To understand PCA fully, it is essential to grasp the underlying mathematical concepts. PCA relies on computations related to eigenvalues and eigenvectors, which are fundamental concepts in linear algebra. Eigenvalues represent the variance or importance of a particular component, while eigenvectors denote the direction or pattern associated with it.

Steps of PCA Algorithm

The PCA algorithm can be divided into several steps:

1. Standardize the dataset: PCA requires the data to be standardized to ensure fair comparisons between variables.
2. Calculate the covariance matrix: The covariance matrix helps in understanding the relationships between different variables.
3. Compute eigenvectors and eigenvalues: Using the covariance matrix, we calculate the eigenvectors and eigenvalues.
4. Sort eigenvectors: The eigenvectors are sorted based on their corresponding eigenvalues to identify the most significant components.
5. Select the desired number of principal components: Determine how many principal components to retain based on the explained variance.
6. Transform the data: Transform the original data into the new coordinate system defined by the principal components.

Understanding Eigenvalues and Eigenvectors