Symmetric Orthogonalization Research Articles

Guest Editors' Introduction: Special Section on ISIP 2011

This special section comprises of nine selected papers from the fourth International Symposium on Intelligent Information Technology and Security Informatics (ISIP 2011). The conference received 310 paper submissions from 11 countries and regions, of which 157 papers were selected for presentation after a rigorous review process. From these 157 research papers, through two rounds of reviewing, the guest editors selected nine as the best papers on the Multimedia track of the Conference. The candidates of the Special Issue are all the authors, whose papers have been accepted and presented at the ISIP 2011, with the contents not been published elsewhere before. The ISIP 2011 was co-sponsored by Henan Polytechnic University, China; Peoples' Friendship University of Russia, Russia; Feng Chia University, Taiwan; Jiangxi University of Science and Technology, China;Fudan University, China; South China University of Technology, China; Nanchang Hang Kong University, China; Jiaxing University, China; Academy Publisher of Finland, Finland and took place on August 19-22, 2011, in Jiaozuo, China. “Speech Separation in the Vehicle Environment Based on FastICA Algorithm”, by Jindong Zhang, Guihe Qin and Ye Liu. In this paper, the FastICA algorithm in signal process and statistics was studied and used to separate the driver’s speech in the vehicle environment, and realizes the pretreatment in recognizing driver’s speech. “Semantic Analysis of Traffic Video Using Image Understanding”, by Jian Wu, Zhi-ming Cui, Heng-jun Yue, and Guang-ming Zhang. This paper introduces the methods of image understanding and proposes a video semantic analysis framework using scene analysis for recognizing some semantic events in the traffic video. “Research on Video Quality Assessment”, by Chunting Yang, Yang Liu and Jing Yu. In this paper, research has been focused on developing novel objective evaluation metrics which enable prediction of the perceived quality level. The temporal correlations of video frames and the visual interest feature are considered in this method. Meanwhile the metrics are capable of capturing spatial distortions in video sequences. “Tele-Immersive Interaction with Intelligent Virtual Agents Based on Real-Time 3D Modeling”, by Shujun Zhang and Wan Ching Ho. In this paper author explored the combination of real-time 3D modelling and HAI and proposed a prototype of mixed reality system for tele-immersion. Image-based real-time 3D modeling techniques offer essential ways to support tele-immersion and natural HAI. “The Research of Image Encryption Algorithm Based on Chaos Cellular Automata”, by Shuiping Zhang and Huijune Luo, In this paper, the Research puts forwards an image encryption algorithm based on chaos cellular automata , to take full use of the two-dimensional chaotic system's extreme sensitivity to initial conditions and the features with parallelism, complexity and randomness of two-dimensional reversible cellular automata, to make the encrypted key, encrypted image and original image much more have complexity, randomness and unpredictability. “Improved MFCC Feature Extraction Combining Symmetric ICA Algorithm for Robust Speech Recognition”, by Huan Zhao, Kai Zhao, He Liu and Fei Yu.This paper proposed using symmetric orthogonalization in ICA for projecting log Mel spectrum into a new feature space as a substitute in extracting speech features to solve the problem of cumulative error and unequal weights that deflation orthogonalization brings, so as to improve the robustness of speech recognition systems, and increase the efficiency of estimation at the same time. “A Watermarking Technique based on the Frequency Domain”, by Huang-Chi Cheni, Yu-Wen Chang and Rey-Chue Hwang. In this paper, a modified algorithm is presented to improve the defect of the JPEG quantification in order to reduce the bit error rate (BER) of the retrieved watermark. “Image Copy-Move Forgery Detecting Based on Local Invariant Feature”, Li Jing, and Chao Shao. This paper firstly analyzes and summarizes block matching technique, then introduces a copy-move forgery detecting method based on local invariant feature matching. “OWL-S based Service Composition of Three-dimensional Geometry Modeling”, by Jiangning Yu, Hongming Cai and Ailing Liu. This paper proposes an OWL-S framework for distributed CAD system based on the combination of semantic web service and CAD technology. We would like to take this opportunity to thank the authors for the efforts they put in the preparation of the manuscripts and for their valuable contributions. We wish to express our deepest gratitude to the program committee members for their help in selecting papers for this issue and especially the referees of the extended versions of the selected papers for their thorough reviews under a tight time schedule. Last, but not least, our thanks go to the Editorial Board of the Journal of Multimedia for the exceptional effort they did throughout this process. In closing, we sincerely hope that you will enjoy reading this special issue.

Improved MFCC Feature Extraction Combining Symmetric ICA Algorithm for Robust Speech Recognition

Independent component analysis (ICA), instead of the traditional discrete cosine transform (DCT), is often used to project log Mel spectrum in robust speech feature extraction. The paper proposed using symmetric orthogonalization in ICA for projecting log Mel spectrum into a new feature space as a substitute in extracting speech features to solve the problem of cumulative error and unequal weights that deflation orthogonalization brings, so as to improve the robustness of speech recognition systems, and increase the efficiency of estimation at the same time. Furthermore, the paper studied the nonlinearities of the objective function in ICA and their coefficients, tested them in all kinds of environments , finding that they influenced the recognition rate greatly in speech recognition systems, and applied a new coefficient in the proposed method. Experiments based on HMM and Aurora-2 speech corpus suggested that the new method was superior to deflation-based ICA and MFCC.

Symmetrical orthogonalization within linear space of molecular orbitals

An alternative procedure of orthogonalization involving a metric matrix of the linear vector space formed by the columns of LCAO matrix is introduced. It is proved that this procedure is fully equivalent the original Löwdin’s scheme. Also, a few modifications involving a two-step orthogonalization scheme are outlined and briefly discussed. Numerical results of test calculations of atomic charges for several representative molecules seem to fully validate the newly proposed methodology.

The best constant of Sobolev inequality corresponding to a bending problem of a beam on an interval

Green function of 2-point simple-type self-adjoint boundary value problem for 4-th order linear ordinary differential equation, which represents bending of a beam with the boundary condition as clamped, Dirichlet, Neumann and free. The construction of Green function needs the symmetric orthogonalization method in some cases. Green function is the reproducing kernel for suitable set of Hilbert space and inner product. As an application, the best constants of the corresponding Sobolev inequalities are expressed as the maximum of the diagonal values of Green function.

Solving balanced Procrustes problem with some constraints by eigenvalue decomposition

The balanced Procrustes problem with some special constraints such as symmetric orthogonality and symmetric idempotence are considered. By one time eigenvalue decomposition of the matrix product generated by the matrices A and B , the constrained solutions are constructed simply. Similar strategy is applied to the problem with the corresponding P -commuting constraints with a given symmetric matrix P . Numerical examples are presented to show the efficiency of the proposed methods.

On the Convergence of ICA Algorithms With Symmetric Orthogonalization

Independent component analysis (ICA) problem is often posed as the maximization/minimization of an objective/cost function under a unitary constraint, which presumes the prewhitening of the observed mixtures. The parallel adaptive algorithms corresponding to this optimization setting, where all the separators are jointly trained, are typically implemented by a gradient-based update of the separation matrix followed by the so-called symmetrical orthogonalization procedure to impose the unitary constraint. This article addresses the convergence analysis of such algorithms, which has been considered as a difficult task due to the complication caused by the minimum-(Frobenius or induced 2-norm) distance mapping step. We first provide a general characterization of the stationary points corresponding to these algorithms. Furthermore, we show that fixed point algorithms employing symmetrical orthogonalization are monotonically convergent for convex objective functions. We later generalize this convergence result for nonconvex objective functions. At the last part of the article, we concentrate on the kurtosis objective function as a special case. We provide a new set of critical points based on Householder reflection and we also provide the analysis for the minima/maxima/saddle-point classification of these critical points.

Least squares solutions to the equations [formula omitted] with some constraints

The least squares solutions to the equations AX = B , XC = D with some constraints such as orthogonality, symmetric orthogonality, symmetric idempotence are considered. By one time singular value decomposition or eigenvalue decomposition of the matrix product generated by the coefficient matrices A , C and right hand side matrices B , D , the constrained solutions are constructed simply. Similar strategy is applied to the equations with corresponding P-commuting constraints with given symmetric matrix P. Numerical examples that show the efficiency of the proposed methods are presented.

Molecular Basis SetsA General Similarity-Based Approach for Representing Chemical Spaces

A new method, based on generalized Fourier analysis, is described that utilizes the concept of "molecular basis sets" to represent chemical space within an abstract vector space. The basis vectors in this space are abstract molecular vectors. Inner products among the basis vectors are determined using an ansatz that associates molecular similarities between pairs of molecules with their corresponding inner products. Moreover, the fact that similarities between pairs of molecules are, in essentially all cases, nonzero implies that the abstract molecular basis vectors are nonorthogonal, but since the similarity of a molecule with itself is unity, the molecular vectors are normalized to unity. A symmetric orthogonalization procedure, which optimally preserves the character of the original set of molecular basis vectors, is used to construct appropriate orthonormal basis sets. Molecules can then be represented, in general, by sets of orthonormal "molecule-like" basis vectors within a proper Euclidean vector space. However, the dimension of the space can become quite large. Thus, the work presented here assesses the effect of basis set size on a number of properties including the average squared error and average norm of molecular vectors represented in the space-the results clearly show the expected reduction in average squared error and increase in average norm as the basis set size is increased. Several distance-based statistics are also considered. These include the distribution of distances and their differences with respect to basis sets of differing size and several comparative distance measures such as Spearman rank correlation and Kruscal stress. All of the measures show that, even though the dimension can be high, the chemical spaces they represent, nonetheless, behave in a well-controlled and reasonable manner. Other abstract vector spaces analogous to that described here can also be constructed providing that the appropriate inner products can be directly evaluated as is the case in this work, a problem that is well-known in kernel-based machine learning.

Infrared Spectrum of 4-Methoxypicolinic Acid N-Oxide: Computation of Asymmetric O−H Stretching Band

In this article we studied the strong intramolecularly hydrogen-bonded system 4-methoxypicolinic acid N-oxide. The potential energy surface V = V(rOH,rOO) and the corresponding dipole moment function were calculated using the DFT B3LYP/6-31+G(d,p) level of approximation. The time-independent vibrational Schrödinger equation was solved using a rectangular grid basis set and shifted Gaussian basis set. The vibrational spectrum and metric parameters were also calculated. Effects of deuteration were considered. The calculated vibrational spectra were compared with the experimental spectra. The vibrational transition corresponding to asymmetric O-H stretching that occurs at about 1400 cm-1 compares well with the experimentally assigned O-H asymmetric stretching band centered at 1380 cm-1. The corresponding asymmetric O-D stretching band was predicted to be at 1154 cm-1, while the experimental O-D band was not assigned due to its very low intensity. Several overtones and hot transitions of significant intensities were located in the vicinity of the fundamental O-H stretching frequency, effectively broadening the infrared absorption attributed to the O-H stretching mode. This is in a good agreement with the observed broad protonic absorptions found in the infrared spectra of the title compound and its analogs. We have shown that the Gaussian basis set is the method of choice for a two-dimensional vibrational problem that requires several hundreds of vibrational basis functions and when high accuracy of the eigenvalues is required or when extending the calculations to more vibrational degrees of freedom. We have also demonstrated that for a large number of basis functions the Gramm-Schmidt orthogonalization procedure outperforms symmetric and canonical orthogonalization schemes.

One-Bit-Matching Theorem for ICA, Convex-Concave Programming on Polyhedral Set, and Distribution Approximation for Combinatorics

According to the proof by Liu, Chiu, and Xu (2004) on the so-called one-bit-matching conjecture (Xu, Cheung, and Amari, 1998a), all the sources can be separated as long as there is an one-to-one same-sign correspondence between the kurtosis signs of all source probability density functions (pdf's) and the kurtosis signs of all model pdf's, which is widely believed and implicitly supported by many empirical studies. However, this proof is made only in a weak sense that the conjecture is true when the global optimal solution of an independent component analysis criterion is reached. Thus, it cannot support the successes of many existing iterative algorithms that usually converge at one of the local optimal solutions. This article presents a new mathematical proof that is obtained in a strong sense that the conjecture is also true when any one of local optimal solutions is reached in helping to investigating convex-concave programming on a polyhedral set. Theorems are also provided not only on partial separation of sources when there is a partial matching between the kurtosis signs, but also on an interesting duality of maximization and minimization on source separation. Moreover, corollaries are obtained on an interesting duality, with supergaussian sources separated by maximization and subgaussian sources separated by minimization. Also, a corollary is obtained to confirm the symmetric orthogonalization implementation of the kurtosis extreme approach for separating multiple sources in parallel, which works empirically but lacks mathematical proof. Furthermore, a linkage has been set up to combinatorial optimization from a distribution approximation perspective and a Stiefel manifold perspective, with algorithms that guarantee convergence as well as satisfaction of constraints.

A fixed point approach to stability of a quadratic equation

Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type $f(x+y)+g(x-y)=h(x)+k(y)$, where $f, g, h, k$ are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on $f$.

A new algorithm for rigid body molecular dynamics

The molecular dynamics of a completely rigid molecule is described in terms of external coordinates, namely translations and rotations, and a new algorithm is proposed, which is faster than other known methods and satisfies the constraints up to a desired accuracy. The procedure dispenses with the adoption of Lagrange multipliers and it is derived from an expression previously proposed for the motion of a semirigid molecule, when constraints are imposed to any selected number of intramolecular parameters. The latter need not to be specified for a rigid body but cannot be altogether ignored since it is necessary to guarantee that internal and external coordinates form a complete set of independent variables. This requirement is met by the familiar Eckart–Sayvetz conditions which provide with an iterative procedure for the evaluation, through symmetric orthogonalization, of a matrix of rotation. It turns out that only a first approximation of this matrix is necessary, therefore a final algorithm is proposed, based on the definition of infinitesimal angles of rotation about the mass center.

On the orthogonal stability of the pexiderized quadratic equation

The Hyers–Ulam stability of the conditional quadratic functional equation of Pexider type x ⊥ y is established where ⊥ is a symmetric orthogonality in the sense of Rätz and f is odd.

Full inclusion of symmetry in constructing Wannier functions: Chemical bonding in MgO and TiO2 crystals

Chemical bonding in MgO and TiO2 crystals is analyzed using a minimal basis consisting of atomic-type Wannier functions (AWFs) centered at atomic sites in the crystal and constructed from Bloch states of the energy bands originating from the valence states of the atoms. A method proposed earlier for constructing Wannier functions is improved. Symmetrization of the initial Bloch function basis and symmetrical orthogonalization of the generalized Bloch functions greatly reduces computational effort. The prior symmetrization of the Bloch function basis is of fundamental importance in constructing AWFs, because the latter functions have to be centered at the atomic sites and possess the symmetry of the atomic functions in the crystal. The principle that should be followed in selecting the conduction bands originating from the valence states of the atoms of the crystal is formulated. The Bloch functions are calculated using the LCAO approximation within the Hartree-Fock method and density-functional theory. Using the calculated Bloch functions, a minimal valence AWF basis is constructed and calculations of the local characteristics of the electronic structure (atomic charge, bond order, atomic valence) are performed for the MgO and TiO2 crystals. According to the analysis performed, the covalent component of the chemical bonding in the MgO crystal is negligibly small and TiO2 is a mixed ionic and covalent crystal with pronounced covalent bonding.

On Löwdin's method of symmetric orthogonalization*

AbstractAn elementary direct proof is given for the stationarity property of Löwdin's symmetric orthogonalization scheme. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Symmetric approximation of frames and bases in Hilbert spaces

We introduce the symmetric approximation of frames by normalized tight frames extending the concept of the symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces. We prove existence and uniqueness results for the symmetric approximation of frames by normalized tight frames. Even in the case of the symmetric orthogonalization of bases, our techniques and results are new. A crucial role is played by whether or not a certain operator related to the initial frame or basis is Hilbert-Schmidt.

On some ways of modifying semiempirical quantum chemical methods

The problems of semiempirical quantum chemical calculations of (a) spin densities in paramagnetic organometallics, (b) hydrogen bonds, and (c) bond energies and the structure of transition-metal compounds are discussed. Some modifications of the existing semiempirical quantum chemical method are presented. An extended NDDO approximation has been developed. This scheme includes explicit symmetric orthogonalization of the core Hamiltonian and the use of Hellmann's effective core potential for core-electron interaction. © 1996 John Wiley & Sons, Inc.

Probabilistic forcing in quantum logics

It is shown that an orthomodular lattice can be axiomatized as an ortholattice with a unique operation of identity (bi-implication) instead of the operation of implication, and a corresponding algebraic unified quantum logic is formulated. A statistical YES-NO physical interpretation of the quantum logical propositions is then provided to establish a support for a novel YES-NO representation of quantum logic which prompts a conjecture about a possible completion of quantum logic by means of probabilistic forcing. In this paper we shall anwser two basic questions of quantum' logics, present a novel probabilistic representation of the logic and of quantum measurements, and propose a probabilistic forcing as a possible tool for completing quantum logic. The questions are, first, whether there is a unique object language operation which can take over the role of the unique classical operation of implication (conditional, set-theoretic inclusion), and, second, whether there is a relation which is more appropriate for set-theoretic representation of quantum-theoretic measurements than the usual irreflexive and symmetric orthogonality relation. We answer the first question in the positive by substituting the biimplication for the implication and the equality for the ordering relation, thus at the same time making the ordering within quantum sets irrelevant. This renders the usual techniques of quantum logic as a deductive inferential theory inappropriate and ascribes quantum deductive logic a particular equational meaning. The result is obtained in Section 2.

Modifications for ab initio calculations of the moderately large-embedded-cluster model. Hydrogen adsorption on a lithium surface

The moderately large-embedded-cluster (MLEC) model of Grimley, Pisani, Ravenek, and others are modified so that the model is more easily applicable to ab initio calculations. We give a linewidth to each discrete energy level of a cluster for simulating the density of states of a bulk metal and for preventing from the singularity. The dependence of the calculated results on this linewidth is shown to be small. Symmetric orthogonalization of a basis set and a new convergence algorithm are adopted in writing up our ab initio program. These modifications give a rapid convergence of the density matrix in the self-consistent-field calculation. Test calculations are performed for hydrogen adsorption on a Li (100) surface with the use of several cluster and embedded cluster models.

Nonsymmetrical orthogonalization as a consequence of charge and moment conservation

It is shown that charge and moment conservation via a nonsymmetrical partitioning of two-center contributions of the respective matrix elements on each of the two atoms is not compatible with the symmetric orthogonalization. A nonsymmetrical orthogonalization technique is proposed via the Cholesky decomposition. This method allows to retain earlier procedures for the calculation of bonding and valence based on orthogonalized orbitals. This technique gives better trends for charges and valences already in small basis sets than other standard procedures.