Feature Engineering: Converting Numerical Data into Categorical Data

four key techniques to convert numerical features into categorical data:

1. Binning & Binarization
2. Discretization
3. Quantile Binning
4. KMeans Binning

1. Binning & Binarization

Definition:

• Binning groups continuous numerical values into discrete intervals or “bins.”
• Binarization converts numerical data into binary (0/1) values based on a threshold.

Example: Converting exam scores into pass/fail categories.

import pandas as pd
# Sample exam scores
scores = [55, 72, 48, 91, 67, 82]
df = pd.DataFrame({'score': scores})
# Binarization: pass if score >= 60
df['pass'] = (df['score'] >= 60).astype(int)
print(df)

Diagram:

Score: 48  55  67  72  82  91
Pass:   0   0   1   1   1   1

Key Points:

• Good for threshold-based feature creation
• Useful when model needs binary inputs

Use Case: Converting exam scores into pass/fail categories.
Visual: Bar chart showing scores mapped to 0 (fail) and 1 (pass).

2. Discretization (Equal-Width Binning)

Definition:
Discretization transforms continuous numerical values into intervals of equal width.

Example: Divide app downloads (0–1000000) into 5 bins of equal width.

downloads = [100, 1500, 2500, 4000, 10000, 25000, 50000, 100000, 500000, 1000000]
df = pd.DataFrame({'downloads': downloads})

# Equal-width binning
df['equal_width_bin'] = pd.cut(df['downloads'], bins=5)
print(df)

Diagram:

Bins:        0-200k | 200k-400k | 400k-600k | 600k-800k | 800k-1M
Downloads:  100,1500,...500000,1000000

Key Points:

• Simple to implement
• Bin widths are equal, but number of data points per bin may vary

Use Case: Grouping app downloads into fixed ranges (0–200k, 200k–400k, etc.) for easier analysis.
Visual: Histogram showing bins of equal width with frequency counts.

3. Quantile Binning (Equal-Frequency Binning)

Definition:
Quantile binning divides data into bins with approximately equal numbers of observations, even if bin widths vary.

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Example: Split app downloads into 4 bins with equal frequency.

df['quantile_bin'] = pd.qcut(df['downloads'], q=4)
print(df)

Diagram:

Bin 1: 100-4000
Bin 2: 4000-50000
Bin 3: 50000-100000
Bin 4: 100000-1000000

Key Points:

• Ensures balanced bins in terms of data points
• Useful for skewed data

Use Case: Handling skewed datasets like app downloads to ensure each bin has roughly equal data points.
Visual: Countplot showing equal-frequency bins, each containing a similar number of observations.

4. KMeans Binning

Definition:
KMeans binning uses clustering to group numerical values into bins based on similarity rather than range or frequency.

Example: Grouping salaries into 3 bins using KMeans.

from sklearn.cluster import KMeans
import numpy as np

salaries = np.array([30000, 45000, 50000, 60000, 75000, 100000]).reshape(-1,1)
kmeans = KMeans(n_clusters=3, random_state=0).fit(salaries)
labels = kmeans.labels_
print(labels)

Diagram:

Cluster 0: 30000, 45000
Cluster 1: 50000, 60000
Cluster 2: 75000, 100000

Key Points:

• Adaptive binning based on data distribution
• Handles non-linear patterns well

Use Case: Grouping salaries into clusters based on similarity rather than range.
Visual: Scatter plot with salary values colored by KMeans cluster labels.

Summary Table

Key

• Binning & Binarization are useful for threshold-based simplification
• Discretization is intuitive but may create uneven data distribution
• Quantile Binning balances the number of points per bin
• KMeans Binning adapts to data distribution using clustering

Mastering these four techniques will make your feature engineering much more robust, especially when working with skewed or large datasets.