Creating interaction features in Data Analysis Python - Performance & Efficiency

Time Complexity: Creating interaction features

O(n x m²)

Understanding Time Complexity

When we create interaction features, we combine columns to capture relationships.

We want to know how the time to create these features grows as data size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

def create_interactions(df):
    cols = df.columns
    for i in range(len(cols)):
        for j in range(i+1, len(cols)):
            df[f'{cols[i]}_x_{cols[j]}'] = df[cols[i]] * df[cols[j]]
    return df

This code creates new features by multiplying every pair of columns in the DataFrame.

Identify Repeating Operations

• Primary operation: Nested loops over columns to create pairwise products.
• How many times: For each pair of columns, one multiplication per row.

How Execution Grows With Input

As the number of columns grows, the pairs grow roughly like the square of columns.

Input Size (columns)	Approx. Operations (multiplications)
10	45 x rows
100	4,950 x rows
1000	499,500 x rows

Pattern observation: The number of pairs grows quickly as columns increase, so work grows roughly with the square of columns times rows.

Final Time Complexity

Time Complexity: O(n x m²)

This means the time grows linearly with the number of rows and quadratically with the number of columns.

Common Mistake

[X] Wrong: "Creating interaction features only depends on the number of rows."

[OK] Correct: Because the number of column pairs grows with the square of columns, the columns count heavily affects time.

Interview Connect

Understanding how feature creation scales helps you explain your data preparation choices clearly and confidently.

Self-Check

"What if we only created interaction features for a selected subset of columns? How would the time complexity change?"

Practice

1. What is the main purpose of creating interaction features in data analysis?

easy

A. To capture the combined effect of two or more features on the target

B. To remove irrelevant features from the dataset

C. To reduce the size of the dataset by merging columns

D. To convert categorical data into numerical data

Solution

1. Step 1: Understand interaction features

   Interaction features combine two or more features to capture their joint effect on the target variable.

2. Step 2: Compare options

   Only To capture the combined effect of two or more features on the target describes capturing combined effects, which is the purpose of interaction features.

3. Final Answer:

   To capture the combined effect of two or more features on the target -> Option A

4. Quick Check:

   Interaction features capture combined effects = A [OK]

Hint: Interaction features combine columns to show joint effects [OK]

Common Mistakes:

• Confusing interaction features with feature selection
• Thinking interaction features reduce dataset size
• Mixing interaction features with encoding categorical data

2. Which of the following Python code snippets correctly creates an interaction feature df['A_B'] by multiplying columns 'A' and 'B' in a DataFrame df?

easy

A. df['A_B'] = df['A'] * df['B']

B. df['A_B'] = df['A'].concat(df['B'])

C. df['A_B'] = df['A'].append(df['B'])

D. df['A_B'] = df['A'] + df['B']

Solution

1. Step 1: Identify correct operation for interaction

   Interaction features are often created by multiplying columns to capture joint effects.

2. Step 2: Check code syntax

   df['A_B'] = df['A'] * df['B'] uses multiplication (*) between columns, which is correct syntax in pandas.

3. Final Answer:

   df['A_B'] = df['A'] * df['B'] -> Option A

4. Quick Check:

   Multiplying columns creates interaction feature = D [OK]

Hint: Multiply columns with * to create interaction features [OK]

Common Mistakes:

• Using + instead of * for interaction
• Using append or concat which are for combining rows or DataFrames
• Syntax errors from wrong method calls

3. Given the DataFrame df below:

   A  B
0  2  3
1  4  5
2  6  7

What will be the output of df['A_B'] = df['A'] * df['B']; df['A_B'].tolist()?

medium

A. [2, 4, 6]

B. [5, 9, 13]

C. [6, 20, 42]

D. [3, 5, 7]

Solution

1. Step 1: Multiply each row's values in columns A and B

   Row 0: 2*3=6, Row 1: 4*5=20, Row 2: 6*7=42

2. Step 2: Convert the new column to list

   The list is [6, 20, 42]

3. Final Answer:

   [6, 20, 42] -> Option C

4. Quick Check:

   Row-wise multiplication = [6, 20, 42] [OK]

Hint: Multiply row values, then list() to see results [OK]

Common Mistakes:

• Adding instead of multiplying values
• Confusing column names or indices
• Returning original columns instead of interaction

4. Consider this code snippet to create an interaction feature:

df['A_B'] = df['A'] * df['B']
df['A_B'] = df['A_B'].apply(lambda x: x if x > 10 else 0)

What is the error in this code if df['A'] and df['B'] contain numeric values?

medium

A. The apply function should be used on rows, not on a column

B. No error; the code correctly creates and modifies the interaction feature

C. The lambda function syntax is incorrect

D. Multiplying columns directly causes a runtime error

Solution

1. Step 1: Check multiplication of columns

   Multiplying two numeric columns in pandas works correctly and creates a new column.

2. Step 2: Check apply with lambda on the new column

   Applying a lambda function to modify values conditionally is valid syntax and works on a Series.

3. Final Answer:

   No error; the code correctly creates and modifies the interaction feature -> Option B

4. Quick Check:

   Column multiplication and apply lambda are valid = A [OK]

Hint: apply with lambda on Series is valid for conditional changes [OK]

Common Mistakes:

• Thinking apply only works on DataFrame rows
• Assuming multiplication causes errors with numeric columns
• Misreading lambda function syntax

5. You have a dataset with columns age and income. You want to create an interaction feature to capture how age modifies the effect of income on spending. Which code snippet correctly creates this interaction feature and then normalizes it by dividing by the maximum value?

hard

A. df['age_income'] = (df['age'] * df['income']) / df['age'].max()

B. df['age_income'] = df['age'] * df['income'] / df['income'].min()

C. df['age_income'] = (df['age'] + df['income']) / df['income'].max()

D. df['age_income'] = (df['age'] * df['income']) / (df['age'] * df['income']).max()

Solution

1. Step 1: Create interaction by multiplying age and income

   Multiplying captures how age modifies income effect.

2. Step 2: Normalize by dividing by max of the interaction feature

   Dividing by (df['age'] * df['income']).max() scales the new feature between 0 and 1.

3. Final Answer:

   df['age_income'] = (df['age'] * df['income']) / (df['age'] * df['income']).max() -> Option D

4. Quick Check:

   Multiply then normalize by max interaction = B [OK]

Hint: Multiply columns then divide by max of product to normalize [OK]

Common Mistakes:

• Normalizing by max of only one column instead of product
• Adding columns instead of multiplying for interaction
• Using min instead of max for normalization