Non-negative Matrix Factorization (NMF) has been widely exploited to learn latent features from data. However, previous NMF models often assume a fixed number of features, say p features, where p is simply searched by experiments. Moreover, it is even difficult to learn binary features, since binary matrix involves more challenging optimization problems. In this paper, we propose a new Bayesian...

Mesoscopic N-atom systems derive their structural and dynamical properties from processes coupled across multiple scales in space and time. A multiscale method for simulating these systems in the friction dominated regime from the underlying N-atom formulation is presented. The method integrates notions of multiscale analysis, Trotter factorization, and a hypothesis that the momenta conjugate t...

We thank anonymous referee #2 for the constructive and helpful criticism. A detailed response to the comments of reviewer #2 follows below. Specific comments 1. Title of paper. The title has been changed to better describe the content of the manuscript as suggested by the reviewer: “Contribution of residential wood combustion and other sources to hourly winter aerosol in Northern Sweden d...

We study thermal Casimir and quantum nonretarded Lifshitz interactions between dielectrics in general geometries. We map the calculation of the classical partition function onto a determinant, which we discretize and evaluate with the help of Cholesky factorization. The quantum partition function is treated by path integral quantization of a set of interacting dipoles and reduces to a product o...

Spectrogram factorization is a recent and promising alternative to sinusoidal or source/filter modeling for analysis/resynthesis systems aimed at musical creation. This paper presents a framework designed to perform a wide range of sound manipulations based on Non-negative Matrix Factorization (NMF), including a set of new techniques for creating artificial cross-components not present in the o...

Abstract—Nonnegative matrix factorization (NMF) is an emerging technique with a wide spectrum of potential applications in data analysis. Mathematically, NMF can be formulated as a minimization problem with nonnegative constraints. This problem is currently attracting much attention from researchers for theoretical reasons and for potential applications. Currently, the most popular approach to ...

ECG Arrhythmia Classification Based on Wavelet Packet Transform and Sparse Non-Negative Matrix Factorization

Spectral envelope is one of the most important features that characterize the timbre of an instrument sound. However, it is difficult to use spectral information in the framework of conventional spectrogram decomposition methods. We overcome this problem by suggesting a simple way to provide a constraint on the spectral envelope calculated by linear prediction. In the first part of this study, ...

Nonnegative Matrix Factorization (NMF) is a standard tool for data analysis. An important variant is the Sparse NMF problem. A natural measure of sparsity is the L0 norm, however its optimization is NP-hard. Here, we consider a sparsity measure linear in the ratio of the L1 and L2 norms, and propose an efficient algorithm to handle the norm constraints which arise when optimizing this measure. ...