Automatic music transcription using low rank non-negative matrix decomposition

Abstract

Abstract-Automatic Music Transcription (AMT) is concerned with the problem of producing the pitch content of a piece of music given a recorded signal. Many methods rely on sparse or low rank models, where the observed magnitude spectra are represented as a linear combination of dictionary atoms corresponding to individual pitches. Some of the most successful approaches use Non-negative Matrix Decomposition (NMD) or Factorization (NMF), which can be used to learn a dictionary and pitch activation matrix from a given signal. Here we introduce a further refinement of NMD in which we assume the transcription itself is approximately low rank. The intuition behind this approach is that the total number of distinct activation patterns should be relatively small since the pitch content between adjacent frames should be similar. A rank penalty is introduced into the NMD objective function and solved using an iterative algorithm based on Singular Value thresholding. We find that the low rank assumption leads to a significant increase in performance compared to NMD using β-divergence on a standard AMT dataset.

A Hierarchical Latent Mixture Model for Polyphonic Music Analysis

“…The underlying idea is that similar frames should use the same latent factors in their reconstruction, and that these latent factors will then adapt to specific commonly-occurring pitch combinations. Furthermore by limiting the size of the individual models, the resulting transcription is likely to be locally low rank which has been shown to improve AMT performance over standard NMF/PLCA [13]. For example, a local model with a rank of r can learn r different combinations of pitches in order to account for local changes in active pitches, relative amplitudes and decay profiles.…”

“…Note the similarity between this and the Low Rank Matrix Decomposition approach [13], where here we have explicitly factored the P (p | t), as opposed to placing a nuclear-norm constraint on the transcription matrix. Combining ( 4…”

“…We compared the results of the proposed Hierarchical Latent Mixture Model (HLMM) to several related approaches: β Non-negative Matrix Decomposition (β-NMD), Weighted β Non-negative Matrix Factorization (Wβ-NMF) [20], low rank Non-negative Matrix Decomposition (LR-β-NMD) [13] and the best performing system reported by O'Hanlon et al [21], which was Group-Sparse Non-negative Matrix Decomposition using KL-divergence and a subspace pitch-dictionary (GS-KL-NMD). The results are summarized in Table I where we report the per-track average precision, recall and F-measure using the best threshold value τ .…”

Klasik Türk müziğinde makam tanıma için veri madenciliği kullanımı

“…Batı müziği üzerinde yapılan sayısallaştırma çalışmaları, otomatik müzik transkripsiyonu denilen akustik bir müzik sinyalini müzikal gösterime dönüştürme noktasına varmıştır [1]. Bu konu üzerinde literatürde birçok çalışma bulunmaktadır [2,3]. Klasik Türk Müziği birçok yapısal özelliği ile Batı Müziğinden oldukça farklıdır.…”