Approximate Non-Negative Matrix Factorization Task
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An Approximate Non-Negative Matrix Factorization Task is a non-negative matrix factorization task that is an approximate matrix factorization task (to find two nonnegative matrices W and H such that a given nonnegative matrix V is approximately equal to the matrix product of W and H.)
- AKA: Approximate NNMF.
- Context:
- It can be solved by a Approximate Non-Negative Matrix Factorization System (that implements a Approximate Non-Negative Matrix Factorization Algorithm).
- It can support a Non-Negative Basis Vectors Vector Finding Task.
- It can (typically) be represented as:
- Example(s):
- …
- Counter-Example(s):
- See: Local Search Algorithm, SVD Task.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/non-negative_matrix_factorization#Approximate_non-negative_matrix_factorization Retrieved:2015-5-1.
- Usually the number of columns of W and the number of rows of H in NMF are selected so the product WH will become an approximation to V. The full decomposition of V then amounts to the two non-negative matrices W and H as well as a residual U, such that: V = WH + U. The elements of the residual matrix can either be negative or positive.
When W and H are smaller than V they become easier to store and manipulate. Another reason for factorizing V into smaller matrices W and H, is that if one is able to approximately represent the elements of V by significantly less data, then one has to infer some latent structure in the data.
- Usually the number of columns of W and the number of rows of H in NMF are selected so the product WH will become an approximation to V. The full decomposition of V then amounts to the two non-negative matrices W and H as well as a residual U, such that: V = WH + U. The elements of the residual matrix can either be negative or positive.