Rotation in PCA is very important as it maximizes the separation within the variance obtained by all the components because of which interpretation of components would become easier. If the components are not rotated, then we need extended components to describe variance of the components.
In Principal Component Analysis (PCA), rotation of components is important for several reasons:
- Interpretability: Rotating the principal components allows for a clearer interpretation of the underlying structure of the data. It helps in identifying and understanding the meaningful patterns and relationships among variables.
- Orthogonality: Rotating the components ensures that they remain orthogonal to each other. This orthogonality property simplifies the interpretation and analysis of the components, as they are independent of each other.
- Variance Maximization: PCA aims to capture the maximum variance in the data with a minimal number of components. Rotating the components helps in maximizing the variance along the principal axes, thereby retaining the most informative features of the data.
- Dimensionality Reduction: Rotating the components often leads to a more compact representation of the data, which facilitates dimensionality reduction. By aligning the axes with the directions of maximum variance, the rotated components can effectively capture the essential information in fewer dimensions.
- Simplicity and Stability: Rotated components tend to have simpler structures and are more stable across different datasets. This simplification and stability make the interpretation and generalization of the results more reliable.
In summary, rotation of components in PCA enhances interpretability, maintains orthogonality, maximizes variance, facilitates dimensionality reduction, and improves the simplicity and stability of the analysis. Therefore, it is a crucial step in extracting meaningful insights from high-dimensional data.