# mxnet.ndarray.L2Normalization¶

mxnet.ndarray.L2Normalization(data=None, eps=_Null, mode=_Null, out=None, name=None, **kwargs)

Normalize the input array using the L2 norm.

For 1-D NDArray, it computes:

out = data / sqrt(sum(data ** 2) + eps)


For N-D NDArray, if the input array has shape (N, N, …, N),

with mode = instance, it normalizes each instance in the multidimensional array by its L2 norm.:

for i in 0...N
out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps)


with mode = channel, it normalizes each channel in the array by its L2 norm.:

for i in 0...N
out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps)


with mode = spatial, it normalizes the cross channel norm for each position in the array by its L2 norm.:

for dim in 2...N
for i in 0...N
out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps)
-dim-


Example:

x = [[[1,2],
[3,4]],
[[2,2],
[5,6]]]

L2Normalization(x, mode='instance')
=[[[ 0.18257418  0.36514837]
[ 0.54772252  0.73029673]]
[[ 0.24077171  0.24077171]
[ 0.60192931  0.72231513]]]

L2Normalization(x, mode='channel')
=[[[ 0.31622776  0.44721359]
[ 0.94868326  0.89442718]]
[[ 0.37139067  0.31622776]
[ 0.92847669  0.94868326]]]

L2Normalization(x, mode='spatial')
=[[[ 0.44721359  0.89442718]
[ 0.60000002  0.80000001]]
[[ 0.70710677  0.70710677]
[ 0.6401844   0.76822126]]]


Defined in src/operator/l2_normalization.cc:L196

Parameters
• data (NDArray) – Input array to normalize.

• eps (float, optional, default=1e-10) – A small constant for numerical stability.

• mode ({'channel', 'instance', 'spatial'},optional, default='instance') – Specify the dimension along which to compute L2 norm.

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays