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Blind Source Separation by Sparse Decomposition in a Signal Dictionary
, 2000
"... Introduction In blind source separation an N-channel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the M- ..."
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Cited by 270 (33 self)
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Introduction In blind source separation an N-channel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the M-dimensional source signal s(t). Many natural signals can be sparsely represented in a proper signal dictionary s i (t) = K X k=1 C ik ' k (t) (1.2) The scalar functions ' k
Monaural sound source separation by nonnegative matrix factorization with temporal continuity and sparseness criteria
- IEEE Trans. On Audio, Speech and Lang. Processing
, 2007
"... Abstract—An unsupervised learning algorithm for the separation of sound sources in one-channel music signals is presented. The algorithm is based on factorizing the magnitude spectrogram of an input signal into a sum of components, each of which has a fixed magnitude spectrum and a time-varying gain ..."
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Cited by 185 (30 self)
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Abstract—An unsupervised learning algorithm for the separation of sound sources in one-channel music signals is presented. The algorithm is based on factorizing the magnitude spectrogram of an input signal into a sum of components, each of which has a fixed magnitude spectrum and a time-varying gain. Each sound source, in turn, is modeled as a sum of one or more components. The parameters of the components are estimated by minimizing the reconstruction error between the input spectrogram and the model, while restricting the component spectrograms to be nonnegative and favoring components whose gains are slowly varying and sparse. Temporal continuity is favored by using a cost term which is the sum of squared differences between the gains in adjacent frames, and sparseness is favored by penalizing nonzero gains. The proposed iterative estimation algorithm is initialized with random values, and the gains and the spectra are then alternatively updated using multiplicative update rules until the values converge. Simulation experiments were carried out using generated mixtures of pitched musical instrument samples and drum sounds. The performance of the proposed method was compared with independent subspace analysis and basic nonnegative matrix factorization, which are based on the same linear model. According to these simulations, the proposed method enables a better separation quality than the previous algorithms. Especially, the temporal continuity criterion improved the detection of pitched musical sounds. The sparseness criterion did not produce significant improvements. Index Terms—Acoustic signal analysis, audio source separation, blind source separation, music, nonnegative matrix factorization, sparse coding, unsupervised learning. I.
A Survey of Dimension Reduction Techniques
, 2002
"... this paper, we assume that we have n observations, each being a realization of the p- dimensional random variable x = (x 1 , . . . , x p ) with mean E(x) = = ( 1 , . . . , p ) and covariance matrix E{(x )(x = # pp . We denote such an observation matrix by X = i,j : 1 p, 1 ..."
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Cited by 137 (0 self)
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this paper, we assume that we have n observations, each being a realization of the p- dimensional random variable x = (x 1 , . . . , x p ) with mean E(x) = = ( 1 , . . . , p ) and covariance matrix E{(x )(x = # pp . We denote such an observation matrix by X = i,j : 1 p, 1 n}. If i and # i = # (i,i) denote the mean and the standard deviation of the ith random variable, respectively, then we will often standardize the observations x i,j by (x i,j i )/ # i , where i = x i = 1/n j=1 x i,j , and # i = 1/n j=1 (x i,j x i )
A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals
, 2000
"... Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article it is assumed that the original, complex valued source signals are mutually statis ..."
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Cited by 128 (1 self)
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Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article it is assumed that the original, complex valued source signals are mutually statistically independent, and the problem is solved by the independent component analysis (ICA) model. ICA is a statistical method for transforming an observed multidimensional random vector into components that are mutually as independent as possible. In this article, a fast xed-point type algorithm that is capable of separating complex valued, linearly mixed source signals is presented and its computational efficiency is shown by simulations. Also, the local consistency of the estimator given by the algorithm is proved.
A robust and precise method for solving the permutation problem of frequency-domain blind source separation
- IEEE Trans. on Speech and Audio Processing 12
, 2004
"... This paper presents a robust and precise method for solving the permutation problem of frequency-domain blind source separation. It is based on two previous approaches: the direction of arrival estimation and the inter-frequency correlation. We discuss the advantages and disadvantages of the two app ..."
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Cited by 115 (27 self)
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This paper presents a robust and precise method for solving the permutation problem of frequency-domain blind source separation. It is based on two previous approaches: the direction of arrival estimation and the inter-frequency correlation. We discuss the advantages and disadvantages of the two approaches, and integrate them to exploit their respective advantages. We also present a closed form formula to estimate the directions of source signals from a separating matrix obtained by ICA. Experimental results show that our method solved permutation problems almost perfectly for a situation that two sources were mixed in a room whose reverberation time was 300 ms. 1.
A linear non-gaussian acyclic model for causal discovery
- J. Machine Learning Research
, 2006
"... In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to ..."
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Cited by 101 (28 self)
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In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of continuous-valued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have non-Gaussian distributions of non-zero variances. The solution relies on the use of the statistical method known as independent component analysis, and does not require any pre-specified time-ordering of the variables. We provide a complete Matlab package for performing this LiNGAM analysis (short for Linear Non-Gaussian Acyclic Model), and demonstrate the effectiveness of the method using artificially generated data and real-world data.
BValidating the independent components of neuroimaging time series via clustering and visualization
- NeuroImage
, 2004
"... and visualization ..."
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On the best rank-1 approximation of higher-order supersymmetric tensors
- SIAM J. Matrix Anal. Appl
, 2002
"... Abstract. Recently the problem of determining the best, in the least-squares sense, rank-1 approximation to a higher-order tensor was studied and an iterative method that extends the wellknown power method for matriceswasproposed for itssolution. Thishigher-order power method is also proposed for th ..."
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Cited by 79 (1 self)
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Abstract. Recently the problem of determining the best, in the least-squares sense, rank-1 approximation to a higher-order tensor was studied and an iterative method that extends the wellknown power method for matriceswasproposed for itssolution. Thishigher-order power method is also proposed for the special but important class of supersymmetric tensors, with no change. A simplified version, adapted to the special structure of the supersymmetric problem, is deemed unreliable, asitsconvergence isnot guaranteed. The aim of thispaper isto show that a symmetric version of the above method converges under assumptions of convexity (or concavity) for the functional induced by the tensor in question, assumptions that are very often satisfied in practical applications. The use of this version entails significant savings in computational complexity as compared to the unconstrained higher-order power method. Furthermore, a novel method for initializing the iterative processisdeveloped which hasbeen observed to yield an estimate that liescloser to the global optimum than the initialization suggested before. Moreover, its proximity to the global optimum is a priori quantifiable. In the course of the analysis, some important properties that the supersymmetry of a tensor implies for its square matrix unfolding are also studied.
