Latent semantic analysis (LSA) and correspondence analysis (CA) are two techniques that use a singular value decomposition for dimensionality reduction. LSA has been extensively used to obtain low-dimensional representations that capture relationships among documents and terms. In this article, we present a theoretical analysis and comparison of the two techniques in the context of document-term matrices. We show that CA has some attractive properties as compared to LSA, for instance that effects of margins, that is, sums of row elements and column elements, arising from differing document lengths and term frequencies are effectively eliminated so that the CA solution is optimally suited to focus on relationships among documents and terms. A unifying framework is proposed that includes both CA and LSA as special cases. We empirically compare CA to various LSA-based methods on text categorization in English and authorship attribution on historical Dutch texts and find that CA performs significantly better. We also apply CA to a long-standing question regarding the authorship of the Dutch national anthem Wilhelmus and provide further support that it can be attributed to the author Datheen, among several contenders.

Current limit state surrogate modeling methods for system reliability analysis usually build surrogate models for failure modes individually or build composite limit states. In practical engineering applications, multiple system responses may be obtained from a single setting of inputs. In such cases, building surrogate models individually will ignore the correlation between different system responses and building composite limit states may be computationally expensive because the nonlinearity of composite limit state is usually higher than individual limit states. This paper proposes a new efficient Kriging surrogate modeling approach for system reliability analysis by constructing composite Kriging surrogates through selection of Kriging surrogates constructed individually and Kriging surrogates built based on singular value decomposition. The resulting composite surrogate model will combine the advantages of both types of Kriging surrogate models and thus reduce the number of required training points. A new stopping criterion and a new surrogate model refinement strategy are proposed to further improve the efficiency of this approach. The surrogate models are refined adaptively with high accuracy near the active failure boundary until the proposed new stopping criterion is satisfied. Three numerical examples including a series, a parallel, and a combined system are used to demonstrate the effectiveness of the proposed method.

A new nonlinear robust filter is proposed in this paper to deal with the outliers of an integrated Global Positioning System/Strapdown Inertial Navigation System (GPS/SINS) navigation system. The influence of different design parameters for an H∞ cubature Kalman filter is analysed. It is found that when the design parameter is small, the robustness of the filter is stronger. However, the design parameter is easily out of step in the Riccati equation and the filter easily diverges. In this respect, a singular value decomposition algorithm is employed to replace the Cholesky decomposition in the robust cubature Kalman filter. With large conditions for the design parameter, the new filter is more robust. The test results demonstrate that the proposed filter algorithm is more reliable and effective in dealing with the outliers in the data sets produced by the integrated GPS/SINS system.

Appropriate topology and coefficients have a great impact on their models' performances. This paper proposes an enhanced group method of data handling (GMDH) algorithm using a modified Levenberg–Marquardt (LM) method. In this work, evolutionary algorithm and LM techniques are deployed simultaneously for optimal design of both connectivity configuration and associated coefficients of each candidate solution in the evolving population combination. However, use of singular value decomposition technique with LM is considered as a novel method to overcome the problem of initial guess, which is presented for the first time in this research. In order to illustrate the benefits of the proposed algorithm, it has been applied in a Malaysian manufacturing company for forecasting in inventory control. Moreover, a comparison between the basic GMDH algorithm and the enhanced GMDH algorithm is made, and the results show that the accuracy of the proposed method is considerably high with reasonable reduction in processing time. Therefore, the enhanced GMDH method can be used to replace old techniques in an inventory control system to generate a structure when it is applied to a Kanban setting in the just in time system.

The subject of the paper is the old and well-known linear least squares method for determining the lattice dimension of a crystalline phase from the peak locations of a powder diffraction pattern. Approximations, limits, and extensions of the method are discussed with reference to the assignment of hkl indices to an experimental multiphase pattern.

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. These filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. However, in several cases, non-monotonic sequences of filters may appear more appropriate. In this paper, we study a hard-thresholding regularization method that extends the spectral cut-off procedure to non-monotonic sequences. We provide several oracle inequalities, showing the method to be nearly optimal under mild assumptions. Contrary to similar methods discussed in the literature, we use here a non-linear threshold that appears to be adaptive to all degrees of irregularity, whether the problem is mildly or severely ill-posed. Finally, we extend the method to inverse problems with noisy operator and provide efficiency results in a conditional framework.

An artificial intelligence (AI) algorithm to automate symbolic design reformulation is an enduring challenge in design automation. Existing research shows that design tools either require high levels of knowledge engineering or large databases of training cases. To address these limitations, we present a singular value decomposition (SVD) and unsupervised clustering-based method that performs design reformulation by acquiring semantic knowledge from the syntax of design representations. The development of the method was analogically inspired by applications of SVD in statistical natural language processing and digital image processing. We demonstrate our method on an analytically formulated hydraulic cylinder design problem and an aeroengine design problem formulated using a nonanalytic design structure matrix form. Our results show that the method automates various design reformulation tasks on problems of varying sizes from different design domains, stated in analytic and nonanalytic representational forms. The behavior of the method presents observations that cannot be explained by pure symbolic AI approaches, including uncovering patterns of implicit knowledge that are not readily encoded as logical rules, and automating tasks that require the associative transformation of sets of inputs to experiences. As an explanation, we relate the structure and performance of our algorithm with findings in cognitive neuroscience, and present a set of theoretical postulates addressing an alternate perspective on how symbols may interact with each other in experiences to reify semantic knowledge in design representations.

This work describes a systematic methodology for the synthesis of tendon-driven manipulators. A method for enumerating the topology of tendon routings is first established. To conform with the enumerated structures, the kinematic synthesis of the manipulator using singular value decomposition is then developed. Design equations for synthesizing a general tendon-driven manipulator with isotropic transmission characteristics are subsequently derived. It is shown that the design methodology may give designers wider selection in determining the tendon routing topology than prior methods by other literature.

In 1977 D. G. Kendall considered diffusions of shape induced by independent Brownian motions in Euclidean space. In this paper, we consider a different class of diffusions of shape, induced by the projections of a randomly rotating, labelled ensemble. In particular, we study diffusions of shapes induced by projections of planar triangular configurations of labelled points onto a fixed straight line. That is, we consider the process in Σ13 (the shape space of triads in ℝ) that results from extracting the ‘shape information’ from the projection of a given labelled planar triangle as this evolves under the action of Brownian motion in SO(2). We term the thus-defined diffusions Radon diffusions and derive explicit stochastic differential equations and stationary distributions. The latter belong to the family of angular central Gaussian distributions. In addition, we discuss how these Radon diffusions and their limiting distributions are related to the shape of the initial triangle, and explore whether the relationship is bijective. The triangular case is then used as a basis for the study of processes in Σ1k arising from projections of an arbitrary number, k, of labelled points on the plane. Finally, we discuss the problem of Radon diffusions in the general shape space Σnk.

Singularities of a manipulator have been addressed repeatedly. However, the singularities and the degree(s) of freedom, as a matter of fact, are two different aspects of the mobility of a manipulator. Consequently, this paper dedicates to discussing the mobility properties through mobility space, which synchronously define the type, number and direction characteristics of the independent motions that the manipulator should execute. The mobility space of a manipulator can be obtained with reciprocal screws of the manipulator via singular value decomposition, which instantaneously depicts the singularity and mobility problems of the manipulators. Application example demonstrates that this methodology can investigate the all-sided mobility properties of parallel manipulators.

Genetic algorithm (GA) and singular value decomposition (SVD) are deployed for the optimal design of both Gaussian membership functions of antecedents and the vector of linear coefficients of consequents, respectively, of adaptive neurofuzzy inference systems (ANFIS) networks that are used for modeling of the explosive cutting process of plates by shaped charges. The aim of such modeling is to show how the depth of penetration varies with the variation of important parameters, namely, the apex angle, standoff, liner thickness, and mass of charge. It is demonstrated that SVD can be effectively used to optimally find the vector of linear coefficients of conclusion parts in ANFIS models and their Gaussian membership functions in premise parts are determined by a GA.

One challenge in the analysis of event-related potentials (ERPs) is to identify task-related differences in scalp topography. The multivariate Partial Least Squares (PLS) analysis was used to identify the spatiotemporal distribution of ERP differences related to experimental manipulations. Two simulations included latency shifts and amplitude changes at peaks with temporal overlap. PLS identified effects only at modeled timepoints and electrodes. In contrast, principal components analysis identified differences at most timepoints. We also demonstrated that PLS identified combinations of waveform differences, not isolated sources. ERP components in an auditory oddball task were also assessed with PLS. The primary distinction was between ERPs on hit and correct rejection trials, expressed at multiple timepoints and electrodes. PLS provides a mechanism to describe experimental differences in ERP waveforms, simultaneously across the head.

This study presents a fast inverse kinematics algorithm for a class of robots, including PUMA and SCARA. It decomposes a robot Jacobian into a product of sub-matrices to locate singularities. Singular value decomposition (SVD) is applied to each singular sub-matrix to find a local least-squares inverse. Perfect inverses are derived for all non-singular sub-matrices. The proposed algorithm is extremely fast. A total inverse requires 54 flops for PUMA and 43 for SCARA. Simulation and experiment are conducted to test the accuracy and real-time speed of the algorithm.

The effects of 1,1,1,3,3,3-hexafluoro-isopropanol (HFIP) on the conformation of cytochrome c (cyt c) at pH 1.9 were studied using a combination of spectroscopic and physical methods. Analysis varying the HFIP concentration showed that a compact denatured conformation (MHF) accumulates in a low concentration range of HFIP in the middle of structural transition from the highly unstructured acid-denatured state to the highly helical alcohol-denatured state of cyt c. This contrasts clearly with the effect of isopropanol (IP), in which no compact conformation accompanied with the transition. Analysis varying concentrations of HFIP and NaCl concurrently showed that the MHF state of cyt c is essentially identical to the salt-induced molten-globule (MG) state, and the MG state in the presence of salt was also stabilized by a low concentration of HFIP. Furthermore, 2,2,2-trifluoroethanol stabilized MHF similarly to HFIP, supporting the proposition that the specific effect observed for HFIP is caused by fluorination of alcohol. The mechanism stabilizing compact conformation by HFIP remains unclear, but is probably distinct from that of salts and polyols, which are also known to stabilize the MG-like state.