A Guide to Scaling and Normalizing Data for ML Models

A crucial stage in machine learning is data preparation, which guarantees that models are given meaningful, organized data to train on. Scaling and normalizing are two of the most important preprocessing methods for enhancing the precision, effectiveness, and stability of machine learning models.

Many algorithms demand that input characteristics be on a same scale, especially those that use distance computations, such support vector machines (SVM), k-nearest neighbours (KNN), and linear regression. The model may give some features an excessive amount of weight if feature values differ greatly, which could result in biased predictions.

In order to improve model performance, this guide examines the distinctions between scaling and normalization, the approaches taken, and the appropriate times to employ each methodology.

Why Scaling and Normalization Are Important

Numerical values with varying magnitudes or units are frequently present in raw data. For example, a house's square footage could range from 500 to 5000 in a dataset that predicts property values, and its number of bedrooms could range from 1 to 5. Even though both are equally important, a model may give square footage more weight than the number of bedrooms because it offers a wider range of numbers.

The key reasons for scaling and normalizing data are:

• Enhancing model convergence: When features have a similar scale, many optimization procedures, including gradient descent, work better and achieve faster, more stable convergence.

• Improving accuracy: Models are able to produce more objective and precise predictions when features are appropriately scaled.

• Preventing numerical instability: Significant variations in feature magnitudes can lead to computational problems, particularly for machine learning models such as SVMs and neural networks.

• Making sure that distance computations are improved: Euclidean distance is the foundation of distance-based algorithms like KNN and clustering techniques, and improper data scaling can distort it.

Understanding Scaling and Normalization

Although often used interchangeably, scaling and normalization are distinct concepts.

• Scaling transforms data to ensure that numerical values fall within a specific range, such as 0 to 1 or -1 to 1.

• Normalization adjusts values so that they follow a common distribution, often ensuring that they have a mean of 0 and a standard deviation of 1.

Scaling Methods

Min-Max Scaling (Rescaling)

Min-Max scaling transforms data by adjusting feature values within a fixed range, typically between 0 and 1. The formula is:

Where:

• X is the original value of the feature.

• ​ and ​ are the minimum and maximum values of the feature.

• X′ is the rescaled value.

Min-Max scaling preserves the relationships between data points but is highly sensitive to outliers. This method is commonly used in deep learning and neural networks, where features should be on a consistent scale.

Standardization (Z-score Normalization)

Standardization scales features so that they have a mean of 0 and a standard deviation of 1. It is calculated using the formula:

Where:

• μ is the mean of the feature.

• σ is the standard deviation of the feature.

• X′ is the standardized value.

This method is particularly useful when data follows a normal distribution. It is widely applied in algorithms such as logistic regression and linear regression, where maintaining the statistical properties of the data is important.

Normalization Methods

L1 Normalization (Least Absolute Deviation or Manhattan Norm)

L1 normalization scales feature values so that the sum of their absolute values equals 1. It is computed as:

This technique is beneficial when working with sparse datasets, such as text-based models where word frequencies need to be normalized.

L2 Normalization (Least Squares Normalization or Euclidean Norm)

L2 normalization scales values so that the sum of the squares of the transformed values equals 1. It is given by:

L2 normalization is commonly used in machine learning models such as SVM and k-means clustering, ensuring that all features contribute equally to distance calculations.

When to Use Scaling vs. Normalization

The choice between scaling and normalization depends on the characteristics of the dataset and the type of machine learning model being used.

Criteria	Scaling (Min-Max, Standardization)	Normalization (L1, L2)
When feature ranges vary significantly	Yes	No
When features follow a normal distribution	Yes (Standardization)	No
When using distance-based models (KNN, SVM)	Yes	No
When working with sparse data (text, NLP)	No	Yes
When data has outliers	No (Min-Max is sensitive to outliers)	Yes (L1 handles outliers well)

General Guidelines

• Use Min-Max Scaling when working with deep learning models, as it ensures consistent feature ranges.

• Use Standardization when data follows a normal distribution and is used in models such as logistic regression or SVM.

• Use L1 or L2 Normalization when working with sparse datasets, especially in natural language processing (NLP) or probabilistic models.

Example Use Case: Predicting House Prices

Suppose a dataset contains information about houses, including square footage, the number of bedrooms, and the price. The features have different units and ranges:

• Square footage: 500 to 5000

• Number of bedrooms: 1 to 5

• House price: $50,000 to $500,000

If the model assigns weights to these features without scaling, it may give undue importance to square footage simply because it has larger values.

Solution:

• Min-Max Scaling can be applied to ensure that all features are in the range 0 to 1, making them comparable.

• Standardization may be used if the dataset follows a normal distribution.

• L2 Normalization might be helpful if text-based features, such as property descriptions, are included.

Conclusion

In machine learning, scaling and normalizing are crucial preprocessing methods that guarantee features are suitably modified, assisting models in operating more effectively. Depending on the dataset and the machine learning technique being utilized, one can choose between standardization, normalization, or Min-Max scaling. The performance of the model can be greatly impacted by knowing how to properly preprocess data. Enrol in our courses today to improve your data science and machine learning abilities and obtain a deeper understanding of data pretreatment, machine learning algorithms, and best practices.