Variable Length Windowing to Improve Non-Negative Matrix Factorization of Music Signals
Bibliographic record
Abstract
Non-negative matrix factorization(NMF) has shown positive results in learning musical notes over other blind source separation techniques like independent component analysis (ICA) and principal component analysis (PCA).The magnitude short time Fourier transform (STFT) is typically given as input for the non-negative matrix factorization algorithm for learning.Non-negative matrix factorization treats each frame of the magnitude short time Fourier transform as independent and identically distributed vectors.Due to fixed length windowing, a single note might be spread across multiple frames with varying proportions of the note structure.Improving the stationarity characteristics of the signal within the STFT is expected to improve the qualitative performance of note extraction by the NMF algorithm.To this extent, we propose a signal dependent variable length window based STFT to effectively capture the stationarity of the signal within each frame of the magnitude STFT.In this thesis, automatic detection of note onsets in music is studied.Many reduction techniques have been developed in the literature for reducing the timefrequency representation of the signal to a one dimension detection function to detect note onsets.We have come up with an onset detection technique that makes few assumptions about underlying structure of music and works well across a wide variety of music.A novel approach to extract note onset timings using the Itakura-Saito divergence is proposed.The remainder of the thesis explores the use of a variable length window based STFT versus the fixed length window based STFT for NMF decomposition, and how the Itakura-Saito divergence based onset detection works in comparison to other techniques.iii H obtained on factorization of fixed length window based STFT keeping W matrix fixed.This W matrix is available on factorization of variable length window based STFT . . . . . . . . . . . . . . . . . . .Bar plot of similarity measure of derived notes with ground truth notes using Bhattacharyya distance. . . . . . . . .
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".