A Provably Correct and Robust Algorithm for Convolutive Nonnegative Matrix Factorization
In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an NMF with additional sequential structure. This model is useful in a number of applications, such as audio source separation and neural sequence identification. While a number of heuristic algorithms have been proposed to solve CNMF, to the best of our knowledge no provably correct algorithms have been developed. We present an algorithm that takes advantage of the NMF model underlying CNMF and exploits existing algorithms for separable NMF to provably find a solution under certain conditions. Our approach guarantees the solution in low noise settings, and runs in polynomial time. We illustrate its effectiveness on synthetic datasets, and on a singing bird audio sequence.
Code (1)
Tasks
Audio Source SeparationSimilar Papers 제목 키워드 기반
Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updates
Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extend…
Time SeriesTime Series AnalysisSemi-Supervised Convolutive NMF for Automatic Piano Transcription
Automatic Music Transcription, which consists in transforming an audio recording of a musical performance into symbolic format, remains a difficult Music Information Retrieval task. In this work, which focuses on piano t…
Information RetrievalMusic Information RetrievalMusic TranscriptionRetrievalSuccessive Projection Algorithm Robust to Outliers
The successive projection algorithm (SPA) is a fast algorithm to tackle separable nonnegative matrix factorization (NMF). Given a nonnegative data matrix $X$, SPA identifies an index set $\mathcal{K}$ such that there exi…
Document ClassificationHyperspectral UnmixingSingle Particle AnalysisSemidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyp…
Document ClassificationHyperspectral UnmixingSingle Particle AnalysisModel Selection for Nonnegative Matrix Factorization by Support Union Recovery
Nonnegative matrix factorization (NMF) has been widely used in machine learning and signal processing because of its non-subtractive, part-based property which enhances interpretability. It is often assumed that the late…
Model Selection