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Maximum Marginal Likelihood Estimation for Nonnegative Dictionary Learning in the Gamma-Poisson Model

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2012年第10期60卷 5163-5175页

作者： Dikmen, Onur Fevotte, Cedric Telecom ParisTech F-75014 Paris France CNRS LTCI Paris France

In this paper we describe an alternative to standard nonnegative matrix factorization (NMF) for nonnegative dictionary learning, i.e., the task of learning a dictionary with nonnegative values from nonnegative data, under the assumption of nonnegative expansion coefficients. A popular cost function used for NMF is the Kullback-Leibler divergence, which underlies a Poisson observation model. NMF can thus be considered as maximization of the joint likelihood of the dictionary and the expansion coefficients. This approach lacks optimality because the number of parameters (which include the expansion coefficients) grows with the number of observations. In this paper we describe variational Bayes and Monte-Carlo EM algorithms for optimization of the marginal likelihood, i.e., the likelihood of the dictionary where the expansion coefficients have been integrated out (given a Gamma prior). We compare the output of both maximum joint likelihood estimation (i.e., standard NMF) and maximum marginal likelihood estimation (MMLE) on real and synthetical datasets. In particular we present face reconstruction results on CBCL dataset and text retrieval results over the musiXmatch dataset, a collection of word counts in song lyrics. The MMLE approach is shown to prevent overfitting by automatically pruning out irrelevant dictionary columns, i.e., embedding automatic model order selection.

关键词： Automatic relevance determination model order selection Monte Carlo EM nonnegative matrix factorization sparse coding variational EM

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Denoising MMW image using the combination method of contourlet and KSC shrinkage

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NEUROCOMPUTING 2012年 83卷 229-233页

作者： Shang, Li Su, Pin-gang Liu, Tao Suzhou Vocat Univ Dept Elect Informat Engn Suzhou 215104 Jiangsu Peoples R China Univ Sci & Technol China Dept Automat Hefei 230026 Anhui Peoples R China Southeast Univ State Key Lab Millimeter Waves Nanjing 210096 Jiangsu Peoples R China

A new denoising method of milli-meter wave (MMW) image using contourlet and kurtosis based sparse coding (KSC) is proposed in this paper. KSC is a high-order statistical method and can efficiently extract image feature coefficients. Contourlet method has the decomposition property of orientation and the energy variation for images. Further, using the shrinkage threshold that is determined by the sparse prior distribution of feature coefficients extracted in the contourlet transform field, the unknown noise contained in MMW image can be reduced efficiently. In test, an artificial MMW image and a true MMW are respectively used to validate our method, further, compared this method with other denoising methods, the simulation results show this method proposed here can obtain the better quality of image restoration. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Contourlet transformation Kurtosis sparse coding Millimeter wave image Denoising

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Binary Willshaw learning yields high synaptic capacity for long-term familiarity memory

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BIOLOGICAL CYBERNETICS 2012年第2期106卷 123-133页

作者： Sacramento, Joao Wichert, Andreas Univ Tecn Lisboa INESC ID P-2744016 Porto Salvo Portugal Univ Tecn Lisboa Inst Super Tecn P-2744016 Porto Salvo Portugal

In this study, we investigate from a computational perspective the efficiency of the Willshaw synaptic update rule in the context of familiarity discrimination, a binary-answer, memory-related task that has been linked through psychophysical experiments with modified neural activity patterns in the prefrontal and perirhinal cortex regions. Our motivation for recovering this well-known learning prescription is two-fold: first, the switch-like nature of the induced synaptic bonds, as there is evidence that biological synaptic transitions might occur in a discrete stepwise fashion. Second, the possibility that in the mammalian brain, unused, silent synapses might be pruned in the long-term. Besides the usual pattern and network capacities, we calculate the synaptic capacity of the model, a recently proposed measure where only the functional subset of synapses is taken into account. We find that in terms of network capacity, Willshaw learning is strongly affected by the pattern coding rates, which have to be kept fixed and very low at any time to achieve a non-zero capacity in the large network limit. The information carried per functional synapse, however, diverges and is comparable to that of the pattern association case, even for more realistic moderately low activity levels that are a function of network size.

关键词： Familiarity memory Willshaw rule Synaptic capacity sparse coding

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Dictionary Learning for Noisy and Incomplete Hyperspectral Images

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SIAM JOURNAL ON IMAGING SCIENCES 2012年第1期5卷 33-56页

作者： Xing, Zhengming Zhou, Mingyuan Castrodad, Alexey Sapiro, Guillermo Carin, Lawrence Duke Univ Dept Elect & Comp Engn Durham NC 27708 USA Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA

We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelength dependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering the potential to significantly reduce the quantity of data that need be measured. To achieve this objective, the imagery is divided into contiguous three-dimensional (3D) spatio-spectral blocks of spatial dimension much less than the image dimension. It is assumed that each such 3D block may be represented as a linear combination of dictionary elements of the same dimension, plus noise, and the dictionary elements are learned in situ based on the observed data (no a priori training). The number of dictionary elements needed for representation of any particular block is typically small relative to the block dimensions, and all the image blocks are processed jointly ("collaboratively") to infer the underlying dictionary. We address dictionary learning from a Bayesian perspective, considering two distinct means of imposing sparse dictionary usage. These models allow inference of the number of dictionary elements needed as well as the underlying wavelength-dependent noise statistics. It is demonstrated that drawing the dictionary elements from a Gaussian process prior, imposing structure on the wavelength dependence of the dictionary elements, yields significant advantages, relative to the more conventional approach of using an independent and identically distributed Gaussian prior for the dictionary elements;this advantage is particularly evident in the presence of noise. The framework is demonstrated by processing hyperspectral imagery with a significant number of voxels missing uniformly at random, with imagery at specific wavelengths missing entirely, and in the presence of substantial additive noise.

关键词： hyperspectral imagery missing data dictionary learning sparse coding Bayesian framework Gaussian process denoising beta process Indian buffet process Gibbs sampler parameter-free interpolation

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sparse nonnegative matrix factorization with l⁰-constraints

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NEUROCOMPUTING 2012年第1期80卷 38-46页

作者： Peharz, Robert Pernkopf, Franz Graz Univ Technol Signal Proc & Speech Commun Lab Intelligent Syst Res Grp A-8010 Graz Austria

Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the l(1)-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the l(0)-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the l(0)-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches. (C) 2011 Elsevier B.V. All rights reserved.

关键词： NMF sparse coding Nonnegative least squares

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sparsely Encoded Hopfield Model with Unit Replacement

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2012年第8期E95D卷 2124-2132页

作者： Miyata, Ryota Kurata, Koji Aonishi, Toru Tokyo Inst Technol Interdisciplinary Grad Sch Sci & Engn Yokohama Kanagawa 2268502 Japan Univ Ryukyus Fac Engn Okinawa 9030213 Japan

We investigate a sparsely encoded Hopfield model with unit replacement by using a statistical mechanical method called self-consistent signal-to-noise analysis. We theoretically obtain a relation between the storage capacity and the number of replacement units for each sparseness a. Moreover, we compare the unit replacement model with the forgetting model in terms of the network storage capacity. The results show that the unit replacement model has a finite value of the optimal sparseness on an open interval 0(1/2 coding) < a < 1 (the limit of sparseness) to maximize the storage capacity for a large number of replacement units, although the forgetting model does not.

关键词： neurogenesis associative memory unit replacement SCSNA sparse coding forgetting process

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Learning Dictionaries With Bounded Self-Coherence

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IEEE SIGNAL PROCESSING LETTERS 2012年第12期19卷 861-864页

作者： Sigg, Christian D. Dikk, Tomas Buhmann, Joachim M. Swiss Fed Off Meteorol & Climatol MeteoSwiss Zurich Switzerland ETH Dept Comp Sci Zurich Switzerland

sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training data matrix into a dictionary and a sparse coding matrix. The learned dictionary is characterized by two properties: the coherence of the dictionary to observations of the signal class, and the self-coherence of the dictionary atoms. A high coherence to the signal class enables the sparse coding of signal observations with a small approximation error, while a low self-coherence of the atoms guarantees atom recovery and a more rapid residual error decay rate for the sparse coding algorithm. The two goals of high signal coherence and low self-coherence are typically in conflict, therefore one seeks a trade-off between them, depending on the application. We present a dictionary learning method with an effective control over the self-coherence of the trained dictionary, enabling a trade-off between maximizing the sparsity of codings and approximating an equi-angular tight frame.

关键词： Coherence dictionary learning sparse coding coherence

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Harnessing plasticity to understand learning and treat disease

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TRENDS IN NEUROSCIENCES 2012年第12期35卷 715-722页

作者： Kilgard, Michael P. Univ Texas Dallas Sch Behav & Brain Sci Richardson TX 75080 USA

A large body of evidence suggests that neural plasticity contributes to learning and disease. Recent studies suggest that cortical map plasticity is typically a transient phase that improves learning by increasing the pool of task-relevant responses. Here, I discuss a new perspective on neural plasticity and suggest how plasticity might be targeted to reset dysfunctional circuits. Specifically, a new model is proposed in which map expansion provides a form of replication with variation that supports a Darwinian mechanism to select the most behaviorally useful circuits. Precisely targeted neural plasticity provides a new avenue for the treatment of neurological and psychiatric disorders and is a powerful tool to test the neural mechanisms of learning and memory.

关键词： vagus nerve stimulation rehabilitation neuropathology sparse coding neuromodulation tinnitus

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PROTOTYPE SELECTION FOR PARAMETER ESTIMATION IN COMPLEX MODELS

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ANNALS OF APPLIED STATISTICS 2012年第1期6卷 383-408页

作者： Richards, Joseph W. Lee, Ann B. Schafer, Chad M. Freeman, Peter E. Univ Calif Berkeley Dept Astron Berkeley CA 94720 USA Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA

Parameter estimation in astrophysics often requires the use of complex physical models. In this paper we study the problem of estimating the parameters that describe star formation history (SFH) in galaxies. Here, high-dimensional spectral data from galaxies are appropriately modeled as linear combinations of physical components, called simple stellar populations (SSPs), plus some nonlinear distortions. Theoretical data for each SSP is produced for a fixed parameter vector via computer modeling. Though the parameters that define each SSP are continuous, optimizing the signal model over a large set of SSPs on a fine parameter grid is computationally infeasible and inefficient. The goal of this study is to estimate the set of parameters that describes the SFH of each galaxy. These target parameters, such as the average ages and chemical compositions of the galaxy's stellar populations, are derived from the SSP parameters and the component weights in the signal model. Here, we introduce a principled approach of choosing a small basis of SSP prototypes for SFH parameter estimation. The basic idea is to quantize the vector space and effective support of the model components. In addition to greater computational efficiency, we achieve better estimates of the SFH target parameters. In simulations, our proposed quantization method obtains a substantial improvement in estimating the target parameters over the common method of employing a parameter grid. sparse coding techniques are not appropriate for this problem without proper constraints, while constrained sparse coding methods perform poorly for parameter estimation because their objective is signal reconstruction, not estimation of the target parameters.

关键词： Astrostatistics high-dimensional statistics physical modeling mixture models model quantization K-means sparse coding

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Iterative Thresholding-based sparse Directional Representation for Efficient Low Bit-Rate Embedded Video coding

Iterative Thresholding-based Sparse Directional Representati...

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Data Compression Conference (DCC)

作者： Zhu, Lingchen Xiong, Hongkai Shanghai Jiao Tong Univ Dept Elect Engn Shanghai 200240 Peoples R China

ISBN: (纸本)9780769543529

The contourlet transform provides a flexible directional image decomposition by employing Laplacian pyramid and uniform directional filter banks. Although it is able to efficiently capture the 2-D piecewise smooth functions with line or curve discontinuities, its major drawbacks of 4/3 redundancy and non-ideal filter banks in Laplacian pyramid are the main obstacles for high performance image/video coding. In this paper, we propose a video coding scheme based on the sharp frequency localized contourlet transform (contourlet/SFL) under the sparse representation framework, in which the iterative thresholding algorithm is applied to get an l(1) norm sparser version of the transform coefficients. In the meantime, considering the fact that strong inter-band and inter-scale dependencies exist in the contourlet/SFL coefficients, a directional embedded image coding system is proposed to propagate the significance status by using the neighbor, cousin and parent significant coefficients as seeds. Experimental results show that the coding performance and visual quality of the sparse contourlet/SFL based video compression scheme are superior to the wavelet-based one, especially on those sequences full of directional structures at low bit rates.

关键词： embedded coding multiscale geometric analysis sparse coding embedded encoding sparse coding Laplacian pyramid Bit rate Video coding profile transformation DIRECTIONAL Filter banks Multiscale analysis Image decomposition Video compression sparse representation

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