# Sparse Hyperparametric Itakura-Saito Nonnegative Matrix Factorization via Bi-Level Optimization

arXiv: https://arxiv.org/abs/2502.17123 · HTML: https://mlsanity.com/paper/2502.17123/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 8 of 8)

- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF](https://mlsanity.com/paper/1907.02404/) (2019)
- [Solving NMF with smoothness and sparsity constraints using PALM](https://mlsanity.com/paper/1910.14576/) (2019)
- [Nonnegative Matrix Factorization with Zellner Penalty](https://mlsanity.com/paper/2012.03889/) (2020)
- [Non-negative tensor factorization for vibration-based local damage detection](https://mlsanity.com/paper/2403.12554/) (2024)
- [Bearing damage detection with orthogonal and non-negative low-rank feature extraction](https://mlsanity.com/paper/2403.12564/) (2024)

## Abstract (arXiv)

The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between reconstruction accuracy and adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence, which is particularly effective for extracting low spectral density components from spectrograms of mixed signals, and benefits from the introduction of sparsity constraints. We propose a new algorithm called SHINBO, which introduces a bi-level optimization framework to automatically and adaptively tune the row-dependent penalty hyperparameters, enhancing the ability of IS-NMF to isolate sparse, periodic signals in noisy environments. Experimental results demonstrate that SHINBO achieves accurate spectral decompositions and demonstrates superior performance in both synthetic and real-world applications. In the latter case, SHINBO is particularly useful for noninvasive vibration-based fault detection in rolling bearings, where the desired signal components often reside in high-frequency subbands but are obscured by stronger, spectrally broader noise. By addressing the critical issue of hyperparameter selection, SHINBO improves the state-of-the-art in signal recovery for complex, noise-dominated environments.