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In this paper, an adaptive adjustment method for the kernel parameter used in the kernel adaptive filters (KAFs) is proposed. The KAF is one of the linear-in-the-parameters (LIP) nonlinear filters, and is based on the kernel method used in machine learning. Typically, the Gaussian kernel function is used, but there is no effective method for automatically adjusting its parameter that influences the...
One popular approach for blind deconvolution is to formulate a maximum a posteriori (MAP) problem with sparsity priors on the gradients of the latent image, and then alternatingly estimate the blur kernel and the latent image. While several successful MAP based methods have been proposed, there has been much controversy and confusion about their convergence, because sparsity priors have been shown...
In this paper, we aim to improve the overall performance of kernel adaptive filters by adaptively combining several component filters with different parameters setting in the practical applications. The convex combination scheme is exploited to incorporate any two parallel diversity branches which could be the component filter or the output of previous combination layer. The proposed convex combination...
The Gaussian kernel least-mean-square (Gaussian KLMS) algorithm has been studied under different implementation conditions. Though analytical models that predict its behavior are available, methodologies for determining the algorithm parameter values to satisfy given design criteria is still missing from the literature. In this paper we propose, test, and validate a methodology for the design of the...
In studying electromagnetic wave diffraction from scatterers with corners, a common approach is to first round the corners, thus producing a smooth surface, and eliminating the singularities introduced by the corners. Numerical methods based upon integral equation formulations can then be readily applied. In order to quantify the effect of such corner rounding we examine the two-dimensional case of...
We present a novel online learning paradigm for nonlinear function estimation based on iterative orthogonal projections in an L2 space reflecting the stochastic property of input signals. An online algorithm is built upon the fact that any finite dimensional subspace has a reproducing kernel, which is given in terms of the Gram matrix of its basis. The basis used in the present study involves multiple...
We present the theory of sequences of random graphs and their convergence to limit objects. Sequences of random dense graphs are shown to converge to their limit objects in both their structural properties and their spectra. The limit objects are bounded symmetric functions on [0,1]2. The kernel functions define an equivalence class and thus identify collections of large random graphs who are spectrally...
Low-rank sparse tensor factorization is a populartool for analyzing multi-way data and is used in domainssuch as recommender systems, precision healthcare, and cybersecurity.Imposing constraints on a factorization, such asnon-negativity or sparsity, is a natural way of encoding priorknowledge of the multi-way data. While constrained factorizationsare useful for practitioners, they can greatly increasefactorization...
We revisit the Wilson-Dirac operator, also referred as Dslash, on NUMA manycore vector machines and thereby seek an efficient supercomputing implementation. Quantum Chro- moDynamics (QCD) is the theory of the strong nuclear force and its discrete formalism is the so-called Lattice Quantum ChromoDynamics (LQCD). Wilson-Dirac is the major computing kernel in LQCD, where a special attention is paid to...
This paper attempts to represent the mapped data in the radial basis function (RBF) feature space under non-negativity constraints and develops a RBF kernel based non-negative matrix factorization (KNMF-RBF) algorithm. Based on an objective function with Frobenius norm, we obtain the multiplicative update rules of our KNMF-RBF approach using kernel theory and gradient descent method. The proposed...
The aim of this paper is to study generalized Blackman-Harris sampling operators, which are defined using a bandlimited window function, which may be not an even one.
In this paper, we focus on promoting multi-label learning task with ensemble learning. Compared to traditional single algorithm methods, it has been recognized that ensemble methods could achieve much better performance than each constituent learned model, especially under the conditional independence of different classifiers. Existing multi-label ensemble algorithms mainly focus on creating diverse...
The Cauchy problem for a linear second-order parabolic equation with 1-periodic measurable coefficients is studied in R + = {(x, t) : x ∊ Rd, t ≥ 0}, d ≥ 2. We focus at the behaviour of the fundamental solution as t → ∞. Its approximations are found with pointwise and integral error estimates of order O (t−(d+j+1)/2) and O(t−(j+1)/2), j = 0,1,…, as t → ∞, respectively. These results are applied to...
We derive the mean squared error convergence rates of kernel density-based plug-in estimators of mutual information measures between two multidimensional random variables X and Y for two cases: 1) X and Y are both continuous; 2) X is continuous and Y is discrete. Using the derived rates, we propose an ensemble estimator of these information measures for the second case by taking a weighted sum of...
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional estimation problems, practitioners are left on their own to choose an appropriate bandwidth for each application in hand. Further, kernel density estimators suffer from...
In this paper we present a new and improved formulation for the Multimode Equivalent Network (MEN) representation of arbitrary waveguide junctions. In the new formulation the Kummer's transformation is used to separate the kernel into dynamic and static parts, by introducing higher order extraction terms. The main difference with respect to the old formulation is that the approximation of the kernel...
This paper addresses the problem of on-line learning for object tracking. Although a variety of techniques have been proposed in literature, a recent benchmark reveals that none of them can work well in all scenarios due to numerous practical challenges, such as illumination variations, motion blur, etc. These challenges occur at different time frames making it hard to design a tracker. In this paper,...
Emotion recognition is critical for everyday living and is essential for meaningful interaction. If we are to progress towards human and machine interaction that is engaging the human user, the machine should be able to recognize the emotional state of the user. Deep Convolutional Neural Networks (CNN) have proven to be efficient in emotion recognition problems. The good degree of performance achieved...
This paper introduces a novel framework for the study of adaptive or online estimation problems for a common class of nonlinear systems governed by ordinary differential equations (ODEs) on ℝd. In contrast to most conventional strategies for ODEs, the approach here embeds the estimate of the unknown nonlinear function appearing in the plant in a reproducing kernel Hilbert space (RKHS), H. The nonlinear...
Classification is at the very center of the supervised learning. In this work, we propose a novel algorithm to classify the test data set with the aid of a vector field, emanating from the training data set. In particular, the vector field is constructed such that the location of each training data point becomes a local minimum of the potential. The test data points are allowed to evolve under the...
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