# Matrix Factorization Task

(Redirected from Matrix Decomposition Task)

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A Matrix Factorization Task is a decomposition task that requires a matrix factorization structure (that decomposes an [math]\displaystyle{ m \times n }[/math] matrix [math]\displaystyle{ X }[/math] into a product of matrices (in some canonical form) - typically into [math]\displaystyle{ m×k }[/math] and [math]\displaystyle{ k×n }[/math] matrices, where typically [math]\displaystyle{ k \ll n }[/math] and [math]\displaystyle{ k \ll m }[/math]).

**Context:****Input:**a Matrix Structure.**output:**a Matrix Factorization Structure.- It can be solved by a Matrix Decomposition System (that implements a matrix decomposition algorithm).
- It can range from being a Nonnegative Matrix Factorization to being a Positive Matrix Factorization to being ...
- It can range from being an Exact Matrix Decomposition Task to being an Approximate Matrix Factorization Task.
- It can range from being a Regularized Matrix Decomposition Task to being an Non-Regularized Matrix Factorization Task.
- It can range from being a Weighted Matrix Decomposition Task to being an Unweighted Matrix Factorization Task.
- It can range from being a Boolean Matrix Decomposition Task to being an Integer Matrix Decomposition Task to being Real Matrix Decomposition Task.
- It can range from being a Low-Rank Matrix Factorization Task to being a Large-Rank Matrix Factorization Algorithm.

**Example(s):****Counter-Example(s):****See:**Lossy Compression, Adjacency Matrix, Latent Factor Algorithm, Linear Algebra Task.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/matrix_decomposition Retrieved:2015-1-17.
- In the mathematical discipline of linear algebra, a
**matrix decomposition**or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.

- In the mathematical discipline of linear algebra, a

### 2007

- (Skillicorn, 2007) ⇒ David Skillicorn. (2007). “Understanding Complex Datasets: Data Mining with Matrix Decompositions." Chapman & Hall/CRC.

### 2002

- (Serre, 2002) ⇒ Denis Serre. (2002). “Matrices. Theory and Applications.” In: Grad. Texts in Math, 216.

### 2001

- (Luo & Hancock, 2001) ⇒ Bin Luo and Edwin R. Hancock. (2001). “Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition.” In: IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(10).