Linear Algebra › Section G · Symmetric matrices and quadratic forms › Topic G.5
Applications to images, statistics, and data
Photographs, survey results and film ratings are all stored as matrices, and the singular value decomposition finds the few patterns that carry most of their information. This topic shows how that idea compresses images, powers principal component analysis and sits inside modern data science.
In this topic
- Data as matrices
- Best low-rank approximation
- Worked example: a rank-1 approximation
- Compressing an image
- Mean-deviation form and the covariance matrix
- Worked example: a covariance matrix
- Principal component analysis
- Worked example: reducing two variables to one
- PCA through the SVD
- Recommendations and modern data
- Common mistakes to avoid
- Key takeaways
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