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104
Learning Overcomplete Representations
, 2000
"... In an overcomplete basis, the number of basis vectors is greater than the dimensionality of the input, and the representation of an input is not a unique combination of basis vectors. Overcomplete representations have been advocated because they have greater robustness in the presence of noise, can ..."
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Cited by 257 (11 self)
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In an overcomplete basis, the number of basis vectors is greater than the dimensionality of the input, and the representation of an input is not a unique combination of basis vectors. Overcomplete representations have been advocated because they have greater robustness in the presence of noise, can be sparser, and can have greater flexibility in matching structure in the data. Overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex. Previous work has focused on finding the best representation of a signal using a fixed overcomplete basis (or dictionary). We present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data. We show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency. This can be viewed as a generalization of the technique of independent component analysis and provides a method for Bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures.
Independent Component Analysis Using an Extended Infomax Algorithm for Mixed SubGaussian and SuperGaussian Sources
, 1999
"... An extension of the infomax algorithm of Bell and Sejnowski (1995) is presented that is able to blindly separate mixed signals with sub and superGaussian source distributions. This was achieved by using a simple type of learning rule first derived by Girolami (1997) by choosing negentropy as a pro ..."
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Cited by 202 (21 self)
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An extension of the infomax algorithm of Bell and Sejnowski (1995) is presented that is able to blindly separate mixed signals with sub and superGaussian source distributions. This was achieved by using a simple type of learning rule first derived by Girolami (1997) by choosing negentropy as a projection pursuit index. Parameterized probability distributions that have suband superGaussian regimes were used to derive a general learning rule that preserves the simple architecture proposed by Bell and Sejnowski (1995), is optimized using the natural gradient by Amari (1998), and uses the stability analysis of Cardoso and Laheld (1996) to switch between sub and superGaussian regimes. We demonstrate that the extended infomax algorithm is able to easily separate 20 sources with a variety of source distributions. Applied to highdimensional data from electroencephalographic (EEG) recordings, it is effective at separating artifacts such as eye blinks and line noise from weaker electrical ...
Convolutive Blind Separation of NonStationary
"... Acoustic signals recorded simultaneously in a reverberant environment can be described as sums of differently convolved sources. The task of source separation is to identify the multiple channels and possibly to invert those in order to obtain estimates of the underlying sources. We tackle the probl ..."
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Cited by 129 (3 self)
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Acoustic signals recorded simultaneously in a reverberant environment can be described as sums of differently convolved sources. The task of source separation is to identify the multiple channels and possibly to invert those in order to obtain estimates of the underlying sources. We tackle the problem by explicitly exploiting the nonstationarity of the acoustic sources. Changing crosscorrelations at multiple times give a sufficient set of constraints for the unknown channels. A least squares optimization allows us to estimate a forward model, identifying thus the multipath channel. In the same manner we can find an FIR backward model, which generates well separated model sources. Furthermore, for more than three channels we have sufficient conditions to estimate underlying additive sensor noise powers. We show good performance in real room environments and demonstrate the algorithm's utility for automatic speech recognition.
A tutorial on onset detection in music signals
 IEEE Transactions in Speech and Audio Processing
, 2004
"... Abstract—Note onset detection and localization is useful in a number of analysis and indexing techniques for musical signals. The usual way to detect onsets is to look for “transient ” regions in the signal, a notion that leads to many definitions: a sudden burst of energy, a change in the shorttim ..."
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Cited by 117 (13 self)
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Abstract—Note onset detection and localization is useful in a number of analysis and indexing techniques for musical signals. The usual way to detect onsets is to look for “transient ” regions in the signal, a notion that leads to many definitions: a sudden burst of energy, a change in the shorttime spectrum of the signal or in the statistical properties, etc. The goal of this paper is to review, categorize, and compare some of the most commonly used techniques for onset detection, and to present possible enhancements. We discuss methods based on the use of explicitly predefined signal features: the signal’s amplitude envelope, spectral magnitudes and phases, timefrequency representations; and methods based on probabilistic signal models: modelbased change point detection, surprise signals, etc. Using a choice of test cases, we provide some guidelines for choosing the appropriate method for a given application.
A probabilistic framework for the adaptation and comparison of image codes
 J. Opt. Soc. Am. A
, 1999
"... We apply a Bayesian method for inferring an optimal basis to the problem of finding efficient image codes for natural scenes. The basis functions learned by the algorithm are oriented and localized in both space and frequency, bearing a resemblance to twodimensional Gabor functions, and increasing ..."
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Cited by 112 (9 self)
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We apply a Bayesian method for inferring an optimal basis to the problem of finding efficient image codes for natural scenes. The basis functions learned by the algorithm are oriented and localized in both space and frequency, bearing a resemblance to twodimensional Gabor functions, and increasing the number of basis functions results in a greater sampling density in position, orientation, and scale. These properties also resemble the spatial receptive fields of neurons in the primary visual cortex of mammals, suggesting that the receptivefield structure of these neurons can be accounted for by a general efficient coding principle. The probabilistic framework provides a method for comparing the coding efficiency of different bases objectively by calculating their probability given the observed data or by measuring the entropy of the basis function coefficients. The learned bases are shown to have better coding efficiency than traditional Fourier and wavelet bases. This framework also provides a Bayesian solution to the problems of image denoising and filling in of missing pixels. We demonstrate that the results obtained by applying the learned bases to these problems are improved over those obtained with traditional techniques. © 1999 Optical Society of America [S07403232(99)031075] OCIS codes: 000.5490, 100.2960, 100.3010.
Efficient coding of natural sounds
 Nature Neuroscience
, 2002
"... The auditory system encodes sound by decomposing the amplitude signal arriving at the ear into multiple frequency bands whose center frequencies and bandwidths are approximately logarithmic functions of the distance from the stapes. This particular organization is thought to result from the adaptati ..."
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Cited by 93 (3 self)
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The auditory system encodes sound by decomposing the amplitude signal arriving at the ear into multiple frequency bands whose center frequencies and bandwidths are approximately logarithmic functions of the distance from the stapes. This particular organization is thought to result from the adaptation of cochlear mechanisms to the statistics of an animal’s auditory environment. Here we report that several basic auditory nerve fiber tuning properties can be accounted for by adapting a population of filter shapes to optimally encode natural sounds. The form of the code is dependent on the class of sounds, resembling a Fourier transformation when optimized for animal vocalizations and a wavelet transformation when optimized for nonbiological environmental sounds. Only for a combined set of vocalizations and environmental sounds does the optimal code follow scaling characteristics that are consistent with physiological data. These results suggest that the population of auditory nerve fibers encode a broad set of natural sounds in a manner that is consistent with information theoretic principles. Correspondence:
A Unifying Informationtheoretic Framework for Independent Component Analysis
, 1999
"... We show that different theories recently proposed for Independent Component Analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pea ..."
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Cited by 82 (8 self)
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We show that different theories recently proposed for Independent Component Analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pearlmutter and Parra (1996) and Cardoso (1997) showed that the infomax approach of Bell and Sejnowski (1995) and the maximum likelihood estimation approach are equivalent. We show that negentropy maximization also has equivalent properties and therefore all three approaches yield the same learning rule for a fixed nonlinearity. Girolami and Fyfe (1997a) have shown that the nonlinear Principal Component Analysis (PCA) algorithm of Karhunen and Joutsensalo (1994) and Oja (1997) can also be viewed from informationtheoretic principles since it minimizes the sum of squares of the fourthorder marginal cumulants and therefore approximately minimizes the mutual information (Comon, 1994). Lambert (19...
Blind Source Separation of Real World Signals
 Proc. ICNN
, 1997
"... We present a method to separate and deconvolve sources which have been recorded in real environments. The use of noncausal FIR filters allows us to deal with nonminimum mixing systems. The learning rules can be derived from different viewpoints such as information maximization, maximum likelihood an ..."
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Cited by 53 (8 self)
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We present a method to separate and deconvolve sources which have been recorded in real environments. The use of noncausal FIR filters allows us to deal with nonminimum mixing systems. The learning rules can be derived from different viewpoints such as information maximization, maximum likelihood and negentropy which result in similar rules for the weight update. We transform the learning rule into the frequency domain where the convolution and deconvolution property becomes a multiplication and division operation. In particular, the FIR polynomial algebra techniques as used by Lambert present an efficient tool to solve true phase inverse systems allowing a simple implementation of noncausal filters. The significance of the methods is shown by the successful separation of two voices and separating a voice that has been recorded with loud music in the background. The recognition rate of an automatic speech recognition system is increased after separating the speech signals. 1 Introduct...
Energybased models for sparse overcomplete representations
 Journal of Machine Learning Research
, 2003
"... We present a new way of extending independent components analysis (ICA) to overcomplete representations. In contrast to the causal generative extensions of ICA which maintain marginal independence of sources, we define features as deterministic (linear) functions of the inputs. This assumption resul ..."
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Cited by 51 (14 self)
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We present a new way of extending independent components analysis (ICA) to overcomplete representations. In contrast to the causal generative extensions of ICA which maintain marginal independence of sources, we define features as deterministic (linear) functions of the inputs. This assumption results in marginal dependencies among the features, but conditional independence of the features given the inputs. By assigning energies to the features a probability distribution over the input states is defined through the Boltzmann distribution. Free parameters of this model are trained using the contrastive divergence objective (Hinton, 2002). When the number of features is equal to the number of input dimensions this energybased model reduces to noiseless ICA and we show experimentally that the proposed learning algorithm is able to perform blind source separation on speech data. In additional experiments we train overcomplete energybased models to extract features from various standard datasets containing speech, natural images, handwritten digits and faces.
A Bayesian approach to source separation
 in Proceedings of Independent Component Analysis Workshop
, 1999
"... The problem of source separation is by its very nature an inductive inference problem. There is not enough information to deduce the solution, so one must use any available information to infer the most probable solution. We demonstrate that source separation problems are wellsuited for the Bayesia ..."
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Cited by 48 (5 self)
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The problem of source separation is by its very nature an inductive inference problem. There is not enough information to deduce the solution, so one must use any available information to infer the most probable solution. We demonstrate that source separation problems are wellsuited for the Bayesian approach which provides a natural and logically consistent method by which one can incorporate prior knowledge to estimate the most probable solution given that knowledge. We derive the BellSejnowski ICA algorithm from first principles, i.e. Bayes ' Theorem and demonstrate how the Bayesian methodology makes explicit the underlying assumptions. We then further demonstrate the power of the Bayesian approach by deriving two separation algorithms that