[Matlab code]

Nonnegative Matrix Factorization (NMF)

- is a technique to factorize nonegative matrix data Y into two left and right matrices: Y ==> A * X.

- is applied into blind source separation (BSS), parts analysis, and noise reduction etc.

Blind Source Separation (BSS)

- A0 = [a1, a2, ..., ar] : original sources

- X0 : mixing matrix

- Y = [y1, y2, ..., yn] : observed sources

BSS tries to estimate original sources by using only Y.

NMF can be used to BSS problem, when Y, A0, and Xo can be assumed as nonnegative matrices.

Smooth NMF for smooth BSS

When original sources are smooth signals, we can impose additional smoothness constraint into the NMF problem. There are two approaches:

We use second approache, and consider the following basis function:

Results

- BSS experiment,

-- from up to bottom :(original, multiplicative NMF [8.9 dB], HALS-NMF [10.1 dB], proposed [12.5 dB])

- Noise Reduction by using Smooth Nonnengative Tensor (Tucker/CP) Factorizations