Graph Pooling Node

Pooling functions combine and simplify data. Multiple data elements from an input matrix are combined into a single element in an output matrix. Below is a representation of a pooling node:

$\\ \begin{bmatrix}\hdots & \hdots &\hdots \\ \hdots & \hdots & \hdots \end{bmatrix} \rightarrow \bigoplus \rightarrow \begin{bmatrix}\cdot & \cdot &\cdot \\ \cdot & \cdot & \cdot \end{bmatrix}$

where:

$\\\bigoplus \, \, \, \mathrm{\textup{node performing a pooling operation}} \\ \\\rightarrow \: \: \: \: \mathrm{\textup{data transfer}} \\ \\ \begin{bmatrix} & \end{bmatrix} \: \: \mathrm{\textup{data matrix}} \\ \\\vdots \: \: \: \:\,\,\,\,\,\,\,\mathrm{\textup{group of data matrix elements}} \\ \\\cdot \: \: \: \:\,\,\,\,\,\,\mathrm{\textup{pooled data matrix element}}$

Types of pooling functions include:

max - the maximum element of an input group is used for the output pooled element
average - the average of the input group elements is used for the output pooled element

Parameters used for the pooling operation include:

filter - sets the dimensions of the filter grouping used for pooling (e.g. 2x2)
stride - sets how many cells the pooling filter moves for each pooling operation (e.g. 1); stride is normally set so that the output volume is an integer and not a fraction
padding - adds zero value cells around an input matrix in order to maintain the same spatial dimensions for the input and output volume

Graph Pooling Node

References