Nonnegative matrix factorization with the Itakura-Saito divergence.

With application to music analysis.

1) Analysis of a short piano excerpt

K = 4

EUC-NMF pitch = 60.8 65.0 68.0 108.4	Component 1 Component 2 Component 3 Component 4
KL-NMF pitch = 60.8 65.0 68.2 108.4	Component 1 Component 2 Component 3 Component 4
IS-NMF/MU pitch = 60.8 65.0 68.0 108.4	Component 1 Component 2 Component 3 Component 4
IS-NMF/EM pitch = 49.0 65.0 72.0 108.4	Component 1 Component 2 Component 3 Component 4

K = 5

EUC-NMF pitch = 60.8 65.0 65.4 68.0 108.4	Component 1 Component 2 Component 3 Component 4 Component 5
KL-NMF pitch = 61.0 65.0 68.0 72.2 108.4	Component 1 Component 2 Component 3 Component 4 Component 5
IS-NMF/MU pitch = 49.0 65.0 72.0 108.4 108.4	Component 1 Component 2 Component 3 Component 4 Component 5
IS-NMF/EM pitch = 61.0 65.0 68.0 108.4 108.4	Component 1 Component 2 Component 3 Component 4 Component 5

K = 6

EUC-NMF pitch = 61.0 65.0 65.4 68.0 72.0 108.4	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6
KL-NMF pitch = 61.0 65.0 68.0 72.0 81.0 108.4	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6
IS-NMF/MU pitch = 61.0 65.0 68.0 72.0 108.4 108.4	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6
IS-NMF/EM pitch = 61.0 65.0 68.0 72.0 108.4 108.4	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6

2) Analysis of early jazz music

Data

EUC-NMF	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6 Component 7 Component 8 Component 9 Component 10
KL-NMF	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6 Component 7 Component 8 Component 9 Component 10
IS-NMF/MU	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6 Component 7 Component 8 Component 9 Component 10
IS-NMF/EM	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6 Component 7 Component 8 Component 9 Component 10
IS-NMF/IG	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6 Component 7 Component 8 Component 9 Component 10 AUDIO RESTORATION Original mono Denoised mono Denoised stereo SOURCE EXTRACTION Acompaniment (Comp. 2) Trombone (Comp. 7) Trumpet & Clarinet (contains also piano notes) (Comp. 1, 3-6, 8, 10)
KL-NMF on magnitude spectrogram	Component 1 Component 2 Component 3 Component 4 Component 5 Component 6 Component 7 Component 8 Component 9 Component 10 Reconstruction