averagePooling2dLayer

Average pooling layer

Description

An average pooling layer performs down-sampling by dividing the input into rectangular pooling regions and computing the average values of each region.

Creation

Syntax

layer = averagePooling2dLayer(poolSize)

layer = averagePooling2dLayer(poolSize,Name,Value)

Description

layer = averagePooling2dLayer(poolSize) creates an average pooling layer and sets the PoolSize property.

layer = averagePooling2dLayer(poolSize,Name,Value) sets the optional Stride and Name properties using name-value pairs. To specify input padding, use the 'Padding' name-value pair argument. For example, averagePooling2dLayer(2,'Stride',2) creates an average pooling layer with pool size [2 2] and stride [2 2]. You can specify multiple name-value pairs. Enclose each property name in single quotes.

Input Arguments

Name-Value Pair Arguments

Use comma-separated name-value pair arguments to specify the size of the zero padding to add along the edges of the layer input or to set the Stride and Name properties. Enclose names in single quotes.

Example: averagePooling2dLayer(2,'Stride',2) creates an average pooling layer with pool size [2 2] and stride [2 2].

'Padding' — Input edge padding

[0 0 0 0] (default) | vector of nonnegative integers | 'same'

Input edge padding, specified as the comma-separated pair consisting of 'Padding' and one of these values:

• 'same' — Add padding of size calculated by the software at training or prediction time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size is ceil(inputSize/stride), where inputSize is the height or width of the input and stride is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, and to the left and right, if possible. If the padding that must be added vertically has an odd value, then the software adds extra padding to the bottom. If the padding that must be added horizontally has an odd value, then the software adds extra padding to the right.

• Nonnegative integer p — Add padding of size p to all the edges of the input.

• Vector [a b] of nonnegative integers — Add padding of size a to the top and bottom of the input and padding of size b to the left and right.

• Vector [t b l r] of nonnegative integers — Add padding of size t to the top, b to the bottom, l to the left, and r to the right of the input.

Example: 'Padding',1 adds one row of padding to the top and bottom, and one column of padding to the left and right of the input.

Example: 'Padding','same' adds padding so that the output has the same size as the input (if the stride equals 1).

Properties

Average Pooling

PoolSize — Dimensions of pooling regions

vector of two positive integers

Dimensions of the pooling regions, specified as a vector of two positive integers [h w], where h is the height and w is the width. When creating the layer, you can specify PoolSize as a scalar to use the same value for both dimensions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions PoolSize.

Example: [2 1] specifies pooling regions of height 2 and width 1.

Stride — Step size for traversing input

[1 1] (default) | vector of two positive integers

Step size for traversing the input vertically and horizontally, specified as a vector of two positive integers [a b], where a is the vertical step size and b is the horizontal step size. When creating the layer, you can specify Stride as a scalar to use the same value for both dimensions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions PoolSize.

Example: [2 3] specifies a vertical step size of 2 and a horizontal step size of 3.

PaddingSize — Size of padding

[0 0 0 0] (default) | vector of four nonnegative integers

Size of padding to apply to input borders, specified as a vector [t b l r] of four nonnegative integers, where t is the padding applied to the top, b is the padding applied to the bottom, l is the padding applied to the left, and r is the padding applied to the right.

When you create a layer, use the 'Padding' name-value pair argument to specify the padding size.

Example: [1 1 2 2] adds one row of padding to the top and bottom, and two columns of padding to the left and right of the input.

PaddingMode — Method to determine padding size

'manual' (default) | 'same'

Method to determine padding size, specified as 'manual' or 'same'.

The software automatically sets the value of PaddingMode based on the 'Padding' value you specify when creating a layer.

• If you set the 'Padding' option to a scalar or a vector of nonnegative integers, then the software automatically sets PaddingMode to 'manual'.

• If you set the 'Padding' option to 'same', then the software automatically sets PaddingMode to 'same' and calculates the size of the padding at training time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size is ceil(inputSize/stride), where inputSize is the height or width of the input and stride is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, and to the left and right, if possible. If the padding that must be added vertically has an odd value, then the software adds extra padding to the bottom. If the padding that must be added horizontally has an odd value, then the software adds extra padding to the right.

PaddingValue — Value used to pad input

0 (default) | 'mean'

Value used to pad input, specified as 0 or 'mean'.

When you use the 'Padding' option to add padding to the input, the value of the padding applied can be one of the following:

• 0 — Input is padded with zeros at the positions specified by the 'Padding' option. The padded areas are included in the calculation of the average value of the pooling regions along the edges.

• 'mean' — Input is padded with the mean of the pooling region at the positions specified by the 'Padding' option. The padded areas are effectively excluded from the calculation of the average value of each pooling region.

Example: 'PaddingValue','mean'

Padding — Size of padding

[0 0] (default) | vector of two nonnegative integers

Note

Padding property will be removed in a future release. Use PaddingSize instead. When creating a layer, use the 'Padding' name-value pair argument to specify the padding size.

Size of padding to apply to input borders vertically and horizontally, specified as a vector [a b] of two nonnegative integers, where a is the padding applied to the top and bottom of the input data and b is the padding applied to the left and right.

Example: [1 1] adds one row of padding to the top and bottom, and one column of padding to the left and right of the input.

Layer

Name — Layer name

'' (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. To include a layer in a layer graph, you must specify a nonempty unique layer name. If you train a series network with the layer and Name is set to '', then the software automatically assigns a name to the layer at training time.

Data Types: char | string

NumInputs — Number of inputs

1 (default)

Number of inputs of the layer. This layer accepts a single input only.

Data Types: double

InputNames — Input names

{'in'} (default)

Input names of the layer. This layer accepts a single input only.

Data Types: cell

NumOutputs — Number of outputs

1 (default)

Number of outputs of the layer. This layer has a single output only.

Data Types: double

OutputNames — Output names

{'out'} (default)

Output names of the layer. This layer has a single output only.

Data Types: cell

Examples

Create Average Pooling Layer

Create an average pooling layer with the name 'avg1'.

layer = averagePooling2dLayer(2,'Name','avg1')

layer = 
  AveragePooling2DLayer with properties:

            Name: 'avg1'

   Hyperparameters
        PoolSize: [2 2]
          Stride: [1 1]
     PaddingMode: 'manual'
     PaddingSize: [0 0 0 0]
    PaddingValue: 0

Include an average pooling layer in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer
    averagePooling2dLayer(2)
    fullyConnectedLayer(10)
    softmaxLayer
    classificationLayer]

layers = 
  7x1 Layer array with layers:

     1   ''   Image Input             28x28x1 images with 'zerocenter' normalization
     2   ''   Convolution             20 5x5 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   ReLU                    ReLU
     4   ''   Average Pooling         2x2 average pooling with stride [1  1] and padding [0  0  0  0]
     5   ''   Fully Connected         10 fully connected layer
     6   ''   Softmax                 softmax
     7   ''   Classification Output   crossentropyex

Create Average Pooling Layer with Nonoverlapping Pooling Regions

Create an average pooling layer with nonoverlapping pooling regions.

layer = averagePooling2dLayer(2,'Stride',2)

layer = 
  AveragePooling2DLayer with properties:

            Name: ''

   Hyperparameters
        PoolSize: [2 2]
          Stride: [2 2]
     PaddingMode: 'manual'
     PaddingSize: [0 0 0 0]
    PaddingValue: 0

The height and width of the rectangular regions (pool size) are both 2. The pooling regions do not overlap because the step size for traversing the images vertically and horizontally (stride) is also 2.

Include an average pooling layer with nonoverlapping regions in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer
    averagePooling2dLayer(2,'Stride',2)
    fullyConnectedLayer(10)
    softmaxLayer
    classificationLayer]

layers = 
  7x1 Layer array with layers:

     1   ''   Image Input             28x28x1 images with 'zerocenter' normalization
     2   ''   Convolution             20 5x5 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   ReLU                    ReLU
     4   ''   Average Pooling         2x2 average pooling with stride [2  2] and padding [0  0  0  0]
     5   ''   Fully Connected         10 fully connected layer
     6   ''   Softmax                 softmax
     7   ''   Classification Output   crossentropyex

Create Average Pooling Layer with Overlapping Pooling Regions

Create an average pooling layer with overlapping pooling regions.

layer = averagePooling2dLayer([3 2],'Stride',2)

layer = 
  AveragePooling2DLayer with properties:

            Name: ''

   Hyperparameters
        PoolSize: [3 2]
          Stride: [2 2]
     PaddingMode: 'manual'
     PaddingSize: [0 0 0 0]
    PaddingValue: 0

This layer creates pooling regions of size [3 2] and takes the average of the six elements in each region. The pooling regions overlap because Stride includes dimensions that are less than the respective pooling dimensions PoolSize.

Include an average pooling layer with overlapping pooling regions in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(5,20)
    reluLayer
    averagePooling2dLayer([3 2],'Stride',2)
    fullyConnectedLayer(10)
    softmaxLayer
    classificationLayer]

layers = 
  7x1 Layer array with layers:

     1   ''   Image Input             28x28x1 images with 'zerocenter' normalization
     2   ''   Convolution             20 5x5 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   ReLU                    ReLU
     4   ''   Average Pooling         3x2 average pooling with stride [2  2] and padding [0  0  0  0]
     5   ''   Fully Connected         10 fully connected layer
     6   ''   Softmax                 softmax
     7   ''   Classification Output   crossentropyex

More About

Average Pooling Layer

An average pooling layer performs down-sampling by dividing the input into rectangular pooling regions and computing the average values of each region.

Pooling layers follow the convolutional layers for down-sampling, hence, reducing the number of connections to the following layers. They do not perform any learning themselves, but reduce the number of parameters to be learned in the following layers. They also help reduce overfitting.

An average pooling layer outputs the average values of rectangular regions of its input. The size of the rectangular regions is determined by the poolSize argument of averagePoolingLayer. For example, if poolSize is [2,3], then the layer returns the average value of regions of height 2 and width 3.

Pooling layers scan through the input horizontally and vertically in step sizes you can specify using the 'Stride' name-value pair argument. If the pool size is smaller than or equal to the stride, then the pooling regions do not overlap.

For nonoverlapping regions (Pool Size and Stride are equal), if the input to the pooling layer is n-by-n, and the pooling region size is h-by-h, then the pooling layer down-samples the regions by h [1]. That is, the output of a max or average pooling layer for one channel of a convolutional layer is n/h-by-n/h. For overlapping regions, the output of a pooling layer is (Input Size – Pool Size + 2*Padding)/Stride + 1.

References

[1] Nagi, J., F. Ducatelle, G. A. Di Caro, D. Ciresan, U. Meier, A. Giusti, F. Nagi, J. Schmidhuber, L. M. Gambardella. ''Max-Pooling Convolutional Neural Networks for Vision-based Hand Gesture Recognition''. IEEE International Conference on Signal and Image Processing Applications (ICSIPA2011), 2011.

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