Non-negative matrix factorization as a feature selection tool for maximum margin classifiers

A method of decomposing a given matrix vector X into two matrix vectors, F and G, comprising:

• providing a data processing device to implement the following steps:
• minimizing a cost function that combine a non-negative matrix factorization, NMF and maximum margin classifier satisfying the following relationship:
• min
• F
• ,
• G
• ≥
• 0
• ⁢
• 
• X
• -
• FG
• 
• 2
• +
• γ
• ⁡
• (
• 
• w
• 
• 2
• +
• C
• ⁢
• ∑
• i
• =
• 1
• n
• ⁢
• L
• ⁡
• (
• y
• i
• ,
• w
• ·
• g
• i
• +
• b
• )
• )
• wherein:
• X∈;
• F∈;
• G∈;
• w∈;
• yi∈{−1,1}∀i;
• gi∈ is the ith column of G;
• symbol (.) represents the dot product of the two vectors;
• L(y,t) is a loss function where t=(w.gi+b), and L(y,t)=max(0,1−yt)p;
• and
• γ is a constant that distributes the relative importance of the two terms in the optimization;
• wherein minimizing the cost function is achieved h successive iterations and γ is the relative between the generative component and the discriminative component of the cost function, γ ranges from 0 to 1 and is increased incrementally during each iteration;
• and
• wherein during each of said iterations, F is updated by the following relationship:
• F
• n
• +
• 1
• =
• F
• n
• ·
• XG
• T
• (
• FG
• )
• ⁢
• G
• T
• .