Feature scaling (also known as data normalization) is the method used to standardize the range of features of data. Since, the range of values of data may vary widely, it becomes a necessary step in data preprocessing while using machine learning algorithms.

Scaling

In scaling (also called min-max scaling), you transform the data such that the features are within a specific range e.g. [0, 1].

where x’ is the normalized value.

Scaling is important in the algorithms such as support vector machines (SVM) and k-nearest neighbors (KNN) where distance between the data points is important. For example, in the dataset containing prices of products; without scaling, SVM might treat 1 USD equivalent to 1 INR though 1 USD = 65 INR.

Normalization

The point of normalization is to change your observations so that they can be described as a normal distribution.

Normal distribution (Gaussian distribution), also known as the bell curve, is a specific statistical distribution where a roughly equal observations fall above and below the mean, the mean and the median are the same, and there are more observations closer to the mean.

For normalization, the maximum value you can get after applying the formula is 1, and the minimum value is 0. So all the values will be between 0 and 1.

In scaling, you’re changing the range of your data while in normalization you’re changing the shape of the distribution of your data.

You need to normalize our data if you’re going use a machine learning or statistics technique that assumes that data is normally distributed e.g. t-tests, ANOVAs, linear regression, linear discriminant analysis (LDA) and Gaussian Naive Bayes.

Standardization

Standardization (also called z-score normalization) transforms your data such that the resulting distribution has a mean of 0 and a standard deviation of 1.

where x is the original feature vector, is the mean of that feature vector, and σ is its standard deviation.

It’s widely used in SVM, logistics regression and neural networks.

Applications

In stochastic gradient descent, feature scaling can sometimes improve the convergence speed of the algorithm. In support vector machines, it can reduce the time to find support vectors.