In this paper, we propose a musical onset detection method, with reference to polyphonic piano music. This method operates on a frame-by-frame basis and exploits a suitable time-frequency representation of the audio signal. The solution proposed consists of an onset detection algorithm based on Short-Time Fourier Transform (STFT) and Non-Negative Matrix Factorization (NMF). To validate this met...

The ongoing European Refugee Crisis has been one of the most popular trending topics on Twitter in the past 8 months. This paper applies topic modeling on bulks of tweets to discover the hidden patterns within these social media discussions. In particular, we perform topic analysis through solving Non-negative Matrix Factorization (NMF) as an Inexact Alternating Least Squares problem. We accele...

In this paper, we propose a musical onset detection method, with reference to polyphonic piano music. The solution proposed consists of an onset detection algorithm based on Short-Time Fourier Transform (STFT) and Non-Negative Matrix Factorization (NMF). This method operates on a frame-by-frame basis and exploits a suitable binary time-frequency representation of the audio signal. To validate t...

In this paper, we demonstrate a simulator for real-time speech enhancement based on a non-negative matrix factorization (NMF) technique. In particular, we propose an online noise adaptation method in an NMF framework, which is activated during non-speech intervals and used for adapting noise bases for NMF. Thus, incoming noisy speech is decomposed by using such adapted noise bases and universal...

The process of deciding which skills are involved in a given task is tedious and challenging. Means to automate it are highly desirable, even if only partial automation that provides supportive tools can be achieved. A recent technique based on Non-negative Matrix Factorization (NMF) was shown to offer valuable results, especially due to the fact that the resulting factorization allows a straig...

Multiplicative update algorithms have encountered a great success to solve optimization problems with nonnegativity constraints, such as the famous non-negative matrix factorization (NMF) and its many variants. However, despite several years of research on the topic, the understanding of their convergence properties is still to be improved. In this paper, we show that Lyapunov’s stability theor...

Abstract. This paper aims at improving non-negative matrix factorization (NMF) to facilitate data compression. An evolutionary updating strategy is proposed to solve the NMF problem iteratively based on three sets of updating rules including multiplicative, firefly and survival of the fittest rules. For data compression application, the quality of the factorized matrices can be evaluated by mea...

The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012a) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometri...

We analyze the geometry behind the problem of non-negative matrix factorization (NMF) and devise yet another NMF algorithm. In contrast to the vast majority of algorithms discussed in the literature, our approach does not involve any form of constrained gradient descent or alternating least squares procedures but is of purely geometric nature. In other words, it does not require advanced mathem...

We exploit the biconvex nature of the Euclidean non-negative matrix factorization (NMF) optimization problem to derive optimization schemes based on sequential quadratic and second order cone programming. We show that for ordinary NMF, our approach performs as well as existing stateof-the-art algorithms, while for sparsity-constrained NMF, as recently proposed by P. O. Hoyer in JMLR 5 (2004), i...