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instancenorm

Normalize across each channel for each observation independently

Description

The instance normalization operation normalizes the input data across each channel for each observation independently. To improve the convergence of training the convolutional neural network and reduce the sensitivity to network hyperparameters, use instance normalization between convolution and nonlinear operations such as relu.

After normalization, the operation shifts the input by a learnable offset β and scales it by a learnable scale factor γ.

The instancenorm function applies the layer normalization operation to dlarray data. Using dlarray objects makes working with high dimensional data easier by allowing you to label the dimensions. For example, you can label which dimensions correspond to spatial, time, channel, and batch dimensions using the 'S', 'T', 'C', and 'B' labels, respectively. For unspecified and other dimensions, use the 'U' label. For dlarray object functions that operate over particular dimensions, you can specify the dimension labels by formatting the dlarray object directly, or by using the 'DataFormat' option.

Note

To apply instance normalization within a layerGraph object or Layer array, use instanceNormalizationLayer.

example

dlY = instancenorm(dlX,offset,scaleFactor) applies the instance normalization operation to the input data dlX and transforms using the specified offset and scale factor.

The function normalizes over grouped subsets of the 'S' (spatial), 'T' (time), and 'U' (unspecified) dimensions of dlX for each observation in the 'C' (channel) and 'B' (batch) dimensions, independently.

For unformatted input data, use the 'DataFormat' option.

dlY = instancenorm(dlX,offset,scaleFactor,'DataFormat',FMT) applies the instance normalization operation to the unformatted dlarray object dlX with format specified by FMT using any of the previous syntaxes. The output dlY is an unformatted dlarray object with dimensions in the same order as dlX. For example, 'DataFormat','SSCB' specifies data for 2-D image input with format 'SSCB' (spatial, spatial, channel, batch).

dlY = instancenorm(___Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in previous syntaxes. For example, 'Epsilon',3e-5 sets the variance offset to 3e-5.

Examples

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Create randomized input data with two spatial, one channel, and one observation dimension.

width = 12;
height = 12;
channels = 6;
numObservations = 16;
X = randn(width,height,channels,numObservations);
dlX = dlarray(X,'SSCB'); 

Create the learnable parameters.

offset = dlarray(zeros(channels,1));
scaleFactor = dlarray(ones(channels,1));

Calculate the instance normalization.

dlZ = instancenorm(dlX,offset,scaleFactor);

View the size and format of the normalized data.

size(dlZ)
ans = 1×4

    12    12     6    16

dims(dlZ)
ans = 
'SSCB'

Input Arguments

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Input data, specified as a formatted dlarray, an unformatted dlarray, or a numeric array.

If dlX is an unformatted dlarray or a numeric array, then you must specify the format using the 'DataFormat' option. If dlX is a numeric array, then either scaleFactor or offset must be a dlarray object.

dlX must have a 'C' (channel) dimension.

Offset β, specified as a formatted dlarray, an unformatted dlarray, or a numeric array with one nonsingleton dimension with size matching the size of the 'C' (channel) dimension of the input dlX.

If offset is a formatted dlarray object, then the nonsingleton dimension must have label 'C' (channel).

Scale factor γ, specified as a formatted dlarray, an unformatted dlarray, or a numeric array with one nonsingleton dimension with size matching the size of the 'C' (channel) dimension of the input dlX.

If scaleFactor is a formatted dlarray object, then the nonsingleton dimension must have label 'C' (channel).

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'Epsilon',3e-5 sets the variance offset to 3e-5.

Dimension order of unformatted input data, specified as the comma-separated pair consisting of 'DataFormat' and a character vector or string scalar FMT that provides a label for each dimension of the data.

When specifying the format of a dlarray object, each character provides a label for each dimension of the data and must be one of the following:

  • 'S' — Spatial

  • 'C' — Channel

  • 'B' — Batch (for example, samples and observations)

  • 'T' — Time (for example, time steps of sequences)

  • 'U' — Unspecified

You can specify multiple dimensions labeled 'S' or 'U'. You can use the labels 'C', 'B', and 'T' at most once.

You must specify 'DataFormat' when the input data is not a formatted dlarray.

Example: 'DataFormat','SSCB'

Data Types: char | string

Variance offset for preventing divide-by-zero errors, specified as the comma-separated pair consisting of 'Epsilon' and a numeric scalar. The specified value must be greater than 1e-5. The default value is 1e-5.

Data Types: single | double

Output Arguments

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Normalized data, returned as a dlarray. The output dlY has the same underlying data type as the input dlX.

If the input data dlX is a formatted dlarray, dlY has the same dimension labels as dlX. If the input data is not a formatted dlarray, dlY is an unformatted dlarray with the same dimension order as the input data.

Algorithms

The instance normalization operation normalizes the elements xi of the input by first calculating the mean μI and variance σI2 over the spatial and time dimensions for each channel in each observation independently. Then, it calculates the normalized activations as

xi^=xiμIσI2+ϵ,

where ϵ is a constant that improves numerical stability when the variance is very small.

To allow for the possibility that inputs with zero mean and unit variance are not optimal for the operations that follow instance normalization, the instance normalization operation further shifts and scales the activations using the transformation

yi=γx^i+β,

where the offset β and scale factor γ are learnable parameters that are updated during network training.

Extended Capabilities

Introduced in R2021a