半监督FSVM在羽绒菱节识别中的应用

目前,我国对羽绒种类的识别主要由人工借助于显微镜完成,这种方法存在许多不足。提出将半监督FSVM算法引入到羽绒识别中,用半监督学习方法以少量的训练样本为基础,扩大训练样本集的规模,同时利用FSVM的特性减少半监督学习所带来的误差;利用半监督FSVM对经过处理的羽绒二值化图像中的菱节进行识别。该方法提高了菱节识别的准确率。     

求解二维对流扩散方程的投影迭代法

鉴于目前流行的求解大型稀疏代数方程组的投影迭代法中,为提高迭代效率,在迭代前通常需要对稀疏矩阵进行预处理,改善迭代矩阵的条件数,从而减少迭代次数,这使得发展稀疏矩阵的存储技术变得尤为关键。基于二维对流扩散方程的四阶紧致差分格式,将其转化为代数方程组,得到其三对角块形式的系数矩阵,利用稀疏矩阵存储技术和预条件迭代法进行求解,并与传统的中心差分格式所得数值解进行比较,充分说明了方法的高效性和可靠性。     

数据挖掘中关联规则Apriori算法

深入研究关联规则算法, 针对Apriori算法瓶颈问题提出了一种改进算法, 该算法在构建向量矩阵的基础上, 只需要扫描一次事务数据库, 通过优化连接和剪枝, 提高了算法的运行效率. 研究和实验表明, 改进后的算法在大规模的事务数据库中, 较Apriori算法有明显的优势.     

在Mathematica环境下实现交互式矩阵初等变换

在Mathematica7.0环境下,实现了交互式矩阵初等变换。使用时只需选择矩阵初等变换的类型,并输入相应的变换参数,即可完成相应的初等变换并以可视化的方式显示矩阵初等变换的步骤及结果。在线性代数的教学中采用此交互式矩阵初等变换,可以在课堂中随时改变实例并进行演示来提高多媒体教学内容的灵活性。     

Approaches to extended non-quadratic stability and stabilization conditions for discrete-time Takagi–Sugeno fuzzy systems

This paper provides simple and effective linear matrix inequality (LMI) characterizations for the stability and stabilization conditions of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To do this, more general classes of non-parallel distributed compensation (non-PDC) control laws and non-quadratic Lyapunov functions are presented. Unlike the conventional non-quadratic approaches using only current-time normalized fuzzy weighting functions, we consider not only the current-time fuzzy weighting functions but also the l-step-past (l?0) and one-step-ahead ones when constructing the control laws and Lyapunov functions. Consequently, by introducing additional decision variables, it can be shown that the proposed conditions include the existing ones found in the literature as particular cases. Examples are given to demonstrate the effectiveness of the approaches.     

Time-relevant stability of 2D systems

For many 2D systems, one of the independent variables plays a distinct role in the evolution of the trajectories; since often this special independent variable is time, we call such systems ‘time-relevant’. In this paper, we introduce a stability notion for time-relevant systems described by higher-order difference equations. We give algebraic tests in terms of the location of the zeros of the determinant of a polynomial matrix describing the system. We also give an LMI characterization of time-relevant stability involving only constant matrices.     

Certifying spatially uniform behavior in reaction–diffusion PDE and compartmental ODE systems

We present a condition that guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction–diffusion PDE with Neumann boundary conditions. This condition makes use of the Jacobian matrix of the reaction terms and the second Neumann eigenvalue of the Laplacian operator on the given spatial domain, and eliminates the global Lipschitz assumptions commonly used in mathematical biology literature. We then derive numerical procedures that employ linear matrix inequalities to certify this condition, and illustrate these procedures on models of several biochemical reaction networks. Finally, we present an analog of this PDE result for the synchronization of a network of identical ODE models coupled by diffusion terms. From a systems biology perspective, the main contribution of the paper is to blend analytical and numerical tools from nonlinear systems and control theory to derive a relaxed and verifiable condition for spatial uniformity of biological processes.     

Enhanced clustering of biomedical documents using ensemble non-negative matrix factorization

Searching and mining biomedical literature databases are common ways of generating scientific hypotheses by biomedical researchers. Clustering can assist researchers to form hypotheses by seeking valuable information from grouped documents effectively. Although a large number of clustering algorithms are available, this paper attempts to answer the question as to which algorithm is best suited to accurately cluster biomedical documents. Non-negative matrix factorization (NMF) has been widely applied to clustering general text documents. However, the clustering results are sensitive to the initial values of the parameters of NMF. In order to overcome this drawback, we present the ensemble NMF for clustering biomedical documents in this paper. The performance of ensemble NMF was evaluated on numerous datasets generated from the TREC Genomics track dataset. With respect to most datasets, the experimental results have demonstrated that the ensemble NMF significantly outperforms classical clustering algorithms of bisecting K-means, and hierarchical clustering. We compared four different methods for constructing an ensemble NMF. For clustering biomedical documents, this research is the first to compare ensemble NMF with typical classical clustering algorithms, and validates ensemble NMF constructed from different graph-based ensemble algorithms. This is also the first work on ensemble NMF with Hybrid Bipartite Graph Formulation for clustering biomedical documents.     

Extending metric multidimensional scaling with Bregman divergences

Sum of weighted square distance errors has been a popular way of defining stress function for metric multidimensional scaling (MMDS) like the Sammon mapping. In this paper we generalise this popular MMDS with Bregman divergences, as an example we show that the Sammon mapping can be thought of as a truncated Bregman MMDS (BMMDS) and we show that the full BMMDS improves upon the Sammon mapping on some standard data sets and investigate the reasons underlying this improvement. We then extend a well known family of MMDS, that deploy a strategy of focusing on small distances, with BMMDS and investigate limitations of the strategy empirically. Then an opposite strategy is introduced to create another family of BMMDS that gives increasing mapping quality. A data preprocessing method and a distance matrix preprocessing are introduced.     

Ensemble data assimilation in the presence of cloud

In numerical weather prediction (NWP) data assimilation (DA) methods are used to combine available observations with numerical model estimates. This is done by minimising measures of error on both observations and model estimates with more weight given to data that can be more trusted. For any DA method an estimate of the initial forecast error covariance matrix is required. For convective scale data assimilation, however, the properties of the error covariances are not well understood.An effective way to investigate covariance properties in the presence of convection is to use an ensemble-based method for which an estimate of the error covariance is readily available at each time step. In this work, we investigate the performance of the ensemble square root filter (EnSRF) in the presence of cloud growth applied to an idealised 1D convective column model of the atmosphere. We show that the EnSRF performs well in capturing cloud growth, but the ensemble does not cope well with discontinuities introduced into the system by parameterised rain. The state estimates lose accuracy, and more importantly the ensemble is unable to capture the spread (variance) of the estimates correctly. We also find, counter-intuitively, that by reducing the spatial frequency of observations and/or the accuracy of the observations, the ensemble is able to capture the states and their variability successfully across all regimes.