The pooling operation involves sliding a two-dimensional filter over each channel of feature map and summarising the features lying within the region covered by the filter.
For a feature map having dimensions nh x nw x nc, the dimensions of output obtained after a pooling layer is
(nh - f + 1) / s x (nw - f + 1)/s x nc
where,
-> nh - height of feature map
-> nw - width of feature map
-> nc - number of channels in the feature map
-> f - size of filter
-> s - stride length
A common CNN model architecture is to have a number of convolution and pooling layers stacked one after the other.
Why to use Pooling Layers?
Pooling layers are used to reduce the dimensions of the feature maps. Thus, it reduces the number of parameters to learn and the amount of computation performed in the network.
The pooling layer summarises the features present in a region of the feature map generated by a convolution layer. So, further operations are performed on summarised features instead of precisely positioned features generated by the convolution layer. This makes the model more robust to variations in the position of the features in the input image.
Types of Pooling Layers
Max Pooling
Max pooling is a pooling operation that selects the maximum element from the region of the feature map covered by the filter. Thus, the output after max-pooling layer would be a feature map containing the most prominent features of the previous feature map.
This can be achieved using MaxPooling2D layer in keras as follows:
Code #1 : Performing Max Pooling using keras
import numpy as np
from keras.models import Sequential
from keras.layers import MaxPooling2D
# define input image
image = np.array([[2, 2, 7, 3],
[9, 4, 6, 1],
[8, 5, 2, 4],
[3, 1, 2, 6]])
image = image.reshape(1, 4, 4, 1)
# define model containing just a single max pooling layer
model = Sequential(
[MaxPooling2D(pool_size = 2, strides = 2)])
# generate pooled output
output = model.predict(image)
# print output image
output = np.squeeze(output)
print(output)
Output:
[[9. 7.]
[8. 6.]]
Average Pooling
Average pooling computes the average of the elements present in the region of feature map covered by the filter. Thus, while max pooling gives the most prominent feature in a particular patch of the feature map, average pooling gives the average of features present in a patch.
Code #2 : Performing Average Pooling using keras
import numpy as np
from keras.models import Sequential
from keras.layers import AveragePooling2D
# define input image
image = np.array([[2, 2, 7, 3],
[9, 4, 6, 1],
[8, 5, 2, 4],
[3, 1, 2, 6]])
image = image.reshape(1, 4, 4, 1)
# define model containing just a single average pooling layer
model = Sequential(
[AveragePooling2D(pool_size = 2, strides = 2)])
# generate pooled output
output = model.predict(image)
# print output image
output = np.squeeze(output)
print(output)
Output:
[[4.25 4.25]
[4.25 3.5 ]]
Global Pooling
Global pooling reduces each channel in the feature map to a single value. Thus, an nh x nw x nc feature map is reduced to 1 x 1 x nc feature map. This is equivalent to using a filter of dimensions nh x nw i.e. the dimensions of the feature map.
Further, it can be either global max pooling or global average pooling.
Code #3 : Performing Global Pooling using keras
import numpy as np
from keras.models import Sequential
from keras.layers import GlobalMaxPooling2D
from keras.layers import GlobalAveragePooling2D
# define input image
image = np.array([[2, 2, 7, 3],
[9, 4, 6, 1],
[8, 5, 2, 4],
[3, 1, 2, 6]])
image = image.reshape(1, 4, 4, 1)
# defne gm_model containing just a single global-max pooling layer
gm_model = Sequential(
[GlobalMaxPooling2D()])
# define ga_model containing just a single global-average pooling layer
ga_model = Sequential(
[GlobalAveragePooling2D()])
# generate pooled output
gm_output = gm_model.predict(image)
ga_output = ga_model.predict(image)
# print output image
gm_output = np.squeeze(gm_output)
ga_output = np.squeeze(ga_output)
print("gm_output: ", gm_output)
print("ga_output: ", ga_output)
Output:
gm_output: 9.0
ga_output: 4.0625