Matrix Decomposition
- PCA: Principle Component Analysis
- SVD: Singular Value Decomposition
- LDA: Linear Discriminant Analysis
- NMF: Non-negative Matrix Factorization
- NMF: with Sparse Constraints
- Linear Sparse Coding
Overview
$$A_{n \times m} = B_{n \times k}C_{k \times m}$$
- $B$ captures the common features in $A$
- $C$ carries specific characteristics of the original samples
- $n \times m \rightarrow (n+m) \times k$
- $ k<<n $
- In PCA: $B$ is eigenvectors
- In SVD: $B$ is right (column) eigenvectors
- In LDA: $B$ is discriminant directions
- In NMF: $B$ is local features