What is PCA?
Principal Component Analysis (PCA) is a dimensionality-reduction technique that finds the main directions of variation in the data and projects it onto these directions.
PCA steps:
- 1. Data centering (subtracting the mean)
- 2. Calculating the covariance matrix
- 3. Finding eigenvalues and eigenvectors
- 4. Sort by eigenvalues
- 5. Principal Component Projection
Apply:
- • Data visualization
- • Noise reduction in data
- • Accelerate ML algorithms
- • Image compression
100
0.70
2
50
Original data
PCA
Custom values
EXPLAINED VARIATION
Metrics
Total variation:
0.00
Saved variation:
0.00
Lost variance:
0.00
Correlation PC1-PC2:
0.00
Common questions
According to the 80-20 rule: enough components for explaining 80% of variance, or elbow point on the eigenvalues graph.
Yes, but the least important information (noise) is lost. PCA retains maximum variance in data.
Yes, due to weights of original variables. But interpretation can be difficult for high-dimensional data.
When important variable interpretation, nonlinear dependencies, or all variables need to be preserved.
SVD is a more general matrix decomposition method. PCA can be implemented via SVD, but not vice versa.