pooling¶

pooling(data=None, kernel=_Null, pool_type=_Null, global_pool=_Null, cudnn_off=_Null, pooling_convention=_Null, stride=_Null, pad=_Null, p_value=_Null, count_include_pad=_Null, layout=_Null, out=None, name=None, **kwargs)¶

Performs pooling on the input.

The shapes for 1-D pooling are

data and out: (batch_size, channel, width) (NCW layout) or (batch_size, width, channel) (NWC layout),

The shapes for 2-D pooling are

data and out: (batch_size, channel, height, width) (NCHW layout) or (batch_size, height, width, channel) (NHWC layout),

out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1])

The definition of f depends on pooling_convention, which has two options:

valid (default):
```
f(x, k, p, s) = floor((x+2*p-k)/s)+1
```
full, which is compatible with Caffe:
```
f(x, k, p, s) = ceil((x+2*p-k)/s)+1
```

When global_pool is set to be true, then global pooling is performed. It will reset kernel=(height, width) and set the appropiate padding to 0.

Three pooling options are supported by pool_type:

avg: average pooling
max: max pooling
sum: sum pooling
lp: Lp pooling

For 3-D pooling, an additional depth dimension is added before height. Namely the input data and output will have shape (batch_size, channel, depth, height, width) (NCDHW layout) or (batch_size, depth, height, width, channel) (NDHWC layout).

Notes on Lp pooling:

Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf. L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling. We can see that Lp pooling stands between those two, in practice the most common value for p is 2.

For each window X, the mathematical expression for Lp pooling is:

\(f(X) = \sqrt[p]{\sum_{x}^{X} x^p}\)

Defined in src/operator/nn/pooling.cc:L417

Parameters:

data : ndarray: Input data to the pooling operator.
kernel : Shape(tuple), optional, default=[]: Pooling kernel size: (y, x) or (d, y, x)
pool_type : {‘avg’, ‘lp’, ‘max’, ‘sum’},optional, default=’max’: Pooling type to be applied.
global_pool : boolean, optional, default=0: Ignore kernel size, do global pooling based on current input feature map.
cudnn_off : boolean, optional, default=0: Turn off cudnn pooling and use MXNet pooling operator.
pooling_convention : {‘full’, ‘same’, ‘valid’},optional, default=’valid’: Pooling convention to be applied.
stride : Shape(tuple), optional, default=[]: Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each dimension.
pad : Shape(tuple), optional, default=[]: Pad for pooling: (y, x) or (d, y, x). Defaults to no padding.
p_value : int or None, optional, default=’None’: Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling.
count_include_pad : boolean or None, optional, default=None: Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set to true,or it will be divided by 9 if this is set to false. Defaults to true.
layout : {None, ‘NCDHW’, ‘NCHW’, ‘NCW’, ‘NDHWC’, ‘NHWC’, ‘NWC’},optional, default=’None’: Set layout for input and output. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.
out : ndarray, optional: The output ndarray to hold the result.

Returns:

out : ndarray or list of ndarrays: The output of this function.