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103
Hierarchical Modeling of Local Image Features through LpNested Symmetric Distributions
"... We introduce a new family of distributions, called Lpnested symmetric distributions, whose densities are expressed in terms of a hierarchical cascade of Lpnorms. This class generalizes the family of spherically and Lpspherically symmetric distributions which have recently been successfully used fo ..."
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Cited by 11 (5 self)
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We introduce a new family of distributions, called Lpnested symmetric distributions, whose densities are expressed in terms of a hierarchical cascade of Lpnorms. This class generalizes the family of spherically and Lpspherically symmetric distributions which have recently been successfully used for natural image modeling. Similar to those distributions it allows for a nonlinear mechanism to reduce the dependencies between its variables. With suitable choices of the parameters and norms, this family includes the Independent Subspace Analysis (ISA) model as a special case, which has been proposed as a means of deriving filters that mimic complex cells found in mammalian primary visual cortex. Lpnested distributions are relatively easy to estimate and allow us to explore the variety of models between ISA and the Lpspherically symmetric models. By fitting the generalized Lpnested model to 8 × 8 image patches, we show that the subspaces obtained from ISA are in fact more dependent than the individual filter coefficients within a subspace. When first applying contrast gain control as preprocessing, however, there are no dependencies left that could be exploited by ISA. This suggests that complex cell modeling can only be useful for redundancy reduction for larger image patches. 1
A joint diagonalization method for convolutive blind separation of nonstationary sources
 in the frequency domain,” Proc
"... A joint diagonalization algorithm for convolutive blind source separation by explicitly exploiting the nonstationarity and second order statistics of signals is proposed. The algorithm incorporates a nonunitary penalty term within the crosspower spectrum based cost function in the frequency domain ..."
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Cited by 10 (6 self)
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A joint diagonalization algorithm for convolutive blind source separation by explicitly exploiting the nonstationarity and second order statistics of signals is proposed. The algorithm incorporates a nonunitary penalty term within the crosspower spectrum based cost function in the frequency domain. This leads to a modification of the search direction of the gradientbased descent algorithm and thereby yields more robust convergence performance. Simulation results show that the algorithm leads to faster speed of convergence, together with a better performance for the separation of the convolved speech signals, in particular in terms of shape preservation and amplitude ambiguity reduction, as compared to Parra’s nonstationary algorithm for convolutive mixtures. 1.
The Conjoint Effect of Divisive Normalization and Orientation Selectivity on Redundancy Reduction in Natural Images
"... Bandpass filtering, orientation selectivity, and contrast gain control are prominent features of sensory coding at the level of V1 simple cells. While the effect of bandpass filtering and orientation selectivity can be assessed within a linear model, contrast gain control is an inherently nonlinear ..."
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Cited by 9 (4 self)
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Bandpass filtering, orientation selectivity, and contrast gain control are prominent features of sensory coding at the level of V1 simple cells. While the effect of bandpass filtering and orientation selectivity can be assessed within a linear model, contrast gain control is an inherently nonlinear computation. Here we employ the class of Lp elliptically contoured distributions to investigate the extent to which the two features—orientation selectivity and contrast gain control—are suited to model the statistics of natural images. Within this framework we find that contrast gain control can play a significant role for the removal of redundancies in natural images. Orientation selectivity, in contrast, has only a very limited potential for redundancy reduction. 1
Robust learning of discriminative projection for multicategory classification on the Stiefel manifold
 in Proc. IEEE CS Conf. Comput. Vis. Pattern Recognit
, 2008
"... Learning a robust projection with a small number of training samples is still a challenging problem in face recognition, especially when the unseen faces have extreme variation in pose, illumination, and facial expression. To address this problem, we propose a framework formulated under statistical ..."
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Cited by 9 (0 self)
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Learning a robust projection with a small number of training samples is still a challenging problem in face recognition, especially when the unseen faces have extreme variation in pose, illumination, and facial expression. To address this problem, we propose a framework formulated under statistical learning theory that facilitates robust learning of a discriminative projection. Dimensionality reduction using the projection matrix is combined with a linear classifier in the regularized framework of lasso regression. The projection matrix in conjunction with the classifier parameters are then found by solving an optimization problem over the Stiefel manifold. The experimental results on standard face databases suggest that the proposed method outperforms some recent regularized techniques when the number of training samples is small. 1.
Quantization on the Grassmann manifold: Applications to precoded MIMO wireless systems
 in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2005
"... This paper studies the problem of quantization of a source that lives on the complex Grassmann manifold. The special structure of the Grassmann manifold and the distortion measures that are defined on it differentiates this problem from the traditional problem of vector quantization in Euclidean spa ..."
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Cited by 8 (1 self)
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This paper studies the problem of quantization of a source that lives on the complex Grassmann manifold. The special structure of the Grassmann manifold and the distortion measures that are defined on it differentiates this problem from the traditional problem of vector quantization in Euclidean spaces. Assuming a uniform source distribution along with a distortion based on chordal distance, codebook design algorithms are mentioned and rate distortion tradeoffs are studied. The expected distortion for such a quantizer is approximately characterized. These results are then applied to the performance analysis of a multiple antenna wireless communication system. 1.
A Design Framework for Limited Feedback MIMO Systems with ZeroForcing DFE
, 2008
"... We consider the design of multipleinput multipleoutput communication systems with a linear precoder at the transmitter, zeroforcing decision feedback equalization (ZFDFE) at the receiver, and a lowrate feedback channel that enables communication from the receiver to the transmitter. The channel ..."
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Cited by 7 (1 self)
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We consider the design of multipleinput multipleoutput communication systems with a linear precoder at the transmitter, zeroforcing decision feedback equalization (ZFDFE) at the receiver, and a lowrate feedback channel that enables communication from the receiver to the transmitter. The channel state information (CSI) available at the receiver is assumed to be perfect, and based on this information the receiver selects a suitable precoder from a codebook and feeds back the index of this precoder to the transmitter. Our approach to the design of the components of this limited feedback scheme is based on the development, herein, of a unified framework for the joint design of the precoder and the ZFDFE under the assumption that perfect CSI is available at both the transmitter and the receiver. The framework is general and embraces a wide range of design criteria. This framework enables us to characterize the statistical distribution of the optimal precoder in a standard Rayleigh fading environment. Using this distribution, we show that codebooks constructed from Grassmann packings minimize an upper bound on an average distortion measure, and hence are natural candidates for the codebook in limited feedback systems. Our simulation studies show that the proposed limited feedback scheme can provide significantly better performance at a lower feedback rate than existing schemes in which the detection order is fed back to the transmitter.
Linear Dimensionality Reduction for MarginBased Classification: HighDimensional Data and Sensor Networks
, 2011
"... Lowdimensional statistics of measurements play an important role in detection problems, including those encountered in sensor networks. In this work, we focus on learning lowdimensional linear statistics of highdimensional measurement data along with decision rules defined in the lowdimensional ..."
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Cited by 7 (2 self)
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Lowdimensional statistics of measurements play an important role in detection problems, including those encountered in sensor networks. In this work, we focus on learning lowdimensional linear statistics of highdimensional measurement data along with decision rules defined in the lowdimensional space in the case when the probability density of the measurements and class labels is not given, but a training set of samples from this distribution is given. We pose a joint optimization problem for linear dimensionality reduction and marginbased classification, and develop a coordinate descent algorithm on the Stiefel manifold for its solution. Although the coordinate descent is not guaranteed to find the globally optimal solution, crucially, its alternating structure enables us to extend it for sensor networks with a messagepassing approach requiring little communication. Linear dimensionality reduction prevents overfitting when learning from finite training data. In the sensor network setting, dimensionality reduction not only prevents overfitting, but also reduces power consumption due to communication. The learned reduceddimensional space and decision rule is shown to be consistent and its Rademacher complexity is characterized. Experimental results are presented for a variety of datasets, including those from existing sensor networks, demonstrating the potential of our methodology in comparison with other dimensionality reduction approaches.
NEWTON METHOD FOR RIEMANNIAN CENTROID COMPUTATION IN NATURALLY REDUCTIVE HOMOGENEOUS SPACES
"... We address the problem of computing the Riemannian centroid of a constellation of points in a naturally reductive homogeneous manifold. We note that many interesting manifolds used in engineering (such as the special orthogonal group, Grassman, sphere, positive definite matrices) possess this struct ..."
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Cited by 7 (3 self)
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We address the problem of computing the Riemannian centroid of a constellation of points in a naturally reductive homogeneous manifold. We note that many interesting manifolds used in engineering (such as the special orthogonal group, Grassman, sphere, positive definite matrices) possess this structure. We develop an intrinsic Newton scheme for the centroid computation. This is achieved by exploiting a formula that we introduce for obtaining the Hessian of the squared Riemannian distance on naturally reductive homogeneous spaces. Some results of finding the centroid of a constellation of points in these spaces are presented, which evidence the quadratic convergence of the Newton method derived herein. These computer simulation results show that, as expected, the Newton method has a faster convergence rate than the usual gradientbased approaches.
Y.H.: A framework of constraint preserving update schemes for optimization on Stiefel manifold
 Institue of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sicences (2012
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