Quantitative Analysis · Data Science · Machine Learning

Methods of Scaling Data for Machine Learning

Why scale feature data?

Scaling is an important preprocessing step in machine learning, especially when dealing with features that have different scales or units. Scaling is done to ensure that all features contribute equally to the learning process and to improve the performance and convergence of machine learning algorithms.

Here’s why feature scaling is necessary:

Equal Weight to Features

Many machine learning algorithms, such as gradient-based optimization methods (e.g., gradient descent), are sensitive to the scale of input features. Features with larger scales can dominate the learning process, causing the algorithm to focus primarily on them and neglect smaller-scaled features. Scaling the features ensures that all features are given equal weight during training.

Faster Convergence

Scaling helps optimization algorithms converge faster. When features have different scales, the algorithm may take longer to find the optimal solution because it needs more steps to adjust weights and biases correctly. Scaling speeds up convergence by making the optimization landscape more even.


Algorithms that involve regularization, like Ridge and Lasso regression, are influenced by the magnitude of feature coefficients. Scaling ensures that regularization treats all features fairly and doesn’t favor one over another simply due to the scale.

Distance-Based Algorithms

Algorithms that rely on distance calculations, such as k-nearest neighbors and support vector machines, can be sensitive to the scale of features. Unscaled features can lead to incorrect distances and consequently misclassification or poor performance.

Dimensionality Reduction

Techniques like Principal Component Analysis (PCA) are affected by the scale of features. Scaling ensures that features with larger scales don’t dominate the variance calculations during dimensionality reduction.

Some Algorithms Require Scaling

Certain algorithms, like k-nearest neighbors and k-means clustering, use distances between data points to make decisions. Scaling is essential for these algorithms to produce meaningful results, whereas others such as Decision Trees and Random Forests do not require scaling at all and can learn from the raw data without any transformation.

Scaling your feature data before applying a machine learning algorithm is crucial to ensure that features are treated fairly, the algorithm converges effectively, and your model performs optimally.

Scaling Methods

To bring the different features in your dataset to a comparable scale for training a machine learning classifier, you can use various scaling techniques. The choice of scaler depends on the characteristics of your data such as the distribution and presence of outliers as well as the classifier you’re planning to use.

Scalers are typically applied column-wise, which means they operate independently on each feature column of your dataset rather than on individual rows. The goal of scaling is to transform each feature (individually) so that they are on a similar scale without affecting the relationships between the rows, making it easier for machine learning algorithms to converge and perform effectively.

Here’s a simple example to illustrate – Let’s say you have a dataset with four features (columns) and four data points (rows):

Feature 1 Feature 2 Feature 3 Feature 4
10 20 100 2000
20 30 200 5000
30 40 300 4000
40 50 400 3000

Here are a few common scaling techniques to consider:


This scaler standardizes the features by removing the mean and scaling to unit variance. It’s suitable for features that follow a Gaussian distribution and can handle outliers reasonably well. If you’re using a scaler like StandardScaler, it will compute the mean and standard deviation for each feature (column), and then scale each value in the corresponding column using those statistics. After scaling, the data will be transformed as below.
For example: X = (X-mean) / std

Feature 1 Feature 2 Feature 3 Feature 4
-1.34 -1.34 -1.34 -1.34
-0.45 -0.45 -0.45 1.34
0.45 0.45 0.45 0.45
1.34 1.34 1.34 -0.45


This scaler scales the features to a specific range, often [0, 1]. It’s suitable when you want to preserve the relative relationships between the features and your data doesn’t necessarily follow a Gaussian distribution.
For example: X = (X-min) / (max-min)

Feature 1 Feature 2 Feature 3 Feature 4
0.00 0.00 0.00 0.00
0.33 0.33 0.33 1.00
0.67 0.67 0.67 0.67
1.00 1.00 1.00 0.33


RobustScaler is a method used to scale data in a way that is robust to outliers, meaning it is less affected by extreme values compared to some other scaling methods. This scaler is similar to the StandardScaler but uses the median and the interquartile range. RobustScaler is particularly useful when you have data with outliers or when you want to ensure that extreme values don’t heavily impact your scaled data.

Feature 1 Feature 2 Feature 3 Feature 4
-1.00 -1.00 -1.00 -1.00
-0.33 -0.33 -0.33 1.00
0.33 0.33 0.33 0.33
1.00 1.00 1.00 -0.33


MaxAbsScaler stretches or shrinks each feature’s values so that the maximum absolute value becomes 1 (or -1), and other values are scaled accordingly. This transformation maintains the relative differences between data points while ensuring they all fit within the same range, making it useful for algorithms that are sensitive to the scale of features. This scaler scales the data to the range [-1, 1] by dividing by the maximum absolute value in each feature. It’s useful when the data contains both positive and negative values.

Feature 1 Feature 2 Feature 3 Feature 4
0.25 0.40 0.25 0.40
0.50 0.60 0.50 1.00
0.75 0.80 0.75 0.80
1.00 1.00 1.00 0.60

It’s often a good practice to experiment with different scalers and observe their effects on your classifier’s performance through cross-validation.  Remember that it’s important to fit the scaler on your training data and then apply the same transformation to both the training and testing data to avoid data leakage and ensure a fair evaluation of your classifier.

Dealing with Non-stationary data

If you have a dataset with a mix of non-stationary features (such as price data) and bounded features (for example ranging between 0 and 100), you need to consider the characteristics of each type of feature and choose an appropriate scaling strategy for each. This situation is quite common in financial data analysis, where you might have a combination of different types of features.

For non-stationary features (like price data), you might want to apply techniques that address their non-stationarity before scaling, as scaling alone might not be sufficient. One common approach is to calculate returns or changes in price over time and then apply scaling to these transformed values. Returns can help make the data more stationary by removing trends. This process is called ‘differencing’. For other bounded features (eg: ranging between 0 and 100), you can apply regular scaling techniques since their nature is more similar to typical numeric features. MinMaxScaler, StandardScaler, or any of the other mentioned scalers can work well for these features, depending on their distribution and the requirements of your machine learning model.

Here’s a suggested approach:

1. Preprocess Non-Stationary Features (Price Data)

  • Calculate returns or differences in price over time to address non-stationarity.
  • Apply any necessary transformations to achieve stationarity, such as log differences or percentage changes.
  • Optionally, apply a scaler that’s appropriate for the transformed price data, keeping in mind the requirements of your model.

2. Preprocess Bounded Features

Apply an appropriate scaling technique (e.g., MinMaxScaler, StandardScaler) to the bounded features that range between 0 and 100.

3. Combine Features

Once you have preprocessed both types of features separately, you can combine them back into a unified dataset for training your machine learning model.

4. Model Training and Cross-Validation

Train and validate your machine learning model using cross-validation. Ensure that the preprocessing steps are consistently applied to both the training and validation/testing datasets to avoid data leakage.

Remember that the choice of preprocessing steps and scalers should be informed by the nature of your data and the requirements of your machine learning algorithm. Experimentation and evaluation are key to finding the best approach for your specific dataset and problem.