# mx.nd.L2Normalization¶

## Description¶

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]]]


## Arguments¶

Argument

Description

data

NDArray-or-Symbol.

Input array to normalize.

eps

float, optional, default=1.00000001e-10.

A small constant for numerical stability.

mode

{‘channel’, ‘instance’, ‘spatial’},optional, default=’instance’.

Specify the dimension along which to compute L2 norm.

## Value¶

out The result mx.ndarray