Search results for "Basis function"

Semisupervised kernel orthonormalized partial least squares

2012

This paper presents a semisupervised kernel orthonormalized partial least squares (SS-KOPLS) algorithm for non-linear feature extraction. The proposed method finds projections that minimize the least squares regression error in Hilbert spaces and incorporates the wealth of unlabeled information to deal with small size labeled datasets. The method relies on combining a standard RBF kernel using labeled information, and a generative kernel learned by clustering all available data. The positive definiteness of the kernels is proven, and the structure and information content of the derived kernels is studied. The effectiveness of the proposed method is successfully illustrated in standard UCI d…

Semisupervised Kernel Feature Extraction for Remote Sensing Image Analysis

2014

This paper presents a novel semisupervised kernel partial least squares (KPLS) algorithm for nonlinear feature extraction to tackle both land-cover classification and biophysical parameter retrieval problems. The proposed method finds projections of the original input data that align with the target variable (labels) and incorporates the wealth of unlabeled information to deal with low-sized or underrepresented data sets. The method relies on combining two kernel functions: the standard radial-basis-function kernel based on labeled information and a generative, i.e., probabilistic, kernel directly learned by clustering the data many times and at different scales across the data manifold. Th…

A family of kernel anomaly change detectors

2014

This paper introduces the nonlinear extension of the anomaly change detection algorithms in [1] based on the theory of reproducing kernels. The presented methods generalize their linear counterparts, under both the Gaussian and elliptically-contoured assumptions, and produce both improved detection accuracies and reduced false alarm rates. We study the Gaussianity of the data in Hilbert spaces with kernel dependence estimates, provide low-rank kernel versions to cope with the high computational cost of the methods, and give prescriptions about the selection of the kernel functions and their parameters. We illustrate the performance of the introduced kernel methods in both pervasive and anom…

Semi-Supervised Remote Sensing Image Classification based on Clustering and the Mean Map Kernel

2008

This paper presents a semi-supervised classifier based on the combination of the expectation-maximization (EM) algorithm for Gaussian mixture models (GMM) and the mean map kernel. The proposed method uses the most reliable samples in terms of maximum likelihood to compute a kernel function that accurately reflects the similarity between clusters in the kernel space. The proposed method improves classification accuracy in situations where the available labeled information does not properly describe the classes in the test image.

Comparison between the MHFEM formulation and a 2nd spatial order FV formulation of the linear groundwater flow problem

2008

Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper a new second spatial approximation order Finite Volum…

Adaptive variable structure fuzzy neural identification and control for a class of MIMO nonlinear system

2013

This paper presents a novel adaptive variable structure (AVS) method to design a fuzzy neural network (FNN). This AVS-FNN is based on radial basis function (RBF) neurons, which have center and width vectors. The network performs sequential learning through sliding data window reflecting system dynamic changes, and dynamic growing-and-pruning structure of FNN. The salient characteristics of the AVS-FNN are as follows: (1) Structure-learning and parameters estimation are performed automatically and simultaneously without partitioning input space and selecting initial parameters a priori. The structure-learning approach relies on the contribution of the size of the output. (2) A set of fuzzy r…

Directionlets: Anisotropic Multidirectional representation with separable filtering

2006

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based pe…

Comparison between the MHFEM formulation and a 2nd spatial order FV formulation of the linear ground problem

2008

Comparison of different 2nd order formulations for the solution of the 2D groundwater flow problem over irregular triangular meshes

2009

Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper, a new MHFE formulation is proposed for the solution …

High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

2011

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by expl…