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. - Apply Transformation:
- Choose a transformation based on skewness and the data's nature.
- Validate Impact:
- Reassess skewness and visualize the data distribution after transformation.
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skewness = data.skew()
print(f"Skewness: {skewness}")
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.
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