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50
1 Dictionary Learning for Sparse Approximations with the Majorization Method
"... Abstract—In order to find sparse approximations of signals, an appropriate generative model for the signal class has to be known. If the model is unknown, it can be adapted using a set of training samples. This paper presents a novel method for dictionary learning and extends the learning problem by ..."
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Cited by 49 (10 self)
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Abstract—In order to find sparse approximations of signals, an appropriate generative model for the signal class has to be known. If the model is unknown, it can be adapted using a set of training samples. This paper presents a novel method for dictionary learning and extends the learning problem by introducing different constraints on the dictionary. The convergence of the proposed method to a fixed point is guaranteed, unless the accumulation points form a continuum. This holds for different sparsity measures. The majorization method is an optimization method that substitutes the original objective function with a surrogate function that is updated in each optimization step. This method has been used successfully in sparse approximation and statistical estimation (e.g. Expectation Maximization (EM)) problems. This paper shows that the majorization method can be used for the dictionary learning problem too. The proposed method is compared with other methods on both synthetic and real data and different constraints on the dictionary are compared. Simulations show the advantages of the proposed method over other currently available dictionary learning methods not only in terms of average performance but also in terms of computation time.
Recovery of sparse translationinvariant signals with continuous basis pursuit
 IEEE Trans Signal Processing
, 2011
"... Abstract—We consider the problem of decomposing a signal into a linear combination of features, each a continuously translated version of one of a small set of elementary features. Although these constituents are drawn from a continuous family, most current signal decomposition methods rely on a �ni ..."
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Cited by 28 (0 self)
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Abstract—We consider the problem of decomposing a signal into a linear combination of features, each a continuously translated version of one of a small set of elementary features. Although these constituents are drawn from a continuous family, most current signal decomposition methods rely on a �nite dictionary of discrete examples selected from this family (e.g., shifted copies of a set of basic waveforms), and apply sparse optimization methods to select and solve for the relevant coef�cients. Here, we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coef�cients. We formulate a constrained convex optimization problem, in which the full set of dictionary coef�cients represents a linear approximation of the signal, the auxiliary coef�cients are constrained so as to only represent translated features, and sparsity is imposed on the primary coef�cients using an L1 penalty. The basis pursuit denoising
M.: Parametric Dictionary Design for Sparse Coding
 IEEE Trans. on Signal Processing
, 2009
"... Abstract—This paper introduces a new dictionary design method for sparse coding of a class of signals. It has been shown that one can sparsely approximate some natural signals using an overcomplete set of parametric functions, e.g. [1], [2]. A problem in using these parametric dictionaries is how to ..."
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Cited by 20 (5 self)
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Abstract—This paper introduces a new dictionary design method for sparse coding of a class of signals. It has been shown that one can sparsely approximate some natural signals using an overcomplete set of parametric functions, e.g. [1], [2]. A problem in using these parametric dictionaries is how to choose the parameters. In practice these parameters have been chosen by an expert or through a set of experiments. In the sparse approximation context, it has been shown that an incoherent dictionary is appropriate for the sparse approximation methods. In this paper we first characterize the dictionary design problem, subject to a constraint on the dictionary. Then we briefly explain that equiangular tight frames have minimum coherence. The complexity of the problem does not allow it to be solved exactly. We introduce a practical method to approximately solve it. Some experiments show the advantages one gets by using these dictionaries.
ON THE USE OF SPARSE TIMERELATIVE AUDITORY CODES FOR MUSIC
 ISMIR 2008
, 2008
"... Many if not most audio features used in MIR research are inspired by work done in speech recognition and are variations on the spectrogram. Recently, much attention has been given to new representations of audio that are sparse and timerelative. These representations are efficient and able to avoid ..."
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Cited by 12 (2 self)
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Many if not most audio features used in MIR research are inspired by work done in speech recognition and are variations on the spectrogram. Recently, much attention has been given to new representations of audio that are sparse and timerelative. These representations are efficient and able to avoid the timefrequency tradeoff of a spectrogram. Yet little work with music streams has been conducted and these features remain mostly unused in the MIR community. In this paper we further explore the use of these features for musical signals. In particular, we investigate their use on realistic music examples (i.e. released commercial music) and their use as input features for supervised learning. Furthermore, we identify three specific issues related to these features which will need to be further addressed in order to obtain the full benefit for MIR applications. 1
A BiologicallyInspired LowBitRate Universal Audio Coder," AES Convention
, 2007
"... The papers at this Convention have been selected on the basis of a submitted abstract and extended precis that have been peer reviewed by at least two qualified anonymous reviewers. This convention paper has been reproduced from the author’s advance manuscript, without editing, corrections, or consi ..."
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Cited by 11 (6 self)
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The papers at this Convention have been selected on the basis of a submitted abstract and extended precis that have been peer reviewed by at least two qualified anonymous reviewers. This convention paper has been reproduced from the author’s advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request and remittance to Audio
Faithful representation of stimuli with a population of integrateandfi re neurons
 Neural Comput
, 2008
"... We consider a formal model of stimulus encoding with a circuit consisting of a bank of filters and an ensemble of integrateandfire neurons. Such models arise in olfactory systems, vision, and hearing. We demonstrate that bandlimited stimuli can be faithfully represented with spike trains generate ..."
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Cited by 8 (3 self)
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We consider a formal model of stimulus encoding with a circuit consisting of a bank of filters and an ensemble of integrateandfire neurons. Such models arise in olfactory systems, vision, and hearing. We demonstrate that bandlimited stimuli can be faithfully represented with spike trains generated by the ensemble of neurons. We provide a stimulus reconstruction scheme based on the spike times of the ensemble of neurons and derive conditions for perfect recovery. The key result calls for the spike density of the neural population to be above the Nyquist rate. We also show that recovery is perfect if the number of neurons in the population is larger than a threshold value. Increasing the number of neurons to achieve a faithful representation of the sensory world is consistent with basic neurobiological thought. Finally we demonstrate that in general, the problem of faithful recovery of stimuli from the spike train of single neurons is ill posed. The stimulus can be recovered, however, from the information contained in the spike train of a population of neurons.
Sparse decomposition of transformationinvariant signals with continuous basis pursuit
 in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP
, 2011
"... Consider the decomposition of a signal into features that undergo transformations drawn from a continuous family. Current methods discretely sample the transformations and apply sparse recovery methods to the resulting finite dictionary. These methods do not exploit the underlying continuous structu ..."
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Cited by 8 (4 self)
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Consider the decomposition of a signal into features that undergo transformations drawn from a continuous family. Current methods discretely sample the transformations and apply sparse recovery methods to the resulting finite dictionary. These methods do not exploit the underlying continuous structure, thereby limiting the ability to produce sparse solutions. Instead, we employ interpolation functions which linearly approximate the manifold of scaled and transformed features. Coefficients are interpreted as interpolation weights, and we formulate a convex optimization problem for obtaining them, enforcing both reconstruction accuracy and sparsity. We compare our method, which we call continuous basis pursuit (CBP) with the standard basis pursuit approach on a sparse deconvolution task. CBP yields substantially sparser solutions without sacrificing accuracy, and does so with a smaller dictionary. We conclude that for signals generated by transformationinvariant processes, a representation that explicitly accommodates the transformation(s) can yield sparser and more interpretable decompositions. Index Terms — sparsity, feature decomposition, basis pursuit, interpolation, invariance 1.
Fractionally Predictive Spiking Neurons
"... Recent experimental work has suggested that the neural firing rate can be interpreted as a fractional derivative, at least when signal variation induces neural adaptation. Here, we show that the actual neural spiketrain itself can be considered as the fractional derivative, provided that the neural ..."
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Cited by 5 (3 self)
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Recent experimental work has suggested that the neural firing rate can be interpreted as a fractional derivative, at least when signal variation induces neural adaptation. Here, we show that the actual neural spiketrain itself can be considered as the fractional derivative, provided that the neural signal is approximated by a sum of powerlaw kernels. A simple standard thresholding spiking neuron suffices to carry out such an approximation, given a suitable refractory response. Empirically, we find that the online approximation of signals with a sum of powerlaw kernels is beneficial for encoding signals with slowly varying components, like longmemory selfsimilar signals. For such signals, the online powerlaw kernel approximation typically required less than half the number of spikes for similar SNR as compared to sums of similar but exponentially decaying kernels. As powerlaw kernels can be accurately approximated using sums or cascades of weighted exponentials, we demonstrate that the corresponding decoding of spiketrains by a receiving neuron allows for natural and transparent temporal signal filtering by tuning the weights of the decoding kernel. 1
Encoding and Decoding Spikes for Dynamic Stimuli
, 2008
"... Naturally occurring sensory stimuli are dynamic. In this article, we consider how spiking neural populations might transmit information about continuous dynamic stimulus variables. The combination of simple encoders and temporal stimulus correlations leads to a code in which information is not readi ..."
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Cited by 5 (0 self)
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Naturally occurring sensory stimuli are dynamic. In this article, we consider how spiking neural populations might transmit information about continuous dynamic stimulus variables. The combination of simple encoders and temporal stimulus correlations leads to a code in which information is not readily available to downstream neurons. Here, we explore a complex encoder that is paired with a simple decoder that allows representation and manipulation of the dynamic information in neural systems. The encoder we present takes the form of a biologically plausible recurrent spiking neural network where the output population recodes its inputs to produce spikes that are independently decodeable. We show that this network can be learned in a supervised manner by a simple local learning rule.