Flavia Esposito

Flavia Esposito, Andersen Ang

Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-one conditions, making their optimization particularly challenging due to the interplay between low-rank structures and constraints. These problems arise in various applications, including machine learning, signal processing, environmental fields, and computational biology. In this paper, we propose a novel manifold optimization approach to tackle these problems efficiently. Our method leverages the geometry of oblique rotation manifolds to reformulate the problem and introduces a new Riemannian optimization method based on Riemannian gradient descent that strictly maintains the simplex constraints. By exploiting the underlying manifold structure, our approach improves optimization efficiency. Experiments on synthetic datasets compared to standard Euclidean and Riemannian methods show the effectiveness of the proposed method.

Laura Selicato, Flavia Esposito, Andersen Ang et al.

The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between the reconstruction accuracy and the adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence, effective for extracting low spectral density components from spectrograms of mixed signals, enhanced with 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 against noise. Experimental results showed SHINBO ensures precise spectral decomposition and demonstrates superior performance in both synthetic and real-world applications. For the latter, SHINBO is particularly useful, as 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 advances the state-of-the-art in signal recovery for complex, noise-dominated environments.