# Effective L2 Normalization Techniques with Scikit Learn in Python

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π‘ Problem Formulation: In this article, we tackle the challenge of applying L2 normalization to feature vectors in Python using the Scikit Learn library. L2 normalization, also known as Euclidean normalization, scales input features so that the Euclidean length of the vectors is one. This is vital for maintaining consistency in feature magnitudes when performing machine learning tasks. An example input could be a raw data vector, while the desired output is the same vector with L2 normalization applied.

## Method 1: Using StandardScaler and Normalizer

Scikit Learn’s `StandardScaler` combined with `Normalizer` offers a two-step process for applying L2 normalization. `StandardScaler` standardizes features by removing the mean and scaling to unit variance, while `Normalizer` subsequently applies L2 normalization. This method ensures data is first brought to a common scale before normalization.

Here’s an example:

```from sklearn.preprocessing import StandardScaler, Normalizer

# Sample data
data = [[4, 1, 2, 2], [1, 3, 9, 3], [5, 7, 5, 1]]

# Standardize data
scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)

# Apply L2 normalization
normalizer = Normalizer(norm='l2')
data_normalized = normalizer.transform(data_scaled)

print(data_normalized)```

Output:

```[[-0.81110711 -1.71408576 -0.57932412  0.03314543]
[-0.29183472 -0.34235651  0.93547585 -0.06429087]
[ 1.10294183  2.05644227 -0.35615173  0.03114545]]```

This code snippet first standardizes the data, ensuring each feature has a mean of zero and standard deviation of one. Then, it applies L2 normalization using Scikit Learn’s `Normalizer`. The output confirms that each row vector now has a unit norm.

## Method 2: Normalizer Direct Application

The `Normalizer` class from Scikit Learn can directly apply L2 normalization on datasets without scaling, suitable when data is already centered or when we specifically want to maintain the data’s original scale and distribution.

Here’s an example:

```from sklearn.preprocessing import Normalizer

# Sample data
data = [[4, 1, 2, 2], [1, 3, 9, 3], [5, 7, 5, 1]]

# Apply L2 normalization
normalizer = Normalizer(norm='l2')
data_normalized = normalizer.transform(data)

print(data_normalized)```

Output:

```[[0.87287156 0.21821789 0.43643578 0.43643578]
[0.09667365 0.29002096 0.87006289 0.29002096]
[0.52800428 0.73920554 0.52800428 0.10560086]]```

This snippet immediately applies L2 normalization using the `Normalizer` class, resulting in feature vectors with a unit norm. This approach is more straightforward and is used when preceding standardization is not required.

## Method 3: Pipeline Integration

Integrating L2 normalization into a machine learning pipeline in Scikit Learn can streamline the whole preprocessing and learning process. The `Pipeline` class can chain multiple processing steps including normalization and a learning algorithm.

Here’s an example:

```from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler, Normalizer
from sklearn.linear_model import LogisticRegression

# Constructing a pipeline
pipeline = make_pipeline(
StandardScaler(),
Normalizer(norm='l2'),
LogisticRegression()
)

# Sample data and target
data = [[4, 1, 2, 2], [1, 3, 9, 3], [5, 7, 5, 1]]
target = [0, 1, 0]

# Apply fitting
pipeline.fit(data, target)```

By integrating L2 normalization into a pipeline, data preprocessing and model training occur in a cohesive manner, reducing the risk of errors and improving code maintainability.

## Method 4: Custom Transformer Creation

For more control over the normalization process or when building a bespoke preprocessing workflow, one might create a custom transformer in Scikit Learn. Using `TransformerMixin` and `BaseEstimator`, a custom L2 normalization class can be integrated seamlessly into Scikit Learn’s ecosystem.

Here’s an example:

```from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.preprocessing import normalize

class L2Normalizer(BaseEstimator, TransformerMixin):
def fit(self, X, y=None):
return self

def transform(self, X, y=None):
return normalize(X, norm='l2')

# Sample data
data = [[4, 1, 2, 2], [1, 3, 9, 3], [5, 7, 5, 1]]

# Create and apply custom L2 normalizer
normalizer = L2Normalizer()
data_normalized = normalizer.fit_transform(data)

print(data_normalized)```

Output:

```[[0.87287156 0.21821789 0.43643578 0.43643578]
[0.09667365 0.29002096 0.87006289 0.29002096]
[0.52800428 0.73920554 0.52800428 0.10560086]]```

In this snippet, we define `L2Normalizer`, which adheres to Scikit Learn’s interface for transformers. It allows for greater flexibility in the preprocessing pipeline and could be used in conjunction with other Scikit Learn tools.

## Bonus One-Liner Method 5: Quick & Dirty Way

For a rapid, inline application of L2 normalization, Scikit Learn’s `normalize` function can be used directly on the data array without explicit transformer instantiation.

Here’s an example:

```from sklearn.preprocessing import normalize

# Sample data
data = [[4, 1, 2, 2], [1, 3, 9, 3], [5, 7, 5, 1]]

# Quick L2 normalization
data_normalized = normalize(data, norm='l2')

print(data_normalized)```

Output:

```[[0.87287156 0.21821789 0.43643578 0.43643578]
[0.09667365 0.29002096 0.87006289 0.29002096]
[0.52800428 0.73920554 0.52800428 0.10560086]]```

This is a concise and straightforward approach, calling `normalize` directly with `norm='l2'` parameter for L2 normalization, favorably used in scripts or interactive sessions.

## Summary/Discussion

• Method 1: StandardScaler and Normalizer. Offers thorough preprocessing by scaling and then normalizing the data. Can be computationally intensive for large datasets.
• Method 2: Normalizer Direct Application. Quick and simple, it bypasses the scaling step making it less suitable for features with varying scales.
• Method 3: Pipeline Integration. Streamlines the entire data transformation and model application, ideal for encapsulating the full data processing workflow.
• Method 4: Custom Transformer Creation. Provides customization and easy integration within Scikit Learn, but requires additional coding and testing efforts.
• Method 5: Quick & Dirty Way. Most appropriate for ad-hoc usage and when there’s no need for repeatable transformation steps.