Calculator Input
Example Data Table
This example uses five PCA eigenvalues already ordered from largest to smallest.
| Component | Eigenvalue | Explained Variance % | Cumulative Variance % |
|---|---|---|---|
| PC1 | 4.20 | 46.67% | 46.67% |
| PC2 | 2.30 | 25.56% | 72.22% |
| PC3 | 1.40 | 15.56% | 87.78% |
| PC4 | 0.80 | 8.89% | 96.67% |
| PC5 | 0.30 | 3.33% | 100.00% |
In this example, keeping the first three components preserves 87.78% of the total variance while reducing dimensions by 40.00%.
Formula Used
Total Variance = Σλi
Explained Variance for Component i = (λi / Σλi) × 100
Cumulative Variance for k Components = (Σλ1..k / Σλi) × 100
Residual Variance = 100 - Cumulative Variance
Dimension Reduction = (1 - k / n) × 100
This calculator assumes the supplied eigenvalues describe principal components. It ranks them descending, then evaluates retention quality, cumulative coverage, and selection thresholds.
How to Use This Calculator
- Paste PCA eigenvalues into the eigenvalues field.
- Choose how many components you plan to retain.
- Set a target cumulative variance percentage, such as 90% or 95%.
- Enter a Kaiser threshold, usually 1.00 for standardized analyses.
- Pick your preferred decimal precision and add a dataset label.
- Submit the form to see retained variance, residual variance, scree behavior, and target coverage.
- Download the component table as CSV or PDF for review, reporting, or model documentation.
FAQs
1. What does principal component variance show?
It shows how much total dataset variation each principal component explains. Larger percentages indicate components that preserve more information from the original feature space.
2. Why are eigenvalues important in PCA?
Eigenvalues measure the variance captured by each principal component. They are the direct inputs used to compute explained variance ratios and cumulative retained information.
3. Should eigenvalues be entered in descending order?
That is recommended, but this calculator sorts them automatically. Sorting ensures PC1 represents the strongest component and the scree plot follows standard PCA interpretation.
4. What is cumulative explained variance?
Cumulative explained variance is the combined percentage retained after adding components from the top down. It helps decide how many components keep enough information.
5. What does the Kaiser threshold mean?
The Kaiser rule often keeps components with eigenvalues of at least 1. It is a quick screening rule, especially when variables were standardized before PCA.
6. How many components should I keep?
Keep enough components to meet your variance target while maintaining interpretability. Many workflows aim for 80% to 95%, depending on noise tolerance and model goals.
7. Why can the first component dominate variance?
Strong feature correlation can concentrate shared variation into the first principal component. A dominant PC1 often indicates a major underlying structure in the dataset.
8. When should I avoid aggressive dimension reduction?
Avoid it when smaller components still carry important business meaning, class separation, or anomaly signals. High compression can remove useful nuance even if variance loss looks modest.