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82
Families of Alpha Beta and GammaDivergences: Flexible and Robust Measures of Similarities
, 2010
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Tensor Displays: Compressive Light Field Synthesis using Multilayer Displays with Directional Backlighting
 ACM Transactions on Graphics (Proc. SIGGRAPH
, 2012
"... Figure 1: Wide field of view glassesfree 3D display using tensor displays. (Left) We introduce a new family of light field displays, dubbed tensor displays, comprised of stacks of lightattenuating layers (e.g., multilayer LCDs). Rapid temporal modulation of the layers is exploited, in concert with ..."
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Cited by 25 (11 self)
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Figure 1: Wide field of view glassesfree 3D display using tensor displays. (Left) We introduce a new family of light field displays, dubbed tensor displays, comprised of stacks of lightattenuating layers (e.g., multilayer LCDs). Rapid temporal modulation of the layers is exploited, in concert with directional backlighting, to allow large separations between viewers. (Right) From left to right: target light field view, photograph of threelayer LCD with uniform backlighting, and photograph of single LCD with directional backlighting. Layers are shown to the right of each photograph. The upper and lower rows depict perspectives seen to the left and to the right of the display, respectively. We introduce tensor displays: a family of compressive light field displays comprising all architectures employing a stack of timemultiplexed, lightattenuating layers illuminated by uniform or directional backlighting (i.e., any lowresolution light field emitter). We show that the light field emitted by anNlayer,Mframe tensor display can be represented by an N thorder, rankM tensor. Using this representation we introduce a unified optimization framework, based on nonnegative tensor factorization (NTF), encompassing all tensor display architectures. This framework is the first to allow joint multilayer, multiframe light field decompositions, significantly reducing artifacts observed with prior multilayeronly and multiframeonly decompositions; it is also the first optimization method for designs combining multiple layers with directional backlighting. We verify the benefits and limitations of tensor displays by constructing a prototype using modified LCD panels and a custom integral imaging backlight. Our efficient, GPUbased NTF implementation enables interactive applications. Through simulations and experiments we show that tensor displays reveal practical architectures with greater depths of field, wider fields of view, and thinner form factors, compared to prior automultiscopic displays.
Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions
"... Lowdimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed, finitedimensional feature representation. Here we consider a diff ..."
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Cited by 24 (12 self)
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Lowdimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed, finitedimensional feature representation. Here we consider a different setting. We assume that each instance corresponds to a continuous probability distribution. These distributions are unknown, but we are given some i.i.d. samples from each distribution. Our goal is to estimate the distances between these distributions and use these distances to perform lowdimensional embedding, clustering/classification, or anomaly detection for the distributions. We present estimation algorithms, describe how to apply them for machine learning tasks on distributions, and show empirical results on synthetic data, real word images, and astronomical data sets. 1
Fast conical hull algorithms for nearseparable nonnegative matrix factorization
 In ACM/IEEE conference on Supercomputing
, 2009
"... The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012a) turns nonnegative matrix factorization (NMF) into a tractable problem. Recently, a new class of provablycorrect NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem a ..."
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Cited by 21 (1 self)
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The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012a) turns nonnegative matrix factorization (NMF) into a tractable problem. Recently, a new class of provablycorrect NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometricperspective, we derive new separable NMF algorithms that are highly scalable and empirically noise robust, and haveseveralotherfavorablepropertiesin relation to existing methods. A parallel implementation of our algorithm demonstrates high scalability on shared and distributedmemory machines. 1.
RealTime Speech Separation by Semisupervised Nonnegative Matrix Factorization
"... Abstract. In this paper, we present an online semisupervised algorithm for realtime separation of speech and background noise. The proposed system is based on Nonnegative Matrix Factorization (NMF), where fixed speech bases are learned from training data whereas the noise components are estimated ..."
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Cited by 17 (8 self)
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Abstract. In this paper, we present an online semisupervised algorithm for realtime separation of speech and background noise. The proposed system is based on Nonnegative Matrix Factorization (NMF), where fixed speech bases are learned from training data whereas the noise components are estimated in realtime on the recent past. Experiments with spontaneous conversational speech and reallife nonstationary noise show that this system performs as well as a supervised NMF algorithm exploiting noise components learned from the same noise environment as the test sample. Furthermore, it outperforms a supervised system trained on different noise conditions. 1
Nonnegative Matrix Factorization: A Comprehensive Review
 IEEE TRANS. KNOWLEDGE AND DATA ENG
, 2013
"... Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception. It incorporates the nonnegativity constraint and thus obtains the partsbased representation as well as enhancing the interpretability of the issue corres ..."
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Cited by 17 (2 self)
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Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception. It incorporates the nonnegativity constraint and thus obtains the partsbased representation as well as enhancing the interpretability of the issue correspondingly. This survey paper mainly focuses on the theoretical research into NMF over the last 5 years, where the principles, basic models, properties, and algorithms of NMF along with its various modifications, extensions, and generalizations are summarized systematically. The existing NMF algorithms are divided into four categories: Basic NMF (BNMF),
Cemgil, “Probabilistic latent tensor factorization
 in LVA/ICA, 2010
"... Abstract. We develop a probabilistic framework for multiway analysis of high dimensional datasets. By exploiting a link between graphical models and tensor factorization models we can realize any arbitrary tensor factorization structure, and many popular models such as CP or TUCKER models with Eucli ..."
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Cited by 13 (0 self)
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Abstract. We develop a probabilistic framework for multiway analysis of high dimensional datasets. By exploiting a link between graphical models and tensor factorization models we can realize any arbitrary tensor factorization structure, and many popular models such as CP or TUCKER models with Euclidean error and their nonnegative variants with KL error appear as special cases. Due to the duality between exponential families and Bregman divergences, we can cast the problem as inference in a model with Gaussian or Poisson components, where tensor factorisation reduces to a parameter estimation problem. We derive the generic form of update equations for multiplicative and alternating least squares. We also propose a straightforward matricisation procedure to convert elementwise equations into the matrix forms to ease implementation and parallelisation.
Evolving Signal Processing for Brain–Computer Interfaces
, 2012
"... This paper discusses the challenges associated with building robust and useful BCI models from accumulated biological knowledge and data, and the technical problems associated with incorporating multimodal physiological, behavioral, and contextual data that may become ubiquitous in the future. ..."
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Cited by 12 (2 self)
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This paper discusses the challenges associated with building robust and useful BCI models from accumulated biological knowledge and data, and the technical problems associated with incorporating multimodal physiological, behavioral, and contextual data that may become ubiquitous in the future.
Nonnegative leastmeansquare algorithm
 IEEE Transactions on Signal Processing
, 2011
"... Abstract—Dynamic system modeling plays a crucial role in the development of techniques for stationary and nonstationary signal processing. Due to the inherent physical characteristics of systems under investigation, nonnegativity is a desired constraint that can usually be imposed on the parameters ..."
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Cited by 12 (9 self)
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Abstract—Dynamic system modeling plays a crucial role in the development of techniques for stationary and nonstationary signal processing. Due to the inherent physical characteristics of systems under investigation, nonnegativity is a desired constraint that can usually be imposed on the parameters to estimate. In this paper, we propose a general method for system identification under nonnegativity constraints. We derive the socalled nonnegative leastmeansquare algorithm (NNLMS) based on stochastic gradient descent, and we analyze its convergence. Experiments are conducted to illustrate the performance of this approach and consistency with the analysis. Index Terms — Adaptive filters, adaptive signal processing, least mean square algorithms, nonnegative constraints, transient analysis. I.
Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for LargeScale Problems
, 2008
"... Recently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving largescale convex minimization problems subject to linear constraints. Since the minimization problems underlying nonnegative matrix factorization (NMF) of large ..."
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Cited by 8 (0 self)
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Recently, a considerable growth of interest in projected gradient (PG) methods has been observed due to their high efficiency in solving largescale convex minimization problems subject to linear constraints. Since the minimization problems underlying nonnegative matrix factorization (NMF) of large matrices well matches this class of minimization problems, we investigate and test some recent PG methods in the context of their applicability to NMF. In particular, the paper focuses on the following modified methods: projected Landweber, BarzilaiBorwein gradient projection, projected sequential subspace optimization (PSESOP), interiorpoint Newton (IPN), and sequential coordinatewise. The proposed and implemented NMF PG algorithms are compared with respect to their performance in terms of signaltointerference ratio (SIR) and elapsed time, using a simple benchmark of mixed partially dependent nonnegative signals.