Quantile-based discretization of continuous variables

Quantile-based discretization involves dividing a continuous variable into discrete intervals or bins based on the distribution of its values. This process ensures that each bin contains approximately the same number of observations, making it useful for creating categories or grouping data into equally sized segments.

Here’s how pd.qcut works:

1. Specify the number of quantiles or the bin edges: You provide either the number of quantiles or an array of quantile edges to pd.qcut.
2. Assign bins to the data: pd.qcut then assigns each observation in the input data to one of the specified bins based on its value. The bins are created such that each bin contains approximately the same number of observations.
3. Return a categorical variable: The function returns a categorical variable with the same length as the input data, where each observation is assigned a category representing the bin it belongs to.

Here’s a basic example:

# assume we have 100 plus cities in the dataset and we cannot do one-hot encoding
df["city"].nunique()

#however, we can reduce the levels by grouping them into 3 major categories based on the column city_development_index values

df["city"] = pd.qcut(
    df["city_development_index"],
    q=[0, 0.25, 0.5, 1],
    labels=["Under_Developed", "Developing", "Developed"],
)

df["city"].value_counts()

Developed          9561
Under_Developed    4838
Developing         4759
Name: city, dtype: int64

This code snippet uses pd.qcut to discretize the values in the “city_development_index” column of the DataFrame df into three categories based on quantiles.

Here’s what each argument does:

• df["city_development_index"]: This selects the column “city_development_index” from the DataFrame df, which presumably contains continuous values representing the development index of different cities.
• q=[0, 0.25, 0.5, 1]: This specifies the quantiles or the bin edges where the continuous variable will be split. In this case, it divides the data into four quantiles: 0-25%, 25-50%, 50-100%.
• labels=["Under_Developed", "Developing", "Developed"]: This provides labels for the resulting categories. The first label corresponds to the lowest quantile range (0-25%), the second label corresponds to the second quantile range (25-50%), and the third label corresponds to the third quantile range (50-100%).

The result is a new categorical column “city” added to the DataFrame df, where each value corresponds to the category label based on the quantile ranges of the “city_development_index”.

For example, if a city has a “city_development_index” value in the range of 0-25%, it will be labeled as “Under_Developed”. If its value falls in the range of 25-50%, it will be labeled as “Developing”, and if its value falls in the range of 50-100%, it will be labeled as “Developed”.