Method of Transforming Skewed Distribution

Transforming Skewed Distributions in Machine Learning

Purpose

To make data distributions closer to normal (Gaussian).
Enhances interpretability of features and benefits machine learning algorithms sensitive to non-normal distributions, such as linear regression and logistic regression.

1. Logarithmic Transformation

Purpose:

Reduces the impact of large values (right-skewed data).
Compresses larger values more than smaller ones.

Syntax:

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import numpy as np

# Applying log transformation
data_log = np.log(data + 1)  # Add 1 to avoid log(0)

Example:

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import pandas as pd
import numpy as np

# Original data
data = pd.Series([1, 10, 100, 1000])

# Log transformation
data_log = np.log(data + 1)

print(data_log)

Output:

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0    0.693
1    2.398
2    4.615
3    6.908
dtype: float64

Use Case:

Suitable for financial data, sales data, or any positively skewed dataset.

2. Square Root Transformation

Purpose:

Similar to logarithmic transformation but less aggressive.
Reduces the skewness of data without compressing large values as much.

Syntax:

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import numpy as np

# Applying square root transformation
data_sqrt = np.sqrt(data)

Example:

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# Original data
data = pd.Series([1, 10, 100, 1000])

# Square root transformation
data_sqrt = np.sqrt(data)

print(data_sqrt)

Output:

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0     1.000
1     3.162
2    10.000
3    31.623
dtype: float64

Use Case:

Works well with moderately skewed data, such as population sizes or counts.

3. Box-Cox Transformation

Purpose:

A flexible method to stabilize variance and make data more normal.
Requires positive data values.

Syntax:

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from scipy.stats import boxcox

# Applying Box-Cox transformation
data_boxcox, lambda_value = boxcox(data)

Example:

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from scipy.stats import boxcox
import pandas as pd

# Original data (all positive values)
data = pd.Series([1, 10, 100, 1000])

# Box-Cox transformation
data_boxcox, lambda_value = boxcox(data)

print(data_boxcox)
print(f"Lambda used: {lambda_value}")

Output:

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[0.000, 0.576, 1.784, 3.545]
Lambda used: 0.206

Use Case:

Suitable for datasets with varying variances or when you need precise control over the transformation.

4. Exponential Transformation

Purpose:

Used to handle left-skewed data by stretching smaller values.
Less common than other transformations.

Syntax:

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import numpy as np

# Applying exponential transformation
data_exp = np.exp(data)

Example:

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# Original data
data = pd.Series([0, 1, 2, 3])

# Exponential transformation
data_exp = np.exp(data)

print(data_exp)

Output:

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0     1.000
1     2.718
2     7.389
3    20.086
dtype: float64

Use Case:

For datasets with left-skewed distributions (e.g., survival rates or small counts).

5. General Guidelines for Transformations

Transformation	Suitable for	Handles skewness	Range of values	Key Parameter
Logarithmic	Right-skewed data	Yes	Positive only	Add constant if data has zeros
Square Root	Moderately skewed	Yes	Positive only	None
Box-Cox	Right-skewed data	Yes	Positive only	Lambda (determined automatically)
Exponential	Left-skewed data	Yes	Any	None

Visualizing the Effect of Transformations

To better understand the impact of transformations, you can plot the distributions before and after transformation:

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import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np

# Original data
data = np.array([1, 10, 100, 1000])

# Transformations
log_data = np.log(data + 1)
sqrt_data = np.sqrt(data)
boxcox_data, _ = boxcox(data)

# Plotting
fig, axes = plt.subplots(1, 4, figsize=(15, 5))

# Original data
sns.histplot(data, kde=True, ax=axes[0])
axes[0].set_title('Original Data')

# Log-transformed
sns.histplot(log_data, kde=True, ax=axes[1])
axes[1].set_title('Log Transformation')

# Square-root transformed
sns.histplot(sqrt_data, kde=True, ax=axes[2])
axes[2].set_title('Square Root Transformation')

# Box-Cox transformed
sns.histplot(boxcox_data, kde=True, ax=axes[3])
axes[3].set_title('Box-Cox Transformation')

plt.tight_layout()
plt.show()

When to Transform Data

Check for Skewness:

Calculate skewness using .skew() or visually inspect with histograms.

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skewness = data.skew()
print(f"Skewness: {skewness}")

Apply Transformation:

Choose a transformation based on skewness and the data's nature.

Validate Impact:

Reassess skewness and visualize the data distribution after transformation.

This guide provides a complete reference for transforming skewed distributions with examples, syntax, and visuals to help you build a strong understanding for your ML journey.