Calculation results
Component details
| Component | Label | Eigenvalue | Variance ratio | Variance percent | Cumulative ratio | Cumulative percent | Remaining percent | Marginal gain | Status |
|---|---|---|---|---|---|---|---|---|---|
| No results yet. | |||||||||
Formula used
The calculator divides each eigenvalue by total variance. It then adds ratios in component order. The first cumulative value meeting the threshold determines retention.
For feature matrices, covariance or correlation eigenvalues are calculated. Optional preprocessing changes the matrix before decomposition. Components are then ranked by descending eigenvalue.
How to use
- Select the input mode matching your data.
- Paste values, upload a file, or load an example.
- Choose preprocessing and variance settings when needed.
- Set a retention threshold or manual component count.
- Choose plot layers and advanced selection methods.
- Calculate, inspect points, and export your report.
Clicking a plotted component updates the selected row. Hovering reveals exact variance details. The threshold slider recalculates recommendations immediately.
Example eigenvalue data
| Component | Eigenvalue | Expected interpretation |
|---|---|---|
| PC1 | 4.80 | Largest single contribution |
| PC2 | 2.10 | Strong additional structure |
| PC3 | 1.25 | Moderate retained information |
| PC4 | 0.78 | Smaller incremental benefit |
| PC5 | 0.42 | Diminishing marginal variance |
Interpretation guide
Steep early rise Few components capture most variance.
Slow rise Information is distributed across many dimensions.
Elbow point Marginal gains begin declining quickly.
Kaiser rule Retain standardized-data components with eigenvalues above one.
Broken stick Compare observed variance against random partition expectations.
Frequently asked questions
What is cumulative explained variance?
It is the total variance retained after adding principal components in order. Higher values preserve more dataset information.
Which threshold should I choose?
Ninety to ninety-five percent is common. The correct choice depends on prediction quality, storage limits, and interpretability.
Should features be standardized?
Standardization is useful when features use different units. Without it, large-scale variables may dominate PCA.
What does the elbow indicate?
The elbow marks diminishing returns. Components after that point often contribute less additional variance.
Why can ratios fail to total one?
Rounded or incomplete inputs may cause small differences. Automatic normalization corrects those totals proportionally.
Can I use a covariance matrix?
Yes. Enter a square symmetric matrix. Its eigenvalues determine each component contribution.
What is the Kaiser criterion?
It retains standardized components with eigenvalues greater than one. It works best with correlation-based PCA.
What does broken-stick comparison show?
It estimates variance expected from random dimension partitions. Observed components above it may be meaningful.
Can the chart compare models?
Yes. Enable comparison and enter additional datasets. Their cumulative curves appear together for inspection.