Variance measures the average squared deviation of values from their mean. In principal component analysis, it represents the dataset’s variability or randomness that a projection aims to preserve. section 3.5
PCA uses variance to guide dimensionality reduction:
- The first principal component captures the maximum variance through a linear combination of the original variables. section 3.5
- Each subsequent component captures additional variance while remaining orthogonal to earlier components. section 3.5
- Choosing a projection that captures more variance helps retain important structure while reducing the number of variables. section 3.5
House-price variables
For house-price data containing area, bedrooms, balconies, and distances to transport, PCA combines variables into new components that capture the dataset’s maximum variance. section 3.5
