{1}{Z}\exp(-\frac{(p_i-\mu')^2}{2{\sigma'}^2})~, \\
&s.t.~~~ p_i = \frac{i}{T}, ~~~ \mu' = \frac{t_1+t_2}{2 \cdot T}~, ~~~ \sigma' = \frac{L}{2}~,\\
&~~~~~~~~i \in \{0,1,...,T-1\}.
\end{split}$$

In each feature map, Algorithm \[GKG\] details the grouping steps to generate merged kernels.

Gaussian Pooling {#sec:3.4}
----------------

![Comparisons of manual extension plus average-pooling strategy (left) and Gaussian pooling strategy (right) for involving temporal contextual information of 