Principal Component Analysis (PCA)
Understanding Explained Variance Ratio (EVR) in simple terms
When working with complex datasets, simplifying the data without losing important information is a major challenge. Principal Component Analysis (PCA) is a powerful technique that helps solve this problem.
A key concept that makes PCA useful is the Explained Variance Ratio (EVR).
What Is PCA?
At its core, PCA transforms a large set of variables into a smaller set while preserving most of the original information.
📊 Why PCA Is Useful
Imagine analyzing a dataset with many features such as height, weight, age, income, and education level. Processing all these variables together can be overwhelming.
PCA identifies the most important directions in the data and reduces dimensionality, making analysis easier and more efficient.
Why Do We Care About Explained Variance Ratio?
When PCA creates new variables called principal components, each component captures a portion of the total variability in the data.
🧠 Intuitive Explanation
Think of summarizing a long story into a few bullet points. Some points capture more essential details than others.
Similarly, in PCA, some principal components are more informative. The Explained Variance Ratio tells us exactly how informative each component is.
How Is EVR Calculated?
EVR compares how much variance a principal component captures relative to the total variance in the dataset.
📐 Step-by-Step Breakdown
- Variance of a Principal Component: Measures how much data spreads along that component
- Total Variance: Sum of variances of all original features
EVR (Component i) = Variance of Component i ----------------------- Total Variance
If a principal component captures 70% of the total variance, its EVR is 0.7.
Interpreting EVR
📈 Example Interpretation
- PC1 EVR = 0.7 → Explains 70% of the data variability
- PC2 EVR = 0.2 → Adds another 20%
Together, these two components explain 90% of the variance.
This means we can safely ignore the remaining components without losing much information.
The 80/20 Rule in PCA
A common rule of thumb is to keep enough components to explain at least 80% of the variance.
This strikes a balance between:
- Simplifying the dataset
- Preserving meaningful information
Conclusion
The Explained Variance Ratio is a crucial tool for deciding how many principal components to keep.
By focusing on components with high EVR, we can reduce dimensionality, simplify analysis, and build more effective models.
💡 Key Takeaways
- PCA reduces complexity while preserving information
- EVR measures how informative each component is
- Higher EVR means more important components
- Keeping ~80–90% variance is usually sufficient
- EVR helps balance simplicity and accuracy
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