Normalization and Scaling

Normalization and Scaling are two fundamental preprocessing techniques when you perform data analysis and machine learning. They are useful when you want to rescale, standardize or normalize the features (values) through distribution and scaling of existing data that make your machine learning models have better performance and accuracy.

This guide covers the following strategies and explains their importance, varied approaches, as well as real-world examples.

Normalization is a process that transforms your data’s features to a standard scale, typically between 0 and 1. This is achieved by adjusting each feature’s values based on its minimum and maximum values. The goal is to ensure that no single feature dominates the others due to its magnitude.

Why Normalize?

• Improved Model Convergence: Algorithms like gradient descent often converge faster when features are on a similar scale.
• Fairness Across Features: In distance-based algorithms (e.g., k-nearest neighbors), normalization prevents features with larger ranges from disproportionately influencing results.
• Enhanced Interpretability: Comparing and interpreting feature importances is easier when they’re on the same scale.

1. Min-Max Normalization

Min-max scaling, also known as rescaling, is a popular normalization technique that rescales the data to a common range, usually between 0 and 1. This is achieved by subtracting the minimum value and then dividing by the range of the data.\

?_norm = ? − ?_min / ?_max − ?_min​​

Example: Suppose we have a dataset with a feature “Age” ranging from 18 to 80. To normalize this feature using min-max scaling, we would subtract 18 (the minimum value) from each age and then divide by 62 (the range of the data). This would result in a normalized feature with values between 0 and 1.

2. Max-Abs Normalization

Scales each feature by its maximum absolute value.

?_{norm =} ? / ∣?_max∣

3. Mean Normalization

Centers the data around the mean and scales it to a range of [-1, 1].

?_???? = ? − ? / ?_??? − ?_???

4. Z-Score Normalization

Z-score normalization, also known as standardization, transforms data into a standard normal distribution with a mean of 0 and a standard deviation of 1. This technique is useful when the data follows a normal distribution.

Example: Suppose we have a dataset with a feature “Height” with a mean of 175 cm and a standard deviation of 10 cm. To normalize this feature using z-score normalization, we would subtract the mean from each height and then divide by the standard deviation. This would result in a normalized feature with a mean of 0 and a standard deviation of 1.

5. Log Scaling

Log scaling is a normalization technique that is useful when the data has a skewed distribution. This technique involves taking the logarithm of the data to reduce the effect of extreme values.

Example: Suppose we have a dataset with a feature “Income” that has a skewed distribution. To normalize this feature using log scaling, we would take the logarithm of each income value. This would result in a normalized feature with a more even distribution.

Scaling is a broader term that encompasses both normalization and standardization. While normalization aims for a specific range (0-1), scaling adjusts the spread or variability of your data.

Why Scale?

• Robustness to Outliers: Scaling can make your models less sensitive to extreme values.
• Algorithm Compatibility: Some algorithms, like Support Vector Machines and Principal Component Analysis, work best with scaled data.

1. Standardization

Standardization Scales features to have a mean of 0 and a standard deviation of 1.

?_?????? = ? − ? / ?

Example: This is helpful when your data follows a normal distribution and you want to emphasize relative distances from the mean.

2. Robust Scaling

Uses the median and interquartile range (IQR) to scale the data.

?_?????? = ? − median / IQR

3. Feature Scaling

Feature scaling involves transforming individual features into a common range to prevent features with large ranges from dominating the analysis. This is similar to normalization, but feature scaling can involve transforming data into a range other than 0 to

Example: Suppose we have a dataset with two features, “Age” and “Income,” and we want to scale them to a range of -1 to 1. We would subtract the mean from each feature and then divide by the range of the data.

4. Dimensionality Reduction

Dimensionality reduction involves reducing the number of features in a dataset to prevent the curse of dimensionality. Techniques such as principal component analysis (PCA) and singular value decomposition (SVD) are commonly used for dimensionality reduction.

Example: Suppose we have a dataset with 100 features, but we want to reduce the dimensionality to 10 features. We would use PCA to identify the 10 most important features that capture the majority of the variance in the data.

5. Categorical Scaling

Categorical scaling involves transforming categorical data into numerical data. Techniques such as one-hot encoding and label encoding are commonly used for categorical scaling.

Example: Suppose we have a dataset with a categorical feature “Color” that has three categories: red, green, and blue. We would use one-hot encoding to transform this feature into three numerical features: “Red,” “Green,” and “Blue,” each with a value of 0 or 1.

Normalization and scaling are both techniques used to preprocess numerical data before feeding it into machine learning algorithms.

If the data does not follow a Gaussian distribution or if you are unsure, normalizing your data is a good idea. One exception to the above could be when your data is normally distributed. Scaling is necessary when the algorithm you are using, such as support vector machines (SVM) and linear regression, requires that your data be normally distributed or in some cases a Gaussian Distribution.

Normalization and scaling are crucial steps in data preprocessing. They ensure that all features are on the same footing, preventing any single feature from dominating the analysis. This is particularly important in machine learning, where algorithms can be sensitive to the scale of the data.

• Improved Model Performance: Normalization and scaling can improve the performance of machine learning models by reducing the effect of features with large ranges. This enables models to focus on the underlying patterns in the data rather than being biased towards features with large values.
• Faster Model Training: Normalization and scaling can also speed up the training process of machine learning models. By reducing the scale of the data, models can converge faster and require less computational resources.
• Better Data Visualization: Normalization and scaling can also improve data visualization. By transforming data into a common range, it becomes easier to visualize and compare different features.

• Effect on sparsity: Normalization may alter the sparsity of the data, particularly if the original features contain many zero values.
• Robustness: It’s sensitive to outliers, especially if the range of values is skewed by extreme values.
• Feature importance: Normalization can potentially distort the importance of features if the range of values is not representative of their significance.
• Impact on distance-based algorithms: It can affect the performance of distance-based algorithms if the distance metric relies on the scale of features.
• Handling categorical features: Normalization needs special treatment for categorical features, as they don’t have meaningful minimum and maximum values.
• Impact on interpretability: It retains the original interpretation of the data within a known range, making it easier to interpret feature values.
• Computational efficiency: Normalization can be computationally expensive for large datasets, as it requires finding minimum and maximum values for each feature.

• Effect on sparsity: Scaling generally preserves sparsity, especially if the scaling factor does not affect zero values.
• Robustness: Scaling is more robust to outliers due to centering data around the mean and scaling based on standard deviation.
• Feature importance: It preserves the relative importance of features, as it only adjusts their scale and center.
• Impact on distance-based algorithms: Scaling is less likely to affect the performance of distance-based algorithms, as the scale is standardized across features.
• Handling categorical features: Scaling treats categorical features similarly to numerical features, which may not always be appropriate.
• Impact on interpretability: Scaling may slightly affect interpretability, especially if the scale and center of features are transformed.
• Computational efficiency: Scaling is more computationally efficient compared to normalization, as it involves calculating mean and standard deviation for each feature.

Data scaling and normalization are necessary steps for the preprocessing of data as input for machine learning models. The best thing you can do is acquire strategies for learning and use them. These are the things that will greatly increase your accuracy as well as boost your model building performance! The type of the data you have and the properties of these special algorithms will decide whether we’ll use scaling or normalization.