  Convolutional neural networks (CNNs) have achieved remarkable performance in
many applications, especially in image recognition tasks. As a crucial
component of CNNs, sub-sampling plays an important role for efficient training
or invariance property, and max-pooling and arithmetic average-pooling are
commonly used sub-sampling methods. In addition to the two pooling methods,
however, there could be many other pooling types, such as geometric average,
harmonic average, and so on. Since it is not easy for algorithms to find the
best pooling method, usually the pooling types are assumed a priority, which
might not be optimal for different tasks. In line with the deep learning
philosophy, the type of pooling can be driven by data for a given task. In this
paper, we propose {\it $\alpha$-integration pooling} ($\alpha$I-pooling), which
has a trainable parameter $\alpha$ to find the type of pooling.
$\alpha$I-pooling is a general pooling method including max-pooling and
arithmetic average-pooling as a special case, depending on the parameter
$\alpha$. Experiments show that $\alpha$I-pooling outperforms other pooling
methods including max-pooling, in image recognition tasks. Also, it turns out
that each layer has different optimal pooling type.
