Data Source and Methodology
All calculations are based on rigorous statistical methodologies as outlined in the guidelines of Example Data Source. All calculations are strictly based on the formulas and data provided by this source.
The Formula Explained
Eigenvectors and Eigenvalues calculation: \( A \cdot v = \lambda \cdot v \), where \( A \) is the covariance matrix, \( v \) is the eigenvector, and \( \lambda \) is the eigenvalue.
Glossary of Variables
- Eigenvector: A vector whose direction remains unchanged when a linear transformation is applied.
- Eigenvalue: A scalar that indicates how much the eigenvector is stretched during the transformation.
How It Works: A Step-by-Step Example
For example, if you have a 3x3 covariance matrix, the PCA calculator will compute the eigenvalues and eigenvectors, allowing you to understand the variance distribution of your dataset.
Frequently Asked Questions (FAQ)
What is Principal Component Analysis?
Principal Component Analysis (PCA) is a technique used to emphasize variation and bring out strong patterns in a dataset.
How does PCA reduce dimensionality?
PCA reduces dimensionality by transforming the original variables into a new set of variables (principal components), which are orthogonal and capture the maximum variance.
Is PCA suitable for categorical data?
PCA is generally not suitable for categorical data, as it relies on the concept of variance, which is not applicable to categorical variables.
How to prepare data for PCA?
Data should be standardized or normalized before applying PCA. This ensures that each variable contributes equally to the analysis.
What are the limitations of PCA?
PCA is sensitive to the scale of the data and can be misleading if the data is not appropriately scaled or normalized.