Porosity of Mutually Nearest and Mutually Furthest Points Problems in Geodesic Space

The notion of superframe in general Hilbert spaces was introduced in the context of multiplexing, which has been widely used in mobile communication network, satellite communication network and computer area network. The notion of oblique dual frame is a generalization of conventional dual frame. It has provided us with a frame-like expansion. Using oblique dual frames one can extend frame expansions to include redundant expansions in which the analysis and synthesis frames lie in different spaces. Given positive integers L, M and N, an N?-periodic set 𝕊 in ?, let 𝒢(g, N, M) be a frame for l ²(𝕊, ? ^L ), and let 𝒢(h, N, M) be a frame for ?(h, N, M) (generated by 𝒢(h, N, M)). This article addresses super Gabor duals of g in ?(h, N, M). We obtain a necessary and sufficient condition on h admitting super oblique Gabor duals of g, and present a parametrization expression of all super oblique Gabor duals and all oblique canonical Gabor duals of g. We also characterize the uniqueness of super oblique Gabor dual and oblique canonical Gabor dual of g. Some examples are also provided.     

Novel classification rule of two-phase test sample sparse representation

In this paper, a novel classifier based on two-phase test sample sparse representation (TPTSSR) classifier and coarse k nearest neighbor (C-kNN) classifier, called novel classification rule of two-phase test sample sparse representation (NCR-TPTSSR) classifier, is proposed for image recognition. Being similar to TPTSSR classifier and C-kNN classifier, NCR-TPTSSR classifier also uses the two phases to classify the test sample. However, the classification rule of NCR-TPTSSR classifier is different to the decision rule of TPTSSR classifier and C-kNN classifier. A large number of experiments on FERET face database, AR face database, JAFFE face database and PolyU FKP database are used to evaluate the proposed algorithm. The experimental results demonstrate that the proposed method achieves better recognition rate than TPTSSR classifier, C-kNN classifier, nearest feature center (NFC) classifier, nearest feature line (NFL) classifier, nearest neighbor (NN) and so on.     

Comparing distance metrics for rotation using the k‐nearest neighbors algorithm for entropy estimation

Distance metrics facilitate a number of methods for statistical analysis. For statistical mechanical applications, it is useful to be able to compute the distance between two different orientations of a molecule. However, a number of distance metrics for rotation have been employed, and in this study, we consider different distance metrics and their utility in entropy estimation using the k‐nearest neighbors (KNN) algorithm. This approach shows a number of advantages over entropy estimation using a histogram method, and the different approaches are assessed using uniform randomly generated data, biased randomly generated data, and data from a molecular dynamics (MD) simulation of bulk water. The results identify quaternion metrics as superior to a metric based on the Euler angles. However, it is demonstrated that samples from MD simulation must be independent for effective use of the KNN algorithm and this finding impacts any application to time series data. © 2013 Wiley Periodicals, Inc.     

An information‐theoretic approach to the prediction of protein structural class

An information‐theoretical approach, which combines a sequence decomposition technique and a fuzzy clustering algorithm, is proposed for prediction of protein structural class. This approach could bypass the process of selecting and comparing sequence features as done previously. First, distances between each pair of protein sequences are estimated using a conditional decomposition technique in information theory. Then, the fuzzy k‐nearest neighbor algorithm is used to identify the structural class of a protein given as set of sample sequences. To verify the strength of our method, we choose three widely used datasets constructed by Chou and Zhou. It is shown by the Jackknife test that our approach represents an improvement in the prediction of accuracy over existing methods. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A projection method and Kronecker product preconditioner for solving Sylvester tensor equations

The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.     

A 21st century technique for food control: Electronic noses

This work examines the main features of modern electronic noses (e-noses) and their most important applications in food control in this new century. The three components of an electronic nose (sample handling system, detection system, and data processing system) are described. Special attention is devoted to the promising mass spectrometry based e-noses, due to their advantages over the more classical gas sensors. Applications described include process monitoring, shelf-life investigation, freshness evaluation, authenticity assessment, as well as other general aspects of the utilization of electronic noses in food control. Finally, some interesting remarks concerning the strengths and weaknesses of electronic noses in food control are also mentioned.     

X‐ray photoelectron spectroscopy and the pattern recognition method—their application to surface studies in CoPd alloys

In the present work, polycrystalline CoPd alloys in varying range of bulk atomic percent composition (Co30Pd70, Co50Pd50 and Co70Pd30) are investigated by means of X‐ray photoelectron spectroscopy (XPS). The results of conventional XPS quantitative multiline (ML) approach are compared to the results obtained on the basis of XPS lines shape analysis, where the selected XPS or X‐ray induced Auger electron (XAES) transitions, are processed using the pattern recognition method known as the fuzzy k‐nearest neighbour (fkNN) rule. The fkNN rule is applied to the following spectra line shapes: Pd MNV, Co 2p, Co LMM, Pd 3d and valence band, analysing electrons in a varying range of selected kinetic energies. Both methods showed the surface segregation of Pd in Co30Pd70 and Co50Pd50 alloys. The results of the ML, the binding energy shift (ΔBE) analysis and the fkNN rule remained in agreement. Discrepancies in quantitative results obtained using different approaches are discussed within the accuracy of the applied methods, differences due to mean escape depth (MED) of electrons in considered transitions, their depth distribution function, the sensitivity of electron transition line shape on the environmental change (weaker effect for the inner shell transitions, and stronger effect for the outer shell transitions and Auger electron spectroscopy (AES) electrons transitions) and the non‐uniform depth profile concentrations. Copyright © 2005 John Wiley & Sons, Ltd.     

基于多阶导数拉曼光谱组合技术的矿物油模式分类

为了实现对法庭科学领域重质矿物油物证的快速、准确、无损的鉴定,该文基于光谱分析技术提出了一种多阶导数光谱数据组合分析的方法。收集了80种不同型号、不同厂家的重质矿物油样本,利用傅里叶变换拉曼光谱分析法采集样本的原始光谱数据和导数光谱数据,并通过结合化学计量学构建分类模型。在构建的主成分分析(PCA)结合径向基函数神经网络(RBF)分类模型中,对单独的原始光谱、一阶导数谱和二阶导数谱数据的训练集准确率分别为80.0%、86.7%和86.2%,测试集准确率分别为73.3%、80.0%和72.7%;对组合后的原始光谱+一阶导数谱、原始光谱+二阶导数谱和一阶导数谱+二阶导数谱数据的分类中,训练集准确率分别为97.0%、96.7%和100%,测试集准确率分别为85.7%、90.0%和100%。结果表明,对组合后的导数光谱与原始光谱构建分类模型,准确率更高。其中,基于一阶导数谱+二阶导数谱数据构建的PCA结合RBF分类模型的结果最为理想,准确率达100%。而K最近邻算法模型由于受到样本不均匀的影响,整体分类准确率均较低。利用组合的导数光谱与原始光谱数据构建分类模型能够实现对重质矿物油样本的快速、准确、无损鉴别,可为光谱组合技术在法庭科学及其他分析测试领域的应用提供一定的借鉴和参考。