Non-negative matrix factorization for polyphonic music transcription

Abstract

In this paper we present a methodology for analyzing polyphonic musical passages comprised by notes that exhibit a harmonically fixed spectral profile (such as piano notes). Taking advantage of this unique note structure we can model the audio content of the musical passage by a linear basis transform and use non-negative matrix decomposition methods to estimate the spectral profile and the temporal information of every note. This approach results in a very simple and compact system that is not knowledge based, but rather learns notes by observation. WASPAA 2003This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. ABSTRACTIn this paper we present a methodology for analyzing polyphonic musical passages comprised by notes that exhibit a harmonically fixed spectral profile (such as piano notes). Taking advantage of this unique note structure we can model the audio content of the musical passage by a linear basis transform and use non-negative matrix decomposition methods to estimate the spectral profile and the temporal information of every note. This approach results in a very simple and compact system that is not knowledge-based, but rather learns notes by observation.

Automatic music transcription: challenges and future directions

“…Non-negative matrix factorisation (NMF) is a technique first introduced as a tool for music transcription in [119]. In its simplest form, the NMF model decomposes an input spectrogram X ∈ R K×N + with K frequency bins and N frames as:…”

Determining Projections of Grain Boundaries from Diffraction Data in Transmission Electron Microscope

“…in ranging from biology (Sotiras et al, 2015, Brunet et al, 2004, nuclear sciences or in to computer sciences (e. g. signal processing and pattern recognition; Smaragdis et al, 2003, Buciu et al, 2004). Devarajan's work focuses on the field of computational biology, however it also gives a remarkable outlook to the capabilities of NMF-analysis (Devarajan, 2008).…”

Sparse coding of auditory features for machine hearing in interference

“…The events or "spikes" in such codes represent sound "particles" that are usually fairly compact in the time-frequency space, and hence too primitive to effectively map higher-level structure of typical sound sources. Sparse coding has also been done in the space of spectral slices, or spectrogram time-frequency products [4,5]. These work fairly well for encoding musical notes in polyphonic music, which is what they were designed for, but are not well suited for sounds of a less periodic or regular sort.…”