Normalizing Data

Learn about data normalization and implement a normalization function.

We'll cover the following

Chapter Goals:

  • Learn how to apply L2 normalization to data

L2 normalization

So far, each of the scaling techniques we've used has been applied to the data features (i.e. columns). However, in certain cases we want to scale the individual data observations (i.e. rows). For instance, when clustering data we need to apply L2 normalization to each row, in order to calculate cosine similarity scores. The Clustering section will cover data clustering and cosine similarities in greater depth.

L2 normalization applied to a particular row of a data array will divide each value in that row by the row's L2 norm. In general terms, the L2 norm of a row is just the square root of the sum of squared values for the row.

X=[x1,x2,...,xm]X = [x_1, x_2, ..., x_m]

XL2=[x1ℓ,x2ℓ,...,xmℓ],where ℓ=∑i=1mxi2X_{L2} = \left[\frac{x_1}{\ell}, \frac{x_2}{\ell}, ..., \frac{x_m}{\ell}\right], \text{where } \ell = \sqrt{\sum_{i = 1}^m x_i^2}

The above formula demonstrates L2 normalization applied to row X to obtain the normalized row of values, XL2.

In scikit-learn, the transformer module that implements L2 normalization is the Normalizer.

The code below shows how to use the Normalizer.

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# predefined data
print('{}\n'.format(repr(data)))
from sklearn.preprocessing import Normalizer
normalizer = Normalizer()
transformed = normalizer.fit_transform(data)
print('{}\n'.format(repr(transformed)))

Time to Code!

The coding exercise in this chapter uses Normalizer (imported in backend) to complete the normalize_data function.

The function will apply L2 normalization to the input NumPy array, data.

Set normalizer equal to Normalizer initialized without any parameters.

Set norm_data equal to normalizer.fit_transform applied with data as the only argument. Then return norm_data.

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def normalize_data(data):
  # CODE HERE
  pass

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