What Is the Principal Component Analysis (PCA) Variance Ratio Calculator?
PCA identifies the directions (eigenvectors) of maximum variance in high-dimensional data.
The explained variance ratio indicates how much information is preserved when projecting data onto fewer dimensions.
How Does the Principal Component Analysis (PCA) Variance Ratio Calculator Work?
Divides individual eigenvalues by the sum of all eigenvalues (matrix trace).
Calculates cumulative percentage of explained variance for the top 3 components.
Evaluates information preservation efficiency.
Principal Component Analysis (PCA) Variance Ratio Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Explained variance ratio as the fractional eigenvalue of total covariance matrix trace.
How to Use the Principal Component Analysis (PCA) Variance Ratio Calculator
- Enter the eigenvalues corresponding to the top 3 sorted principal components.
- Enter the sum of all eigenvalues across the entire covariance or correlation matrix.
Step-by-Step Example Calculation
Multispectral Satellite Image Compression
Input Values:
Understanding Your Result
A cumulative variance above 80-90% means dimensionality can be safely reduced with minimal information loss.
Scree plot elbow criteria typically discard components below an eigenvalue of 1.0 (Kaiser criterion).
Factors That Affect the Result
- Feature correlation: High collinearity among features concentrates variance into the first 1-2 components.
- Feature scaling: Variables with large numeric units artificially dominate unless data is standardized (z-score normalized).
When Should You Use This Calculator?
- Exploratory data analysis, genomic microarray analysis, and image compression.
- Mitigating the "curse of dimensionality" and multicollinearity before training regression models.
Assumptions & Limitations
- Assumes linear relationships; cannot uncover non-linear manifold structures (use t-SNE or UMAP).
- Sensitive to outliers without robust covariance estimation.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard spectral decomposition formula universal in multivariate statistics.