The Data Scientist’s Guide to Scaling: Standard, MinMax & Robust Methods

The Data Scientist’s Guide to Scaling: Standard, MinMax & Robust Methods

In machine learning and data preprocessing, scaling is an essential step to normalize the range of features in the dataset. Proper scaling ensures that the features have consistent scales, which is vital for improving the performance of many machine learning algorithms. Without scaling, some algorithms may be biased toward features with larger values, leading to suboptimal model performance.

Among the various scaling methods, Standard Scaler, MinMax Scaler, and Robust Scaler are the most commonly used. Each of these methods serves a specific purpose depending on the nature of the data, especially when dealing with outliers, the distribution of values, and the machine learning algorithm in use.

In this article, we will dive deep into these three scaling methods, exploring their workings, advantages, and limitations, along with real-world examples and Python code implementations to show how to apply them.


Python Code Snippets

Below are Python code snippets using to apply these scalers:

Visualizing the Scaling Effects:

Code output:


What is Scaling in Data Preprocessing?

Scaling refers to transforming the features of the data to a common scale without distorting the differences in the ranges of the values. Many machine learning models, especially those based on distance metrics (such as K-Nearest Neighbors or Support Vector Machines) and gradient-based methods (like neural networks), benefit from scaled data.

Without scaling, features with larger ranges can disproportionately affect the model's behavior, causing it to ignore features with smaller scales. For example, if one feature represents "income" in thousands of dollars and another represents "age" in years, the model may prioritize "income" because of its larger range.

Scaling ensures that all features contribute equally to the model and that the algorithm performs optimally.


Standard Scaler

The Standard Scaler is a method of scaling that centers the data around zero and scales it according to the standard deviation of the feature. It transforms data to have a mean of 0 and a standard deviation of 1.

How Does Standard Scaler Work?

The formula for standardization (also called z-score normalization) is:

Where:

  • X is the feature value.

  • μ is the mean of the feature.

  • σ is the standard deviation of the feature.

After applying Standard Scaler:

  • The data is centered around 0 (mean = 0).

  • The data has a unit variance (standard deviation = 1).

When to Use the Standard Scaler?

  • Normally Distributed Data: If your data is close to being normally distributed or follows a Gaussian distribution, the Standard Scaler is an ideal choice. It works well when the data's distribution is symmetric.

  • Linear Models: Many models such as Linear Regression, Logistic Regression, and Support Vector Machines (SVMs) assume that the data is centered and normally distributed. Standard scaling helps these models perform better.

Limitations of Standard Scaler:

  • Outliers: Standard Scaler is sensitive to outliers because both the mean and standard deviation are affected by extreme values. If your data contains outliers, the scaling might be skewed.

  • Non-Normal Data: Standard scaling is less effective for data that is not normally distributed or has skewed distributions, as the scaling may still result in inefficient transformations.


MinMax Scaler

The MinMax Scaler scales the data to a fixed range, typically [0, 1]. This is done by subtracting the minimum value of the feature and dividing by the range (difference between the maximum and minimum values).

How Does MinMax Scaler Work?

The formula for MinMax scaling is:

Where:

  • X is the feature value.

  • Xmin​ is the minimum value of the feature.

  • Xmax is the maximum value of the feature.

After applying MinMax scaling:

  • The data is transformed into the range [0, 1].

When to Use the MinMax Scaler?

  • Data with a Known Range: MinMax scaling is useful when the features are constrained to a specific range. For example, if the data already falls between 0 and 1, or you want to compress all values into a specific range for further modeling.

  • Neural Networks: Many modern neural networks benefit from MinMax scaling, as they often perform better when the input features are scaled to the [0, 1] range. Additionally, MinMax scaling helps in faster convergence during training.

Limitations of MinMax Scaler:

  • Sensitivity to Outliers: MinMax scaling is highly sensitive to outliers. Since it uses the minimum and maximum values for scaling, any extreme values will distort the scaling process. A single outlier can compress the entire dataset into a very narrow range.

  • Non-Robust to Changing Data: If the data changes over time (e.g., new data has a larger or smaller minimum or maximum), MinMax scaling will need to be recomputed for the new range, which could lead to inconsistencies in scaled values.


Robust Scaler

The Robust Scaler is designed to be more robust to outliers than the Standard Scaler or MinMax Scaler. It uses the median and the Interquartile Range (IQR), rather than the mean and standard deviation, to center and scale the data.

How Does Robust Scaler Work?

The formula for Robust Scaling is:

Where:

  • X is the feature value.

  • Median is the middle value of the feature values when sorted.

  • IQR (Interquartile Range) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1).

By using the median and IQR:

  • The data is centered around 0 (by subtracting the median).

  • The data is scaled based on the spread of the middle 50% of the data (IQR), making it less sensitive to extreme outliers.

When to Use the Robust Scaler?

  • Data with Outliers: The Robust Scaler is particularly useful when the dataset contains outliers. Since it uses the median and IQR, it is less sensitive to extreme values than the Standard Scaler or MinMax Scaler.

  • Skewed Data: The Robust Scaler is also a good choice when the data has a skewed distribution, as it can handle such data better than methods that rely on mean and standard deviation.

Limitations of Robust Scaler:

  • Not Optimal for Symmetric, Normally Distributed Data: If your data is normally distributed and free of outliers, using the Robust Scaler might not be the best choice. In such cases, other methods like Standard Scaler may work better.

  • Requires More Computation: Computing the median and IQR can be more computationally intensive than using the mean and standard deviation, especially for large datasets.


Comparison of Scaling Methods

Here's a comparison table highlighting the key differences and use cases of each scaler:


Conclusion

The choice of scaling method is crucial for the performance of machine learning models. The Standard Scaler, MinMax Scaler, and Robust Scaler each have unique strengths and weaknesses, making them suitable for different types of data.

  • Standard Scaler works best for data that follows a normal distribution and when using linear models like Linear Regression, Logistic Regression, or Support Vector Machines (SVMs). However, it is sensitive to outliers, which can skew the mean and standard deviation, thereby distorting the scaled values.

  • MinMax Scaler is ideal for algorithms that require a specific feature range, such as neural networks, which often perform better when input features are scaled to the [0, 1] interval. While it preserves the shape of the original distribution, it is highly sensitive to outliers, which can compress the normal data into a narrow band.

  • Robust Scaler is the best choice when your dataset contains outliers or exhibits skewed distributions. By using the median and interquartile range (IQR), it provides a more resilient transformation. Although it may not be as effective for normally distributed data without outliers, its robustness makes it highly practical in real-world scenarios.

Ultimately, the right scaling technique depends on the characteristics of your data and the requirements of your model. It's essential to explore and experiment with different scalers during preprocessing to ensure your model achieves optimal performance.

Remember, scaling isn't just a technical formality, it can make or break your model's accuracy and convergence. Choose wisely!

Paresh Mate

Product Manager | Bridging Technology, Strategy & Customer Value | Customer Success | CRM | MBA Heriot Watt University UK

3mo

The synonyms are normalisation for rescaling between 0 to 1 and standardisation for mean = 0 and Standard deviation = 1

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