Abstract: In face recognition tasks, the existing methods to deal with small sample size problem in linear discriminant analysis (LDA) have their respective drawbacks. However, the recently proposed discriminative common vectors (DCV) method successfully overcomes these drawbacks with high performance in terms of accuracy, real-time performance, and numerical stability. In this paper, the second algorithm in the DCV based on the Gram-Schmidt orthogonalization is extended to the nonlinear case by using kernel method. The Gram-Schmidt orthogonalization procedure in feature space is first presented. Then the algorithm for KDCV is developed which involves performing the Gram-Schmidt orthogonalization procedure twice in feature space. Experiments on ORL database indicate that the proposed KDCV method achieves higher recognition rate than the DCV method.

Abstract: An improved sea mine computer-aided-detection / computer-aided-classification (CAD/CAC) processing string has been developed. The overall CAD/CAC processing string consists of pre-processing, adaptive clutter filtering (ACF), normalization, detection, feature extraction, optimal subset feature selection, feature orthogonalization, classification and fusion processing blocks. The range-dimension ACF is matched both to average highlight and shadow information, while also adaptively suppressing background clutter. For each detected object, features are extracted and processed through an orthogonalization transformation, enabling an efficient application of the optimal log-likelihood-ratio-test (LLRT) classification rule, in the orthogonal feature space domain. The classified objects of 4 distinct processing strings are fused using the classification confidence values as features and either "M-out-of-N" or LLRT-based fusion rules. The utility of the overall processing strings and their fusion was demonstrated with new shallow water high-resolution sonar imagery data. The processing string detection and classification parameters were tuned and the string classification performance was optimized, by appropriately selecting a subset of the original feature set. Two significant improvements were made to the CAD/CAC processing string by employing sub-image adaptive clutter filtering (SACF) and utilizing a repeated application of the subset feature selection / feature orthogonalization / LLRT classification blocks. A new nonlinear (Volterra) feature LLRT fusion algorithm was developed. It was shown that this Volterra feature LLRT fusion of the CAD/CAC processing strings outperforms the "M-out-of-N" and baseline LLRT algorithms, yielding significant improvements over the best single CAD/CAC processing string results, and providing the capability to correctly call all mine targets while maintaining a very low false alarm rate.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Abstract: In this paper, a new approach which is called the common matrix approach is proposed for face recognition. The common matrix for each class can be calculated either using Gram-Schmidt orthogonalization method or using scatter matrix of each class. In both ways, orthonormal mat rices in the indifference subspace represent the directions that contain important discriminative information. The proposed approach overcomes the small sample size problem and the dimensionality problem in face recognition. The applications on AR-Face database give satisfactory results.

Abstract: In this paper we consider the so-called orthogonalization approach for channel modeling. We propose the use of the Prolate Spheroidal Wave Functions (PSWF) as a universal basis capable to span the characteristics of the channel by means of its correlation properties.

Abstract: Estimates are given for the product of the lengths of integer vectors spanning a given linear subspace.

Abstract: A generalized approach for estimating in-band distortion spectrum when a wireless communication signal is processed by a nonlinear amplifier is presented. The output spectrum is represented as the sum of uncorrelated components using Gram-Schmidt orthogonalization without any restriction on the statistical properties of the input signals. The analysis allows the accurate estimation of in-band distortion and hence the effective SNR, Rho and EVM of wireless communication systems. The approach is verified by measurements of in-band distortion using feed-forward cancellation.

Abstract: Visual servoing of constrained dynamical robots has not yet met a formal treatment. Also, notices that due technological constraints, this task is done slowly at velocity reversals, thus dynamic friction arises, which complicates even more the problem. In this paper, a new adaptive scheme for visual servoing of constrained robots subject to dynamic friction is proposed. An image-based control is introduced to produce simultaneous convergence of the constrained visual position and the contact force between the end-effector and the constraint surface. Camera and robot parameters are considered uncertain. This new approach is based on a new formulation of the orthogonalization principle used in force control, coined here visual orthogonalization principle. This allows, under the framework of passivity, to yield a synergetic scheme that fuses camera, encoder and force sensor signals. Simulation results are presented and show that image errors and force errors converge despite uncertainties of friction model.

Abstract: An improved sea mine computer-aided-detection/computer-aided-classification (CAD/CAC) processing string has been developed. The overall CAD/CAC processing string consists of pre-processing, adaptive clutter filtering (ACF), normalization, detection, feature extraction, optimal subset feature selection, feature orthogonalization, classification, and fusion processing blocks. The range-dimension ACF is matched both to average highlight and shadow information, while also adaptively suppressing background clutter. For each detected object, features are extracted and processed through an orthogonalization transformation, enabling an efficient application of the optimal log-likelihood-ratio-test (LLRT) classification rule, in the orthogonal feature space domain. The classified objects of 4 distinct processing strings are fused using the classification confidence values as features and either "M-out-of-N" or LLRT-based fusion rules. The utility of the overall processing strings and their fusion was demonstrated with new shallow water high-resolution sonar imagery data. The processing string detection and classification parameters were tuned and the string classification performance was optimized, by appropriately selecting a subset of the original feature set. Two significant fusion algorithm improvements were made. First, a new nonlinear (Volterra) feature LLRT fusion algorithm was developed. Second, a repeated application of the subset feature selection/feature orthogonalization/Volterra feature LLRT fusion block was utilized. It was shown that this cascaded Volterra feature LLRT fusion of the CAD/CAC processing strings outperforms the "M-out-of-N" and baseline LLRT algorithms, yielding significant improvements over the best single CAD/CAC processing string results, and providing the capability to correctly call all mine targets while maintaining a very low false alarm rate

Abstract: The growing interest into multi-sensor systems able to determine general attributes of a process under monitoring, has also involved the qualitative analysis of liquids; various methodologies to develop taste sensors, often referred to as "e-tongues" have been presented in the literature. The fundamental idea of this paper is to investigate how an adequate signal processing approach applied to a mature and affordable sensor technique (voltammetry) can address the issue of extracting an aggregate chemical information, useful to characterize the liquid under measurement. The methodological approach to the processing of the signal, an application experiment, and the test set which has been built for the experiment are described here. In the proposed approach, dimensionality reduction is obtained using the compaction properties of DCT (discrete cosine transform), where the transform is followed by an iterative orthogonalization procedure for the feature extraction step; the capability of discriminating between different samples is also discussed via representing each collected sequence in a low dimensionality feature space

Abstract: We provide new causal mathematical models of a nonlinear system S which are specifications of a nonlinear operator P/sub p/ of degree p=1,2,.... The operator P/sub p/ is determined from a special orthogonalization procedure and minimization of the mean squared difference between outputs of S and P/sub p/. As a result, these models have smallest possible associated errors in the class of such operators P/sub p/. The causality condition is implemented through the use of specific matrices called lower trapezoidal. The associated computational work is reduced by the use of the orthogonalization procedure. We provide a strict justification of the proposed approach including theorems on an explicit representatoin of the models' parameters, and theorems on the associated error representation. The possible extensions of the proposed approach and its potential applications are outlined.

Abstract: This paper presents a new algorithm that addresses an important issue arising in computation of sensitivity for nonuniform transmission lines using the idea of model reduction through integrated congruence transform. This issue is related extending the concept of implicit basis construction, which was introduced earlier to simulate nonuniform transmission lines, to the task of sensitivity analysis. A new algorithm is presented to compute the orthogonal basis needed to obtain the reduced system used in sensitivity analysis. The proposed algorithm incorporates a new orthogonalization procedure which can be used to find an orthogonal basis for a set of moments derived from inhomogeneous differential equations, but without having to compute those moments explicitly. Numerical results demonstrate that reduced-order systems constructed by the proposed algorithm have improved numerical accuracy in sensitivity computation.

Abstract: This paper extends a recent martingale representation result of [N-S] for a L´evy process to filtrations generated by a rather large class of semimartingales. As in [N-S], we assume the underlying processes have moments of all orders, but here we allow angle brackets to be stochastic. Following their approach, including a chaotic expansion, and incorporating an idea of strong orthogonalization from [D], we show that the stable subspace generated by Teugels martingales is dense in the space of square-integrable martingales, yielding the representation. While discontinuities are of primary interest here, the special case of a (possibly infinite-dimensional) Brownian filtration is an easy consequence.

Abstract: The Gram–Schmidt process is a technique for constructing an orthogonal basis from a basis spanning the same subspace. The technique is used in a number of multivariate applications including battery reduction analyses and multiple regression applications. In the former, the goal is to reduce the number of variables at the same time explaining as much variance in the original variables as possible. In the latter, the goal is to reduce the n-dimensional space (observations) to a p-dimensional space (independent variables). Keywords: orthogonalization; principal components analysis; battery reduction

Abstract: In this paper, an algorithm is developed to construct a set of M orthogonal basis along which signals, whether noisy or noise-free, can be decomposed. Combining a modified Prony signal approximation and Gram-Schmidt orthogonalization schemes (to obtain the orthogonal bases), the proposed method represents the processed signal as the sum of M damped exponentials. It is shown that the employed bases are closely related to the roots of an Mth order forward linear prediction polynomial, satisfying the system. In addition, an optimization procedure is described to optimally adjust these bases to accurately represent the signal under consideration. The proposed procedure finds applications in signal compression and signal de-noising, where it is only necessary to specify the orthogonal basis, as well as the decomposition weights rather than sending the complete signal batch. Illustrative examples are given

Abstract: The paper describes a method of combined expansion and orthogonalization (CEO) of experimental modeshapes. Most model updating and error localization methods require a set of full length, orthogonal with respect to the mass matrix, eigenvectors. In practically every modal experiment, the number of measurements is less than the order of the model, and hence modeshape expansion, i.e., adding the unmeasured degrees of freedom, is required. This step is then followed by orthogonalization with respect to the mass matrix. Most current methods use two separate steps for expansion and orthogonalization, each one optimal by itself but their combination is not optimal. The suggested method combines the two steps into one optimization problem for both steps, and minimizes a quadratic criterion. In the case of an equal number of analytical and experimental modeshapes, the problem coincides with the Procrustes problem and has a closed form solution. Otherwise the solution involves nonlinear equations. Several examples show the advantage of CEO, especially in cases where the measurements are limited either in number or in space, i.e., not spanned through the entire structure.

Abstract: Some current states and new advances in the research of the basic theory of thermal-structural-optical(TSO)integrated analysis,and the interface problem of data transmission in mechanical,thermal and optical program are reviewed.It is demonstrated that Zernike polynomial as data transmission tool fitted process: the data manipulation——the displacement data provided by FEA tools must be translated into either a sag-based or wavefront-based coordinate systems. The polynomial fitting——methods of wavefront fitting using Zernike polynomial are described: least square method and Gram-Schmidt orthogonalization method. On these foundations the data transmission interface program can make the TSO process simple and can increase efficiency.

Abstract: A new method for fitting implicit curves to scattered data is proposed. The method is based on orthogonal matrix projections and singular value decomposition. The incremental aspect of the algorithm deals with each order of data individually in an incrementing manner, whereby a matrix approximation procedure is applied at each level. This determines the fit quality at each step, and hence provides co-linearity detection of each polynomial order. The best implicit polynomial fit of minimal order is provided, which essentially combines object identification and classification with object fitting.

Abstract: In 1970 Kovarik proposed approximate orthogonalization algorithms. One of them (algorithm B) has quadratic convergence but requires at each iteration the inversion of a matrix of similar dimension to the initial one. An attempt to overcome this difficulty was made by replacing the inverse with a finite Neumann series expansion involving the original matrix and its adjoint. Unfortunately, this new algorithm loses the quadratic convergence and requires a large number of terms in the Neumann series which results in a dramatic increase in the computational effort per iteration. In this paper we propose a much simpler algorithm which, by using only the first two terms in a different series expansion, gives us the desired result with linear convergence. Systematic numerical experiments for collocation and Toeplitz matrices are also described.

Abstract: The theoretical framework and experimental validation of a new image-based position-force control is presented in this paper. This scheme produces simultaneous convergence of the constrained visual position and the contact force between the end-effector and the constraint surface. Camera, robot and Jacobian parameters are considered uncertain. This approach is based on a new formulation of the orthogonalization principle used in force control, coined here visual orthogonalization principle. This allows, under the framework of passivity, to yield a synergetic scheme that fuses accordingly camera, encoder and force sensor signals. Furthermore, notice that visual servoing contact tasks are characterized by slow motion, and typically with velocity reversals along the constrained surface due actual technological limitations of the camera, thus, important problems of friction at the joint and contact point arise. Therefore, in this paper, compensation of dynamic joint friction and viscous contact friction are also studied. In order to prove the effectiveness of the theoretical scheme, a Linux-RTAI real-time OS experimental system is used to obtain a direct-drive robot manipulator equipped with six axis JR3 force sensor and a CCD commercial digital fixed camera. Results show an excellent performance

Abstract: In this paper we present a new algorithm for blind source separation (BSS) based on the Constant Norm (CN) criterion for Multiple-Input Multiple-Output (MIMO) communication systems. The treated problem consists in blindly recovering (i.e. without the use of training sequences) the signals transmitted over a linear MIMO memoryless system, which introduces only Inter Stream Interference (ISI). From the proposed algorithm, we deduce two other new algorithms designed especially for QAM signals. The first one is named Constant sQuare Algorithm (CQA) and the second one, which is a weighting between the Constant Modulus Algorithm (CMA) and the CQA to get the advantages of both, is named Constant Dynamic Norm Algorithm (CDNA). At each iteration, the algorithms combine a stochastic gradient update and a Gram-Schmidt orthogonalization procedure. The simulation results show that the proposed algorithms have better performances compared to CMA and Multiuser Kurtosis Algorithm (MUK) with comparable complexity.

Abstract: The paper presents the comparative analysis of the learning algorithms of the radial basis function (RBF) neural networks. Two best adaptive algorithms are considered. One is based on the orthogonal least square (OLS) applying Gram-Schmidt orthogonalization and the second is relying on the support vector machine (SVM) approach. The results of numerical experiments in the classification and regression modes are presented and discussed in the paper.

Abstract: GNU project Gama for adjustment of geodetic networks is presented. Numerical solution of Least Squares Adjustment in the project is based on Singular Value Decomposition (SVD) and General Orthogonalization Algorithm (GSO). Both algorithms enable solution of singular systems resulting from adjustment of free geodetic networks.