关键词： PARAFAC2   direct fitting algorithm  

摘要： The PARAFAC2 decomposition has attracted growing research interest. To compute it, the direct fitting (DF) algorithm is usually employed. In this contribution, we propose to incorporate semi-algebraic approaches for the computation of PARAFAC in the DF algorithm and explore how it should be adapted to largely exploit the resulting diversity in the estimates of factor matrices to enhance the robustness and efficiency. Three versions have been tailored and recommended for different parameter settings according to, e.g., the number of components or tensor dimensions. Extensive numerical simulations have been conducted with both synthetic and measured biomedical as well as wine data to validate the improved performance of the proposed DF algorithms. In addition, it has been shown that applying the geometric search on top of the proposed DF algorithms further boosts their performance.

关键词： Tensor   Canonical polyadic decomposition   Double coupled   Algebraic algorithm   Uniqueness  

摘要： Double coupled canonical polyadic decomposition (DC-CPD) decomposes multiple tensors with coupling in the first two modes, into minimal number of rank-1 tensors that also admit the double coupling structure. It has a particular interest in joint blind source separation (J-BSS) applications. In a preceding paper, we proposed an algebraic algorithm for underdetermined DC-CPD, of which the factor matrices in the first two modes of each tensor may have more columns than rows. It uses a pairwise coupled rank-1 detection mapping to transform a possibly underdetermined DC-CPD into an overdetermined DC-CPD, which can be solved algebraically via generalized eigenvalue decomposition (GEVD). In this paper, we generalize the pairwise or second-order coupled rank-1 detection mapping to an arbitrary order K >= 2. Based on this generalized coupled rank-1 detection mapping, we propose a broad framework for the algebraic computation of DC-CPD, which consists of a series of algorithms with more relaxed working assumptions, each corresponding to a fixed order K >= 2. Deterministic and generic uniqueness conditions are provided. We will show through analysis and numerical results that our new uniqueness conditions for DC-CPD are more relaxed than the existing results for DC-CPD and CPD. We will further show, through simulation results, the performance of the proposed algebraic DC-CPD framework in approximate DC-CPD and a J-BSS application, in comparison with existing DC-CPD and CPD algorithms.

关键词： Ant colony optimisation   swarm intelligence   convergence analysis   stability analysis   EigenAnt Algorithm  

摘要： As a variant of Ant Colony Optimization, the EigenAnt algorithm finds the shortest path between a source node and a destination node based on negative feedback in the form of selective pheromone removal that occurs only on the path which is actually chosen for each trip. EigenAnt algorithm also could change quickly to reflect to the dynamic variety of initial pheromone concentrations and path length etc. However, in general, the solution of EigenAnt algorithm is not always convergent. In this paper, we propose an improved EigenAnt (iEigenAnt) algorithm in terms of both negative and positive feedback;that is, selective pheromone updates are decided by smart ants or stupid ones, which depends whether the amount of the pheromone at the selected path increases or not. The system modelled by our algorithm has a unique equilibrium as the shortest path. Besides, using mathematical analysis, we demonstrate that the equilibrium is global asymptotically stable, i.e., stable and convergent. Finally, we also implement the iEigenAnt algorithm under four different cases and apply it on travelling salesman problem problem, the simulation result shows that our iEigenAnt algorithm is faster convergent and more effective compared to the original EigenAnt algorithm, and some combinatorial optimisation problems can be effectively solved based on our iEigenAnt algorithm.

关键词： 数学模型   污染物含量   动态预测   点源污染物  

摘要： 河流污染物含量动态预测对污染物的治理具有重要作用,为了提高污染物预测准确度,设计基于BioWin数学模型的河流污染物含量动态预测算法。根据实际径流情况归类当前污染河流相关参数,根据径流特征估算当前河流污染物实际通量,圈定污染物范围,划分河流污染物来源,并分别提出污染物含量的计算方法,实现污染物含量的动态预测。试验数据表明,该预测算法有效提高了预测准确率,具有实际应用优势。

关键词： 数学形态滤波   自适应多尺度滤波算法   小波阈值滤波   大地电磁信号   噪声压制  

摘要： 针对实测大地电磁信号资料中常出现的强噪声干扰问题,提出一种基于数学形态滤波和小波阈值滤波结合的大地电磁噪声压制方法。首先,利用自适应多尺度形态滤波算法对含噪信号进行初次滤波,以消除脉冲类干扰。然后,对已处理的信号进行小波阈值滤波提取大尺度强噪声轮廓。最后,剔除强噪声干扰重构大地电磁信号。通过仿真实验对比,在不同强度噪声干扰背景下,所提方法的性能优于普通小波阈值方法,能更多地保留大地电磁原始信号的细节特征。实测资料处理结果表明,该方法能有效地抑制大尺度强噪声干扰和基线偏移的影响,改善视电阻率曲线质量,具有较好的应用前景。

关键词： 算法   数学   信息技术  

摘要： 开学后不久,一位数学老教师抱怨:“为什么要把程序算法这一章节引入数学教学中来,对于程序我是越上越糊涂,我都不知道学生明白没有,为何不把这一部分安排给计算机老师?”的确,针对一部分老教师来说,这一部分有一定的难度。因为作为一名数学教师,在大学时并没有深入研究过程序设计。所以,如何开展算法与程序设计的教学,对一线数学教师来说是一个挑战。

关键词： 数学教学   算法教学   计算机算法   教学模式  

摘要： 该文结合教学案例详细阐述了"数学计算机算法教学法"在教学过程中如何展开,将教学内容如何精心设计成计算机流程图,用以表达、描述和讲解数学思想的实际应用、分析解决问题的策略与思路、计算方法与技巧的工程算法。这种教学模式逻辑性较强,结构性较强,将数学与计算机相融合,为当今信息时代下的数学教学方法改革提供了一种可供选择的、实用性强的教学模式。

关键词： 数学算法   计算机   人工智能  

摘要： 数学算法具有科学性、逻辑性与严谨性,能够帮助人工智能技术在发展的过程中,实现技术的不断发展和超越。可以说,数学算法是计算机人工智能发展中不可获取的元素,很多技术环节和系统功能的实现都有赖于数学算法。在分析了数学算法在计算机人工智能中的应用要点后,探讨了数学算法对于计算机人工智能的推动作用。