Understanding Normalization and Standardization in EDA

Exploratory Data Analysis (EDA) is a fundamental step in data science that involves summarizing the main characteristics of a dataset, often with visual methods. Two key preprocessing techniques in EDA are normalization and standardization. Both aim to transform features into comparable scales but serve different purposes and operate differently. Understanding when and how to use normalization and standardization is crucial for improving the performance of many machine learning algorithms and ensuring meaningful analysis.

What is Normalization?

Normalization rescales the data to a fixed range, usually [0, 1]. This technique, also known as min-max scaling, adjusts the values of numeric features so that the smallest value becomes 0 and the largest becomes 1. The formula for normalization is:

$$X_{norm} = frac{X – X_{min}}{X_{max} – X_{min}}$$

Where:

• $X$ is the original value,

• $X_{min}$ is the minimum value in the feature,

• $X_{max}$ is the maximum value in the feature.

Normalization is particularly useful when features have different units or scales, and you want to bring them to a common scale without distorting differences in the ranges of values.

What is Standardization?

Standardization, also known as z-score normalization, transforms data to have a mean of zero and a standard deviation of one. Instead of bounding values between a range, it adjusts the data distribution to follow a standard normal distribution (Gaussian). The formula is:

$$X_{std} = frac{X – mu}{sigma}$$

Where:

• $X$ is the original value,

• $mu$ is the mean of the feature,

• $sigma$ is the standard deviation of the feature.

Standardization centers the data by subtracting the mean and scales it by the variability, which is essential when the algorithm assumes normally distributed data or when features vary widely in their scales.

Key Differences Between Normalization and Standardization

When to Use Normalization

Normalization is best suited when:

• Features have different units and scales, and you want to bring them to a common scale.

• You are working with algorithms that rely on distance metrics such as K-Nearest Neighbors (KNN), K-Means clustering, or neural networks, where scaled inputs improve convergence.

• The data is not normally distributed, or the model does not assume a Gaussian distribution.

• You want the values constrained within a specific range.

When to Use Standardization

Standardization is preferred when:

• The data approximately follows a normal distribution, or you want to make it more Gaussian-like.

• You are applying algorithms like Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), or linear regression, which assume standardized data.

• The features have different units but also differ in variance.

• The presence of outliers is minimal or acceptable since extreme outliers can affect mean and variance.

Effects on Machine Learning Algorithms

Normalization and standardization can significantly affect the performance of many machine learning algorithms:

• Distance-based algorithms (KNN, K-Means): Sensitive to feature scale; normalization ensures no single feature dominates due to its scale.

• Gradient-based algorithms (Neural Networks, Logistic Regression): Standardized or normalized data can help with faster and more stable convergence.

• Tree-based algorithms (Decision Trees, Random Forests): Less sensitive to feature scaling, so normalization or standardization is usually unnecessary.

• Linear models (Linear Regression, SVMs with linear kernel): Standardization is often critical to balance features and improve interpretability.

Practical Example

Consider a dataset with features like height (in cm), weight (in kg), and income (in dollars). Height ranges between 150-200, weight between 50-120, and income can be in thousands or millions. Directly applying distance-based algorithms would cause income to dominate the distance calculation because of its larger scale.

• Normalization will scale all features between 0 and 1, ensuring each contributes proportionally.

• Standardization will center all features around 0 with a standard deviation of 1, balancing the dataset but keeping the distribution shape.

Steps to Apply Normalization and Standardization

1. Check Data Distribution: Plot histograms or use statistical tests to understand the distribution of each feature.

2. Decide Scaling Technique: Based on distribution and algorithm requirements, choose normalization or standardization.

3. Apply Transformation: Use libraries like Scikit-learn’s MinMaxScaler for normalization or StandardScaler for standardization.

4. Verify Results: Visualize transformed data and check means, variances, or ranges.

5. Use in Model: Feed the scaled data to your machine learning model.

Conclusion

Normalization and standardization are critical preprocessing techniques in EDA, enabling better model performance and interpretability. Choosing the right method depends on the nature of the data and the machine learning algorithm used. Normalization rescales features to a fixed range, ideal for non-Gaussian distributed data and distance-based models. Standardization centers data and adjusts for variance, suitable for Gaussian data and algorithms assuming normality. Mastery of these techniques enhances data quality and drives more accurate and reliable insights.