Unsupervised Learning for Monaural Source Separation Using Maximization–Minimization Algorithm with Time–Frequency Deconvolution †

Abstract

This paper presents an unsupervised learning algorithm for sparse nonnegative matrix factor time–frequency deconvolution with optimized fractional β-divergence. The β-divergence is a group of cost functions parametrized by a single parameter β. The Itakura–Saito divergence, Kullback–Leibler divergence and Least Square distance are special cases that correspond to β=0, 1, 2, respectively. This paper presents a generalized algorithm that uses a flexible range of β that includes fractional values. It describes a maximization–minimization (MM) algorithm leading to the development of a fast convergence multiplicative update algorithm with guaranteed convergence. The proposed model operates in the time–frequency domain and decomposes an information-bearing matrix into two-dimensional deconvolution of factor matrices that represent the spectral dictionary and temporal codes. The deconvolution process has been optimized to yield sparse temporal codes through maximizing the likelihood of the observations. The paper also presents a method to estimate the fractional β value. The method is demonstrated on separating audio mixtures recorded from a single channel. The paper shows that the extraction of the spectral dictionary and temporal codes is significantly more efficient by using the proposed algorithm and subsequently leads to better source separation performance. Experimental tests and comparisons with other factorization methods have been conducted to verify its efficacy.

Target Signal Extraction Method Based on Enhanced ICA with Reference

“…erefore, μ and λ need to be set appropriately so that the Mathematical Problems in Engineering final optimization result of equation (16) is consistent with equation (15). Direction 2: combining the distance metric function and the negative entropy contrast function, we reduce the constrained conditions and establish two forms of cost functions F(w), according to the different transformation forms of min ε(y, r):…”

“…e cost function in equation (17) and the cost function in equation (13) are reciprocal relations, while the cost function in equation 18is positive and negative with the cost function in equation (14). en, the corresponding EICA-R scheme is shown in the following expressions: Mathematical Problems in Engineering e scheme of (19) and (20) is corresponding to the scheme of (15) and (16). It also faces the problem of division operation or scaling factor setting iteration.…”

“…It should be pointed out that ICA is not suitable for underdetermined cases. For underdetermined cases, we can adopt sparse analysis [11][12][13][14], deconvolution [15,16], and other methods. is paper only considers non-underdetermined cases.…”

Self-Adaptive Fault Feature Extraction of Rolling Bearings Based on Enhancing Mode Characteristic of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise

“…However, when a fault become severe, it is not consistent with the development of a fault. The correlation coefficient [27,28] and Kullback-Leibler (K-L) divergence [29][30][31] do not work well for identifying faults. Recently, sample entropy (SE) [32,33], approximate entropy (AE) [34,35] and fuzzy entropy (FE) [36,37] were introduced into the fault diagnosis domain.…”

Reverberant signal separation using optimized complex sparse nonnegative tensor deconvolution on spectral covariance matrix

“…In source separation it is more realistic to consider the effect of the surrounding environment such as reflection of the sources. To address this issue, researchers have considered convolutive mixtures [1][2][3][4][5][6][7] instead of the instantaneous mixture [8][9][10][11]. However, the convolutive mixture is modeled under the narrowband approximation [4] that is not valid when the mixing filter length is greater than the Short-Time Fourier Transform (STFT) windows length, which is the case of the reverberant environment.…”