Designing Kernel Scheme for Classifiers Fusion

In this paper, we propose a special fusion method for combining ensembles of base classifiers utilizing new neural networks in order to improve overall efficiency of classification. While ensembles are designed such that each classifier is trained independently while the decision fusion is performed as a final procedure, in this method, we would be interested in making the fusion process more adaptive and efficient. This new combiner, called Neural Network Kernel Least Mean Square1, attempts to fuse outputs of the ensembles of classifiers. The proposed Neural Network has some special properties such as Kernel abilities,Least Mean Square features, easy learning over variants of patterns and traditional neuron capabilities. Neural Network Kernel Least Mean Square is a special neuron which is trained with Kernel Least Mean Square properties. This new neuron is used as a classifiers combiner to fuse outputs of base neural network classifiers. Performance of this method is analyzed and compared with other fusion methods. The analysis represents higher performance of our new method as opposed to others.Comment: 7 pages IEEE format, International Journal of Computer Science and Information Security, IJCSIS November 2009, ISSN 1947 5500, http://sites.google.com/site/ijcsis

Asymptotics for Nonlinear Integral Equations with Generalized Heat Kernel and Time Dependent Coefficients Using Renormalization Group Technique

In this paper we employ the Renormalization Group (RG) method to study the long-time asymptotics of a class of nonlinear integral equations with a generalized heat kernel and with time-dependent coefficients. The nonlinearities are classified and studied according to its role in the asymptotic behavior. Here we prove that adding nonlinear perturbations classified as irrelevant, the behavior of the solution in the limit $t \to\infty$ remains unchanged from the linear case. In a companion paper, we will include a type of nonlinearities called marginal and we will show that, in this case, the large time limit gains an extra logarithmic decay factor

Human Emotional Facial Expression Recognition

An automatic Facial Expression Recognition (FER) model with Adaboost face detector, feature selection based on manifold learning and synergetic prototype based classifier has been proposed. Improved feature selection method and proposed classifier can achieve favorable effectiveness to performance FER in reasonable processing time

Hyperspectral Image Classification and Clutter Detection via Multiple Structural Embeddings and Dimension Reductions

We present a new and effective approach for Hyperspectral Image (HSI) classification and clutter detection, overcoming a few long-standing challenges presented by HSI data characteristics. Residing in a high-dimensional spectral attribute space, HSI data samples are known to be strongly correlated in their spectral signatures, exhibit nonlinear structure due to several physical laws, and contain uncertainty and noise from multiple sources. In the presented approach, we generate an adaptive, structurally enriched representation environment, and employ the locally linear embedding (LLE) in it. There are two structure layers external to LLE. One is feature space embedding: the HSI data attributes are embedded into a discriminatory feature space where spatio-spectral coherence and distinctive structures are distilled and exploited to mitigate various difficulties encountered in the native hyperspectral attribute space. The other structure layer encloses the ranges of algorithmic parameters for LLE and feature embedding, and supports a multiplexing and integrating scheme for contending with multi-source uncertainty. Experiments on two commonly used HSI datasets with a small number of learning samples have rendered remarkably high-accuracy classification results, as well as distinctive maps of detected clutter regions.Comment: 13 pages, 6 figures (30 images), submitted to International Conference on Computer Vision (ICCV) 201

Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schr\"odinger Equations

A classification of large-time and finite-time blow-up asymptotics of solutions of the Cauchy problem for higher-order Schr\"odinger equations is performed.Comment: 49 page

Classification of Asymptotic Profiles for Nonlinear Schr\"odinger Equations with Small Initial Data

We consider a nonlinear Schr\"odinger equation with a bounded local potential in $R^3$. The linear Hamiltonian is assumed to have two bound states with the eigenvalues satisfying some resonance condition. Suppose that the initial data are localized and small in $H^1$. We prove that exactly three local-in-space behaviors can occur as the time tends to infinity: 1. The solutions vanish; 2. The solutions converge to nonlinear ground states; 3. The solutions converge to nonlinear excited states. We also obtain upper bounds for the relaxation in all three cases. In addition, a matching lower bound for the relaxation to nonlinear ground states was given for a large set of initial data which is believed to be generic. Our proof is based on outgoing estimates of the dispersive waves which measure the relevant time-direction dependent information of the dispersive wave. These estimates, introduced in [16], provides the first general notion to measure the out-going tendency of waves in the setting of nonlinear Schr\"odinger equations.Comment: to appear in Adv. Theor. Math. Phy

Positive solutions of a nonlocal Caputo fractional BVP

We discuss the existence of multiple positive solutions for a nonlocal fractional problem recently considered by Nieto and Pimental. Our approach relies on classical fixed point index.Comment: 8 page

Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions

In this paper, we consider equations involving fully nonlinear nonlocal operators $$F_{\alpha}(u(x)) \equiv C_{n,\alpha} PV \int_{\mathbb{R}^n} \frac{G(u(x)-u(z))}{|x-z|^{n+\alpha}} dz= f(x,u).$$ We prove a maximum principle and obtain key ingredients for carrying on the method of moving planes, such as narrow region principle and decay at infinity. Then we establish radial symmetry and monotonicity for positive solutions to Dirichlet problems associated to such fully nonlinear fractional order equations in a unit ball and in the whole space, as well as non-existence of solutions on a half space. We believe that the methods develop here can be applied to a variety of problems involving fully nonlinear nonlocal operators. We also investigate the limit of this operator as $\alpha \rightarrow 2$ and show that $$F_{\alpha}(u(x)) \rightarrow a(-\Delta u(x)) + b |\bigtriangledown u(x)|^2 .$$Comment: 27 pages. arXiv admin note: text overlap with arXiv:1411.169

Classification of blow-up limits for the sinh-Gordon equation

The aim of this paper is to use a selection process and a careful study of the interaction of bubbling solutions to show a classification result for the blow-up values of the elliptic sinh-Gordon equation $$\Delta u+h_1e^u-h_2e^{-u}=0 \quad \mathrm{in}~B_1\subset\mathbb{R}^2.$$ In particular we get that the blow-up values are multiple of $8\pi.$ It generalizes the result of Jost, Wang, Ye and Zhou \cite{jwyz} where the extra assumption $h_1 = h_2$ is crucially used

Shape Distributions of Nonlinear Dynamical Systems for Video-based Inference

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligenc