Fast and unique Tucker decompositions via multiway blind source separation

2012 ◽  
Vol 60 (3) ◽  
pp. 389-405 ◽  
Author(s):  
G. Zhou ◽  
A. Cichocki

Abstract A multiway blind source separation (MBSS) method is developed to decompose large-scale tensor (multiway array) data. Benefitting from all kinds of well-established constrained low-rank matrix factorization methods, MBSS is quite flexible and able to extract unique and interpretable components with physical meaning. The multilinear structure of Tucker and the essential uniqueness of BSS methods allow MBSS to estimate each component matrix separately from an unfolding matrix in each mode. Consequently, alternating least squares (ALS) iterations, which are considered as the workhorse for tensor decompositions, can be avoided and various robust and efficient dimensionality reduction methods can be easily incorporated to pre-process the data, which makes MBSS extremely fast, especially for large-scale problems. Identification and uniqueness conditions are also discussed. Two practical issues dimensionality reduction and estimation of number of components are also addressed based on sparse and random fibers sampling. Extensive simulations confirmed the validity, flexibility, and high efficiency of the proposed method. We also demonstrated by simulations that the MBSS approach can successfully extract desired components while most existing algorithms may fail for ill-conditioned and large-scale problems.

Author(s):  
Daichi Kitamura ◽  
Shinichi Mogami ◽  
Yoshiki Mitsui ◽  
Norihiro Takamune ◽  
Hiroshi Saruwatari ◽  
...  

2020 ◽  
Author(s):  
Daichi Kitamura ◽  
Kohei Yatabe

Abstract Independent low-rank matrix analysis (ILRMA) is the state-of-the-art algorithm for blind source separation (BSS) in the determined situation (the number of microphones is greater than or equal to that of source signals). ILRMA achieves a great separation performance by modeling the power spectrograms of the source signals via the nonnegative matrix factorization (NMF). Such highly developed source model can effectively solve the permutation problem of the frequency-domain BSS, which should be the reason of the excellence of ILRMA. In this paper, we further improve the separation performance of ILRMA by additionally considering the general structure of spectrogram called consistency, and hence we call the proposed method Consistent ILRMA. Since a spectrogram is calculated by an overlapping window (and a window function induces spectral smearing called main- and side-lobes), the time-frequency bins depend on each other. In other words, the time-frequency components are related each other via the uncertainty principle. Such co-occurrence among the spectral components can be an assistant for solving the permutation problem, which has been demonstrated by a recent study. Based on these facts, we propose an algorithm for realizing Consistent ILRMA by slightly modifying the original algorithm. Its performance was extensively studied through the experiments performed with various window lengths and shift lengths. The results indicated several tendencies of the original and proposed ILRMA which include some topics have not discussed well in the literature. For example, the proposed Consistent ILRMA tends to outperform the original ILRMA when the window length is sufficiently long compared to the reverberation time of the mixing system.


Author(s):  
Shinichi Mogami ◽  
Norihiro Takamune ◽  
Daichi Kitamura ◽  
Hiroshi Saruwatari ◽  
Yu Takahashi ◽  
...  

Author(s):  
Hiroshi Sawada ◽  
Nobutaka Ono ◽  
Hirokazu Kameoka ◽  
Daichi Kitamura ◽  
Hiroshi Saruwatari

This paper describes several important methods for the blind source separation of audio signals in an integrated manner. Two historically developed routes are featured. One started from independent component analysis and evolved to independent vector analysis (IVA) by extending the notion of independence from a scalar to a vector. In the other route, nonnegative matrix factorization (NMF) has been extended to multichannel NMF (MNMF). As a convergence point of these two routes, independent low-rank matrix analysis has been proposed, which integrates IVA and MNMF in a clever way. All the objective functions in these methods are efficiently optimized by majorization-minimization algorithms with appropriately designed auxiliary functions. Experimental results for a simple two-source two-microphone case are given to illustrate the characteristics of these five methods.


Author(s):  
Daichi Kitamura ◽  
Kohei Yatabe

AbstractIndependent low-rank matrix analysis (ILRMA) is the state-of-the-art algorithm for blind source separation (BSS) in the determined situation (the number of microphones is greater than or equal to that of source signals). ILRMA achieves a great separation performance by modeling the power spectrograms of the source signals via the nonnegative matrix factorization (NMF). Such a highly developed source model can solve the permutation problem of the frequency-domain BSS to a large extent, which is the reason for the excellence of ILRMA. In this paper, we further improve the separation performance of ILRMA by additionally considering the general structure of spectrograms, which is called consistency, and hence, we call the proposed method Consistent ILRMA. Since a spectrogram is calculated by an overlapping window (and a window function induces spectral smearing called main- and side-lobes), the time-frequency bins depend on each other. In other words, the time-frequency components are related to each other via the uncertainty principle. Such co-occurrence among the spectral components can function as an assistant for solving the permutation problem, which has been demonstrated by a recent study. On the basis of these facts, we propose an algorithm for realizing Consistent ILRMA by slightly modifying the original algorithm. Its performance was extensively evaluated through experiments performed with various window lengths and shift lengths. The results indicated several tendencies of the original and proposed ILRMA that include some topics not fully discussed in the literature. For example, the proposed Consistent ILRMA tends to outperform the original ILRMA when the window length is sufficiently long compared to the reverberation time of the mixing system.


Author(s):  
Daichi Kitamura ◽  
Nobutaka Ono ◽  
Hiroshi Sawada ◽  
Hirokazu Kameoka ◽  
Hiroshi Saruwatari

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