Non-negative matrix factorisation incorporating greedy Hellinger sparse coding applied to polyphonic music transcription

Abstract

Non-negative Matrix Factorisation (NMF) is a commonly used tool in many musical signal processing tasks, including Automatic Music Transcription (AMT). However unsupervised NMF is seen to be problematic in this context, and harmonically constrained variants of NMF have been proposed. While useful, the harmonic constraints may be constrictive in mixed signals. We have previously observed that recovery of overlapping signal elements using NMF is improved through introduction of a sparse coding step, and propose here the incorporation of a sparse coding step using the Hellinger distance into a NMF algorithm. Improved AMT results for unsupervised NMF are reported.

Online Nonnegative Matrix Factorization With Outliers

“…Several important instances of Csiszár f -divergence have been used in NMF, including the 1 distance [37] and the family of α-divergences [3], [4]. In particular, the α-divergences include Hellinger distance (α = 1/2) [38], [39] and the (generalized) Kullback-Leibler (KL) divergence (α → 1) [40], [41]. Moreover, for these special cases, d…”

Compositional chroma estimation using powered Euclidean distance

“…are αβ-divergences with α = β = η, including Euclidean (η = 1) and Hellinger distances (η = 0.5), which we previously employed in the context of 0 sparse NMF in [22]. We note that a scaling parameter used in (4) is omitted from (5).…”

“…For nearest neighbour experiments we propose to use the minimum Hellinger distance (MHD), which we previously proposed in [22], in a matching pursuit type algorithm:…”