Feature Scaling is a critical step in building accurate and effective machine learning models. One key aspect of feature engineering is scaling, normalization, and standardization, which involves transforming the data to make it more suitable for modeling. These techniques can help to improve model performance, reduce the impact of outliers, and ensure that the data is on the same scale. In this article, we will explore the concepts of scaling, normalization, and standardization, including why they are important and how to apply them to different types of data. By the end of this article, you’ll have a thorough understanding of these essential feature engineering techniques and be able to apply them to your own machine learning projects.

- What is Feature Scaling?
- Why Should we Use Feature Scaling?
- What is Normalization?
- What is Standardization?
- The Big Question – Normalize or Standardize?
- Implementing Feature Scaling in Python
- Comparing Unscaled, Normalized, and Standardized Data
- Applying Scaling to Machine Learning Algorithms
- Frequently Asked Questions

Feature scaling is a preprocessing technique that transforms feature values to a similar scale, ensuring all features contribute equally to the model. It’s essential for datasets with features of varying ranges, units, or magnitudes. Common techniques include standardization, normalization, and min-max scaling. This process improves model performance, convergence, and prevents bias from features with larger values.

Some machine learning algorithms are sensitive to feature scaling, while others are virtually invariant. Let’s explore these in more depth:

Machine learning algorithms like **linear regression**, logistic regression, neural network, PCA (principal component analysis), etc., that use gradient descent as an optimization technique require data to be scaled. Take a look at the formula for gradient descent below:

The presence of feature value X in the formula will affect the step size of the gradient descent. The difference in the ranges of features will cause different step sizes for each feature. To ensure that the gradient descent moves smoothly towards the minima and that the steps for gradient descent are updated at the same rate for all the features, we scale the data before feeding it to the model.

Having features on a similar scale can help the gradient descent converge more quickly towards the minima.

Distance algorithms like KNN, K-means clustering, and SVM(support vector machines) are most affected by the range of features. This is because, behind the scenes, **they are using distances between data points to determine their similarity.**

For example, let’s say we have data containing high school CGPA scores of students (ranging from 0 to 5) and their future incomes (in thousands Rupees):

Since both the features have different scales, there is a chance that higher weightage is given to features with higher magnitudes. This will impact the performance of the machine learning algorithm; obviously, we do not want our algorithm to be biased towards one feature.

Therefore, we scale our data before employing a distance based algorithm so that all the features contribute equally to the result.

The effect of scaling is conspicuous when we compare the Euclidean distance between data points for students A and B, and between B and C, before and after scaling, as shown below:

- Distance AB before scaling =>
- Distance BC before scaling =>
- Distance AB after scaling =>
- Distance BC after scaling =>

Tree-based algorithms, on the other hand, are fairly insensitive to the scale of the features. Think about it, a decision tree only splits a node based on a single feature. The decision tree splits a node on a feature that increases the homogeneity of the node. Other features do not influence this split on a feature.

So, the remaining features have virtually no effect on the split. This is what makes them invariant to the scale of the features!

Normalization, a vital aspect of Feature Scaling, is a data preprocessing technique employed to standardize the values of features in a dataset, bringing them to a common scale. This process enhances data analysis and modeling accuracy by mitigating the influence of varying scales on machine learning models.

**Normalization is a scaling technique in which values are shifted and rescaled so that they end up ranging between 0 and 1. It is also known as Min-Max scaling.**

Here’s the formula for normalization:

Here, Xmax and Xmin are the maximum and the minimum values of the feature, respectively.

- When the value of X is the minimum value in the column, the numerator will be 0, and hence Xâ€™ is 0
- On the other hand, when the value of X is the maximum value in the column, the numerator is equal to the denominator, and thus the value of Xâ€™ is 1
- If the value of X is between the minimum and the maximum value, then the value of Xâ€™ is between 0 and 1

Standardization is another Feature scaling method where the values are centered around the mean with a unit standard deviation. This means that the mean of the attribute becomes zero, and the resultant distribution has a unit standard deviation.

Here’s the formula for standardization:

is the mean of the feature values and is the standard deviation of the feature values. Note that, in this case, the values are not restricted to a particular range.

Now, the big question in your mind must be when should we use normalization and when should we use standardization? Letâ€™s find out!

Normalization | Standardization |
---|---|

Rescales values to a range between 0 and 1 | Centers data around the mean and scales to a standard deviation of 1 |

Useful when the distribution of the data is unknown or not Gaussian | Useful when the distribution of the data is Gaussian or unknown |

Sensitive to outliers | Less sensitive to outliers |

Retains the shape of the original distribution | Changes the shape of the original distribution |

May not preserve the relationships between the data points | Preserves the relationships between the data points |

Equation: (x – min)/(max – min) | Equation: (x – mean)/standard deviation |

However, at the end of the day, the choice of using normalization or standardization will depend on your problem and the machine learning algorithm you are using. There is no hard and fast rule to tell you when to normalize or standardize your data. **You can always start by fitting your model to raw, normalized, and standardized data and comparing the performance for the best results.**

*It is a good practice to fit the scaler on the training data and then use it to transform the testing data. This would avoid any data leakage during the model testing process. Also, the scaling of target values is generally not required.*

Now comes the fun part – putting what we have learned into practice. I will be applying feature scaling to a few machine-learning algorithms on the Big Mart dataset. I’ve taken on the DataHack platform.

I will skip the preprocessing steps since they are out of the scope of this tutorial. But you can find them neatly explained in this article. Those steps will enable you to reach the top 20 percentile on the hackathon leaderboard, so that’s worth checking out!

So, letâ€™s first split our data into training and testing sets:

Before moving to the feature scaling part, letâ€™s glance at the details of our data using the **pd.describe()** method:

We can see that there is a huge difference in the range of values present in our numerical features: **Item_Visibility**, **Item_Weight, Item_MRP, **and **Outlet_Establishment_Year**. Letâ€™s try and fix that using feature scaling!

*Note: You will notice negative values in the Item_Visibility feature because I have taken log-transformation to deal with the skewness in the feature.*

To normalize your data, you need to import the MinMaxScaler from the sklearn library and apply it to our dataset. So, letâ€™s do that!

Letâ€™s see how normalization has affected our dataset:

All the features now have a minimum value of 0 and a maximum value of 1. Perfect!

Try out the above code in the live coding window below!!

Next, letâ€™s try to standardize our data.

To standardize your data, you need to import the StandardScaler from the sklearn library and apply it to our dataset. Here’s how you can do it:

You would have noticed that I only applied standardization to my numerical columns, not the other One-Hot Encoded features. Standardizing the One-Hot encoded features would mean assigning a distribution to categorical features. You donâ€™t want to do that!

But why did I not do the same while normalizing the data? Because One-Hot encoded features are already in the range between 0 to 1. So, normalization would not affect their value.

Right, let’s have a look at how standardization has transformed our data:

The numerical features are now centered on the mean with a unit standard deviation. Awesome!

It is always great to visualize your data to understand the distribution present. We can see the comparison between our unscaled and scaled data using boxplots.

You can notice how scaling the features brings everything into perspective. The features are now more comparable and will have a similar effect on the learning models.

It’s now time to train some machine learning algorithms on our data to compare the effects of different Feature scaling techniques on the algorithm’s performance. I want to see the effect of scaling on three algorithms in particular: K-Nearest Neighbors, Support Vector Regressor, and Decision Tree.

Now, let’s delve into training machine learning algorithms on our dataset to assess the impact of various scaling techniques on their performance. Specifically, I aim to observe the effects of scaling on three key algorithms: K-Nearest Neighbors, Support Vector Regressor, and Decision Tree. This analysis will provide valuable insights into the significance of feature scaling in machine learning and how it influences the outcomes of these algorithms.

As we saw before, KNN is a distance-based algorithm that is affected by the range of features. Let’s see how it performs on our data before and after scaling:

You can see that scaling the features has brought down the RMSE score of our KNN model. Specifically, the normalized data performs a tad bit better than the standardized data.

*Note: I am measuring the RMSE here because this competition evaluates the RMSE.*

SVR is another distance-based algorithm. So letâ€™s check out whether it works better with normalization or standardization:

We can see that scaling the features does bring down the RMSE score. And the standardized data has performed better than the normalized data. Why do you think that’s the case?

The sklearn documentation states that SVM, with RBF kernel, assumes that all the features are centered around zero and variance is of the same order. This is because a feature with a variance greater than that of others prevents the estimator from learning from all the features. Great!

We already know that a Decision tree is invariant to feature scaling. But I wanted to show a practical example of how it performs on the data:

You can see that the RMSE score has not moved an inch on scaling the features. So rest assured when you are using tree-based algorithms on your data!

This tutorial covered the relevance of using feature scaling on your data and how normalization and standardization have varying effects on the working of machine learning algorithms. Remember that there is no correct answer to when to use normalization over standardization and vice-versa. It all depends on your data and the algorithm you are using.

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A. Standardization centers data around a mean of zero and a standard deviation of one, while normalization scales data to a set range, often [0, 1], by using the minimum and maximum values.

A. Standardization ensures algorithmic stability and prevents sensitivity to the scale of input features, improves optimization algorithms’ convergence and search efficiency, and enhances the performance of certain machine learning algorithms.

A. Normalization helps in scaling the input features to a fixed range, typically [0, 1], to ensure that no single feature disproportionately impacts the results. It preserves the relationship between the minimum and maximum values of each feature, which can be important for some algorithms. It also improves the convergence and stability of some machine learning algorithms, particularly those that use gradient-based optimization.

A. We normalize values to bring them into a common scale, making it easier to compare and analyze data. Normalization also helps to reduce the impact of outliers and improve the accuracy and stability of statistical models.

A. To normalize a set of values, we first calculate the mean and standard deviation of the data. Then, we subtract the mean from each value and divide by the standard deviation to obtain standardized values with a mean of 0 and a standard deviation of 1. Alternatively, we can use other normalization techniques such as min-max normalization, where we scale the values to a range of 0 to 1, or unit vector normalization, where we scale the values to have a length of 1.

A. Feature scaling in machine learning is a preprocessing step that normalizes data, ensuring all features contribute equally by converting them to a common scale, improving algorithm performance and convergence.

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Excelent article! Thank you very much for sharing. I have one question. In the post you say: "It is a good practice to fit the scaler on the training data and then use it to transform the testing data.", but I didn't see that in the code you posted. Am I wrong? How would one "fit the scaler on the training data and then use it to transform the testing data"? Thanks a lot again

Hi Ali You fit the scaler on the training data so that it can calculate the necessary parameters, like mean and standard deviation for standardization, and store it for later use using the fit() method. Later you use the transform() function to apply the same transformation on both, train and test dataset. I have used this approach for both, normalization and standardization, in the article in the gists "NormalizationVsStandarization_2.py" and "NormalizationVsStandarization_3.py" respectively. I hope this cleared your doubt. Thanks

Good article! Thank you very much for sharing. I have one question. What the difference between sklearn.preprocessing import MinMaxScaler Normalization and sklearn.preprocessing.Normalizer? When to use MinMaxScaler and when to Normalize?

Hi I hope MinMaxScaler is already clear from the article. Normalizer is also a normalization technique. The only difference is the way it computes the normalized values. By default, it is calculating the l2 norm of the row values i.e. each element of a row is normalized by the square root of the sum of squared values of all elements in that row. As mentioned in the documentation, it is useful in text classification where the dot product of two Tf-IDF vectors gives a cosine similarity between the different sentences/documents in the dataset. Other than that, as I mentioned in the article, there is no sure way to know which scaling technique should be used when. The best way is to create multiple scaled copies of the data and then try them out and see which one gives the best result. Hope this helps.

Excellent article! Easy to understand and good coverage One question: I see that there is a scale() funtion as well from sklearn and short description suggest it to be similar to StandardScaler i.e. scaling to unit variance I could not find more than this explanation. Please can you suggest which on to use which scenario? Thanks in advance!

Hi Subhash I notice two differences between the two functions. First was that the scale() function allows you to standardize your data along any axis. This means that you could even standardize your data row-wise as opposed to feature-wise, which is what happens in StandardScaler(). Second difference was that the scale function has no fit and transform methods, so you cannot apply the same scaling to your test dataset. I would suggest using the StandardScaler() function as I have never used the scale() personally. I hope this helps!

Hi ANIRUDDHA, If we use the same scaler for train and testing, does it affect the testing data because in standardization we need to use the mean of the data. If we take the mean of the train data and scale the test data, it will influence the test data, right?

Scaling your test data according to the train data makes sure that the test data is on the same scale as the training data on which our model was trained on. This way our model will be able to apply the learnings from the training dataset on the testing dataset, which is exactly what we want! If instead, we scale the test data differently, then our model might not be able to discern that difference, thereby giving us incorrect outputs. That way we will never know how well our model is performing. I hope this helps!

Excellent article, thank you for sharing.

This is an excellent write up. Thanks for this.

That graphs really helps in putting things in perspective...thanks !

Hey bro! Great article. It covered a lots of topics that were unclear to me before. I have a basic question. How can I check my data after normalization. You have mentioned to use pd.describe() in "Normalization using sklearn' section. But when I use it I get an error - " module 'pandas' has no attribute 'describe'". Can you tell me how to check my data after normalization? Thank you for your time.

Hi Arnob, glad you liked the article. The command you are looking for is df.describe() not pd.describe(). Try using that, it should work.

I'm quite new to ML, and I definitely find this article very explicit and helpful. Thank you for sharing. My question is regarding outliers. Since normalisation centres the values around 0-1, is it fair to say it rids the data of outliers; as against standardisation, which might not....Simply put, after normalising, will outliers still affect the model?

Excellent article !

Do we need to scale down our test data, if yes then on what bases bcz we mai not know how d test data varies it mai be too large than the train datas max. value. And plz let me know how prepossessing is done on test data before fit is done. Thank you

Thanks for Great Article..!!!

Thanks Bhandari. Easy to understand and very helpful.

hello Zineb. I am writing blogs on Feature Scaling and Hyper Parameter Tuning which is understandable to all levels of machine learning programmers. Please give it a read.

Hi Aniruddha!Quick question - I've seen a few people already mention that standardization is good if the feature follows Gaussian distribution but don't really get why. Mind shedding more light on that?

"What could be the reason behind this quirk?" If you're wondering why there is a computational improvement, it's because of the matrix algebra in the background. It also reduces rounding errors. In layperson terms, it's much easier to do a division with similar numbers e.g. 5/3 vs. 5/0.0003. It's not different for computers.

Hi, Excellent article. Have you worked on an example of linear regression with k-means clustering and feature scaling after train-test split? An example would be helpful to understand the entire process. Cheers for spreading insightful knowledge

Hi !! I would like to share a sample of my data and seek your advice on the featuring scaling methods.

Quite an outstanding article! It answered most of my pressing questions in regards to scaling... Thank You so much.

Thank you for this article. We know that standardization is recommended when the distribution of the features is not Gaussian while normalization is appropriate for Gaussian features. However, in practice, we always have features with both Gaussian and non-Gaussian distributions. What is the better approach in this case? Are we going to combine both approaches for scaling features (i.e. normalization for non-gaussian features and standardization for Gaussian ones) ?