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389
Independent Component Analysis
 Neural Computing Surveys
, 2001
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
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Cited by 1492 (93 self)
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A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1
A fast fixedpoint algorithm for independent component analysis
 Neural Computation
, 1997
"... Abstract. Independent Subspace Analysis (ISA; Hyvarinen & Hoyer, 2000) is an extension of ICA. In ISA, the components are divided into subspaces and components in different subspaces are assumed independent, whereas components in the same subspace have dependencies.In this paper we describe a fixed ..."
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Cited by 429 (19 self)
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Abstract. Independent Subspace Analysis (ISA; Hyvarinen & Hoyer, 2000) is an extension of ICA. In ISA, the components are divided into subspaces and components in different subspaces are assumed independent, whereas components in the same subspace have dependencies.In this paper we describe a fixedpoint algorithm for ISA estimation, formulated in analogy to FastICA. In particular we give a proof of the quadratic convergence of the algorithm, and present simulations that confirm the fast convergence, but also show that the method is prone to convergence to local minima. 1
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
, 2000
"... Introduction In blind source separation an Nchannel 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 193 (32 self)
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Introduction In blind source separation an Nchannel 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 Mdimensional 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
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 87 (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 FixedPoint 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 84 (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 xedpoint 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.
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 onechannel 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 timevarying gain ..."
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Cited by 81 (10 self)
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Abstract—An unsupervised learning algorithm for the separation of sound sources in onechannel 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 timevarying 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 linear nongaussian 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 nonexperimental 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 54 (23 self)
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In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental 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 continuousvalued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have nonGaussian distributions of nonzero variances. The solution relies on the use of the statistical method known as independent component analysis, and does not require any prespecified timeordering of the variables. We provide a complete Matlab package for performing this LiNGAM analysis (short for Linear NonGaussian Acyclic Model), and demonstrate the effectiveness of the method using artificially generated data and realworld data.
Statistical Shape Analysis: Clustering, Learning, and Testing
 IEEE Trans. Pattern Anal. Mach. Intell
, 2005
"... Using a recently proposed geometric representation of planar shapes, we present algorithmic tools for: (i) hierarchical clustering of imaged objects according to the shapes of their boundaries, (ii) learning of probability models for clustered shapes, and (iii) testing of observed shapes under co ..."
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Cited by 51 (6 self)
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Using a recently proposed geometric representation of planar shapes, we present algorithmic tools for: (i) hierarchical clustering of imaged objects according to the shapes of their boundaries, (ii) learning of probability models for clustered shapes, and (iii) testing of observed shapes under competing probability models. Clustering at any level of hierarchy is performed using a mimimum dispersion criterion and a Markov search process. Statistical means of clusters provide shapes to be clustered at the next higher level, thus building a hierarchy of shapes.
A MultiLayer Sparse Coding Network Learns Contour Coding From Natural Images
, 2002
"... An important approach in visual neuroscience considers how the function of the early visual system relates to the statistics of its natural input. Previous studies have shown how many basic properties of the primary visual cortex, such as the receptive fields of simple and complex cells and the sp ..."
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Cited by 49 (10 self)
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An important approach in visual neuroscience considers how the function of the early visual system relates to the statistics of its natural input. Previous studies have shown how many basic properties of the primary visual cortex, such as the receptive fields of simple and complex cells and the spatial organization (topography) of the cells, can be understood as efficient coding of natural images. Here we extend the framework by considering how the responses of complex cells could be sparsely represented by a higherorder neural layer. This leads to contour coding and endstopped receptive fields. In addition, contour integration could be interpreted as topdown inference in the presented model.