Difference between revisions of "10-601 Matrix Factorization"
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You should know: | You should know: | ||
* What PCA is, and how it relates to matrix factorization. | * What PCA is, and how it relates to matrix factorization. | ||
| + | * How to interpret the "cartoons" that we use to illustrate PCA. | ||
* What loss function and constraints are associated with PCA - i.e., what the "PCA Problem" is. | * What loss function and constraints are associated with PCA - i.e., what the "PCA Problem" is. | ||
| + | * How the principle components are related to each other and the data: | ||
| + | ** The earlier components have the highest variance (i.e., for the first components the examples, when re-expressed over the space defined by the new basis, have the largest variance) | ||
| + | ** The components are orthogonal to each other (by construction) | ||
* How to interpret the low-dimensional embedding of instances, and the "prototypes" produced by PCA and MF techniques. | * How to interpret the low-dimensional embedding of instances, and the "prototypes" produced by PCA and MF techniques. | ||
** How to interpret the prototypes in the case of dimension reduction for images. | ** How to interpret the prototypes in the case of dimension reduction for images. | ||
** How to interpret the prototypes in the case of collaborative filtering, and completion of a ratings matrix. | ** How to interpret the prototypes in the case of collaborative filtering, and completion of a ratings matrix. | ||
* How PCA and MF relate to k-means and and EM. | * How PCA and MF relate to k-means and and EM. | ||
Latest revision as of 14:33, 21 April 2016
This a lecture used in the Syllabus for Machine Learning 10-601B in Spring 2016
Slides
Readings
- Murphy Chap 12. PCA is not covered in Mitchell.
- There are also some notes on PCA/SVD that I've written up.
- There's a nice description of the gradient-based approach to MF, and a scheme for parallelizing it,by Gemulla et al.
Summary
You should know:
- What PCA is, and how it relates to matrix factorization.
- How to interpret the "cartoons" that we use to illustrate PCA.
- What loss function and constraints are associated with PCA - i.e., what the "PCA Problem" is.
- How the principle components are related to each other and the data:
- The earlier components have the highest variance (i.e., for the first components the examples, when re-expressed over the space defined by the new basis, have the largest variance)
- The components are orthogonal to each other (by construction)
- How to interpret the low-dimensional embedding of instances, and the "prototypes" produced by PCA and MF techniques.
- How to interpret the prototypes in the case of dimension reduction for images.
- How to interpret the prototypes in the case of collaborative filtering, and completion of a ratings matrix.
- How PCA and MF relate to k-means and and EM.
